PRELIMINARYRESULTSFROMTHEEPOT...

PRELIMINARY RESULTS FROM THE EPOT PROJECT

Technological innovation and automation in the integratedapplications of electromagnetic and potential field methods

in active volcanic areas

Papers Presented at the Second Year Workshop

Edited byCiro Del Negro

Istituto Nazionale di Geofisica e Vulcanologia, Catania, Italy

Table of Contents

Preface: The EPOT ProjectCiro Del Negro................................................................................................................... 7

On the resolution of electromagnetic induction methods in marine explorationof complex volcanic structuresAntonio Troiano, Zaccaria Petrillo, Maria Giulia Di Giuseppe andDomenico Patella............................................................................................................... 9

Characterization of the coherent EM noise due to moving sources onmagnetotelluric dataMaria Giulia Di Giuseppe, Zaccaria Petrillo, Antonio Troiano andDomenico Patella............................................................................................................... 19

On the localisation of long-standing self-potential sources at Vulcano (Italy) byprobability tomographyBoris Di Fiore, Paolo Mauriello and Domenico Patella.................................................. 27

New magnetotelluric response on the Mt. Etna volcanoAnnalisa Zaja and Adele Manzella.................................................................................... 33

Electrical modelling of the shallow structural setting of the Cisternazza-Montagnolaarea (Mt. Etna)Giuseppe Della Monica, Rosa Di Maio, Roberto Scandone, Gianpaolo Cecere,Ciro Del Negro, Prospero De Martino and Francesco Santochirico................................ 39

Bouguer correction for a spherical earth: application to the Etna dataMariano Loddo and Domenico Schiavone......................................................................... 45

Data concerning magnetic susceptibility changes in powdered rock induced bytemperature. Results from Mount Etna and Ustica island specimensAntimo Angelino, Ciro Del Negro, Alberto Incoronato, Rosalba Napoli andPasquale Tiano................................................................................................................... 51

Exploring the time dynamics of geoelectrical and geomagnetical signalsMarianna Balasco, Gerardo Colangelo, Vincenzo Lapenna andLuciano Telesca.................................................................................................................. 57

Non-stationary analysis of geomagnetic field variations for the identification andcharacterisation of volcanomagnetic and seismomagnetic eventsMaurizio Fedi and Mauro La Manna................................................................................. 63

Nonlinear identification and modeling of geomagnetic time series at Etna volcanoAnnamaria Vicari, Gilda Currenti, Ciro Del Negro, Luigi Fortuna andRosalba Napoli................................................................................................................... 71

Inverse modelling of piezomagnetic and electrokinetic data in volcanic areasGiuseppe Nunnari and Ciro Del Negro............................................................................. 81

Table of Contents

5

A graphical computer program for modeling of volcanomagnetic fields: a case studyMount VesuviusRosalba Napoli, Gilda Currenti, Ciro Del Negro, Takeshi Hashimoto, andAnnamaria Vicari................................................................................................................ 89

Project and manufacturing of an autoleveling vectorial magnetometer forvolcanic areas monitoringPaolo Palangio, Claudia Rossi, Achille Zirizzotti, Antonio Meloni andLili Cafarella....................................................................................................................... 97

Technological improvements in gravity monitoring of active volcanoesGennaro Budetta, Daniele Carbone and Filippo Greco.................................................... 103

Fabrication of IPMC and Characterization of its sensorial properties:preliminary resultsClaudia Bonomo, Ciro Del Negro, Luigi Fortuna and Salvatore Graziani....................... 111

Beta version of MADAP: a modular architecture for MAgnetic DAta Processingacquired by volcanic monitoring networksGilda Currenti, Ciro Del Negro, Luigi Fortuna, Salvatore Graziani,Rosalba Napoli, Alessandro Rizzo and Annamaria Vicari................................................. 117

6

Table of Contents

Preface: The EPOT Project

This special issue of “Quaderni di Geofisica” collects proceedings from the Second YearWorkshop of the Coordinated Project “Technological innovation and automation in the integratedapplications of electromagnetic and potential field methods in active volcanic areas” (EPOT) organizedat Catania on December 13, 2002. The EPOT project was supported by Dipartimento di ProtezioneCivile in the frame of the GNV Programme 2000-2003 of the INGV. This research began as a joint proj-ect between Research Institutes and Universities with the aim of improving the investigative capabili-ty of electromagnetic and potential field methods in their various possible applications in active vol-canic areas. Progress achieved in the geophysics of volcanoes over the past few decades, and the rapidtechnological development of recent years, have made a decisive effort both possible and necessary tointroduce automation and a multi-methodological approach as fundamental for the monitoring of activevolcanoes. The integrated approach is probably the only procedure capable of giving a global responseto the volcanological problem and to minimize interpretative ambiguities. In order to achieve theseobjectives we have been working to strongly improve the investigative power of the electromagneticand potential field methods through: (a) development of suitable methods of integrated inversion, (b)application of advanced technologies to process continuously recorded signals, and (c) automation ofmonitoring and management systems and of surveys in real time.

The EPOT project, though centrally coordinated, is separated in 10 Research Units characterizedby homogeneous objectives. The activity reports offer a good summary of the on-going activities in thethree main tasks. The project appears to be moving successfully toward the achievement of the pro-posed goals. During this meeting all partners presented their preliminary results and discussion fol-lowed on how to ensure that the algorithms developed in this project are implemented in real-time mon-itoring procedures and may be used during volcano crises. I wish to thank the authors not only for theircontributions but also for stimulating a fruitful discussion among participants. A comprehensive viewof our present scientific knowledge on the advances in geophysical researches on major Italian volca-noes was provided. The web site for the project is available at the address:http://maglab.ct.ingv.it/epot since July 2002. It is maintained by Geomagnetism Laboratory of INGV-Sezione di Catania and provides updated information about the project, proposed architecture, meet-ings, etc.

I am grateful to all those who were co-opted for their expertise and to all those who providedtime and energy in assisting in this project. Special thanks are expressed to the GNV EvaluationCommittee, including Domenico Giardini of ETH Zurich, Gudmundur Sigvaldasson of NVORejkjavik, and Marjorie Wilson of Leeds University, for all their support and valuable contributions insetting the direction for this project.

I also wish to acknowledge here Enzo Boschi and Paolo Gasparini for having suggested the pub-lication of workshop proceedings on “Quaderni di Geofisica”.

We would like to express our gratitude to several colleagues for their collaborative efforts.Special thanks is addressed to the reviewers for their fine work: Salvatore Baglio (DIEES-Universityof Catania, Italy), Paolo Baldi (DF-University of Bologna, Italy), Tommaso Caltabiano (INGV-Catania,Italy), Daniele Carbone (INGV-Catania, Italy), Angelo De Santis (INGV-Roma, Italy), Maurizio Fedi(DST-University of Naples, Italy), Giovanni Florio (DST-University of Naples, Italy), VincenzoLapenna (IMAA-CNR, Italy), Adele Manzella (IGG-CNR, Italy), Giuseppe Nunnari (DIEES-University of Catania, Italy), Domenico Patella (DSF-University of Naples, Italy), Antonio Rapolla(DST-University of Naples, Italy), Andre Revil (CNRS-CEREGE, France), Agata Siniscalchi (DGG-University of Bari, Italy).

I am appreciative of the help given by all staff members of the Geomagnetism Laboratory ofINGV-CT, and in particular by Rosalba Napoli for her editorial support and assistance throughout theproduction of the special issue.

Ciro Del NegroCoordinator of EPOT

Preface

7

On the Resolution of ElectromagneticInduction Methods in Marine

Exploration of Complex VolcanicStructures

Antonio Troiano1, Zaccaria Petrillo2, Maria GiuliaDi Giuseppe1 and Domenico Patella1

1 Department of Physical Sciences, University FedericoII, Naples, Italy

2 National Institute of Geophysics and Volcanology,Vesuvian Observatory, Naples, Italy

AbstractThe realisation of a standard magnetotel-

luric (MT) sounding requires the measurementsof the horizontal components of the local elec-tric and magnetic fields on the Earth’s surface inorder to obtain the frequency-dependent appar-ent resistivity curve. The application of the MTmethod in marine research has, however, seriousdifficulties as for the measurement of the elec-tric field in sea water. The magnetovariational(MV) method seems more appropriate, sinceonly the magnetic components are measured attwo different levels, generally the sea surfaceand the sea bottom. By these measurements it ispossible to obtain MV apparent resistivitysounding curves against frequency, carryingsimilar information about the electrical structureunderwater as with the MT method. Using theMV approach, the difficulties of the MT methodare avoided, but a difficulty still exists owing tothe motional noise of the magnetometer hangednear the sea surface. In order to eliminate thislast inconvenience, a sea-to-ground magneto-variational (SGMV) method has recently beenproposed, based on the mesurements of only themagnetic components at two different places,namely the sea bottom and a remote land stationopportunely placed over a 1D structure. Thispaper investigates the capability of the SGMVmethod to resolve 2D and 3D prismatic bodiesapproximating a magma chamber placedbeneath a sea-water layer, in view of an applica-tion to the Campi Flegrei caldera (Naples, Italy),in particular to the portion of the caldera extend-ing offshore in the Gulf of Pozzuoli. The mod-elling, performed by a finite difference algo-rithm, has allowed a comparison to be madebetween the standard free-surface MT represen-tations and similar MT images reconstructed bythe SGMV approach. In all cases, the modellinghas confirmed the general capability of the elec-tromagnetic induction methods to resolve com-plex volcanic structures and the comparison hasshown the reliability of the SGMV method in

simulating MT soundings in marine environ-ment.

Key words electromagnetic induction – marinegeophysical exploration - volcano geophysics

1. Introduction

The application of magnetotellurics (MT)to the study of volcanoes on land has gained inrecent years a key role for its high resolutionpower with virtually no limitation as to thedepth of investigation, and for its relatively sim-pler field work which allows costs to be sensiblyreduced. Great interest has also been given tothe possibility of exporting the MT method off-shore to detect magma chambers residingbeneath the sea-water layer.

A pioneer approach to MT sounding withelectric and magnetic sensors immersed in seawater at a depth of few tens of meters dates backto the late 50s of last century, but a series oftechnical problems have always made the appli-cation of standard MT a difficult task in marineenvironment. The main difficulty is related tothe measurement of the electrical (E) field in seawater. On land, the E-field is approximated asthe ratio of the potential drop across a pair ofelectrodes to the separation between them,which must be not less than 100 m, in order forthe E-field to represent the dominant resistivityin the surface layer [Kaufman and Keller, 1981].Obviously, the necessity of such a long bipolecannot easily be satisfied at sea.

A way to avoid the difficulty related tothe electric line layout is the use of the magne-tovariational (MV) method, which allows anMT-like apparent resistivity representation to beretrieved using only two magnetic sensors[Patella and Siniscalchi, 1994]. The two sensorsare normally aligned vertically with the top one,S(t), close to the sea surface and the lower one,S(b), anchored at the sea bottom, as sketched infig.1a. Nonetheless, a difficulty still arises relat-ed, this time, to the measurement of the magnet-ic (H) field, due to lack of stability of the topsensor S(t) hanging in sea water, generatingrecords heavily contaminated by motionalnoise.

Recently, a new way has been paved todeal with electromagnetic (em) induction inmarine research using the so called sea-to-ground magnetovariational (SGMV) layout[Patella et al., 1999]. The new layout consists indisplacing the magnetic sensor at the air-waterboundary from station S(t) to a remote site S2 onland where the subsoil conforms to a 1D struc-

Preliminary results from the EPOT project

9

ture, as in fig.1b. Using the basic MT hypothe-ses that the total H-field at the surface of a 1Dlayered earth is two times the primary H-field,independently of the underlying 1D resistivitysequence [Kaufman and Keller, 1981] and thatthe primary H-field is uniform over largelyextended areas [Zelwer and Morrison, 1972], anew MT-like apparent resistivity representationcan be retrieved without incurring the previous-ly mentioned limitations of the MT and MVmethods [Patella et al., 1999]. The critical pointof the SGMV method is the hypothesis that thesubsoil below S2 has to conform to a 1D struc-ture. This can result in a restriction for the appli-cability of the SGMV method, requiring an apriori knowledge of the geology in the referencesite on land, not always available or totally reli-able.

In this paper we study the SGMVresponse of 2D and 3D structures approximatinga magma chamber. It is a preliminary investiga-tion aiming at establishing the resolution powerof the SGMV method in view of an applicationto the Campi Flegrei caldera, in particular to theportion of the caldera extending offshore in theGulf of Pozzuoli, which has so far never beenexplored. We simulate an application of theSGMV method by a finite difference algorithm[Mackie et al., 1993], and compare the MTresponses derived from the SGMV method(from now on the MT-by-SGMV responses)with the synthetic standard MT responses on thesame structures, in order to highlight the per-formance of the new layout. In this preliminaryinvestigation, all synthetic standard MT andMT-by-SGMV responses in marine environ-ment are always computed as they wereobtained on the free surface of the sea-waterlayer.

An outline of the SGMV theory [Patellaet al., 1999] precedes the numerical simulations,in order to let the reader be acquainted with theformal approach followed to compute the MT-by-SGMV synthetic responses.

2. Theoretical outline

Neglecting displacement currents, thesolution of Helmholtz equation for the planemagnetic field components with eiωt timebehavior in a uniform, highly conductive sea-water layer overlying any complex resistivitystructure, is

(1a)

(1b)

where the wavenumber kz is given as

(2)

and z, ω, µ and ρw are the depth positive down-wards, the angular frequency, the magnetic per-meability taken equal to that of free-space andthe resistivity of the sea water layer, respective-ly. In writing eq.s 1a and 1b we have tacitlyadmitted that the horizontal wavenumbers in thesea water layer are negligible with respect to kz.

Using eq.s 1a and 1b, the magnetic com-ponents

and

at the sea-floor station can easily be written as

(3a)

(3b)

where hw is the thickness of the sea water layer.We suppose ρw and hw are known parameters.

Assuming that S2 is located at the top ofa horizontally layered medium, the magneticfield at S2 can be used to estimate the primarymagnetic field [Kaufman and Keller, 1981]. Asa consequence of eq.s 1a and 1b and due to ageneral uniformity of the primary magnetic fieldover extended areas [Zelwer and Morrison,1972], the magnetic field components and atthe top of the sea water layer (z=0) are estimat-ed as follows

(4a)

(4b)

Eq.s 3a and 3b and eq.s 4a and 4b can beeasily manipulated in order to estimate the elec-tric components in the sea water layer. Theseestimates can be used to simulate a standard MTsounding at any level in the sea water layer. Forthe aim of this study, the electric field compo-

10


Figure 1. (a) The magnetovariational array con-figuration in marine exploration. (b) The sea-to-ground magnetovariational array configuration.


11

nents at the top of the sea water layer are readi-ly obtained as

(5a)

(5b)

where

(6a)

(6b)

and

(7a)

(7b)

The standard MT formulas can thus beused to get reliable estimates of the MT appar-ent resistivities.

3. Numerical simulations

2D model

We show now the results of a simulationcarried out on a 2D model of magma chamberusing the finite difference approach. The 2Dmodel consists of a prismatic body with rectan-gular section and infinite extent in a horizontaldirection, immersed in a 1D hosting mediumwith 3 layers, as in fig.2. The first layer of thehosting medium simulates a sea-water stratum,with thickness of 200 m and resistivity of 0.3

Ωm. The second and third layer represent a con-ductive sedimentary bed, with thickness of 400m and resistivity of 5 Ωm, and a resistive sedi-mentary substratum with resistivity of 100 Ωm,respectively. The 2D prismatic body is placedwithin the substratum and is given a 4×3.4 km2

section and a resistivity of 2 Ωm. Three casesare considered by putting the top of the prismat-ic body at 1, 3 and 5 km of depth below sea level(models 1, 2, and 3 in fig.2).

The simulations consisted in retrievingthe MT-by-SGMV and MT pseudosectionsalong a profile perpendicular to the strike of the2D chamber, in order to test at first the possibil-ity of detecting the target body (the magmachamber) and then the performance of theSGMV method compared with the standard MTmethod. Fig.3 shows the results of the simula-tion for the three cases sketched in fig.2. Indetail, fig.3a refers to model 1, fig.3b to model2 and fig,3c to model 3. In all cases, the simula-tion allows the capability of the standard MTmethod in detecting a magma chamber to beverified, and the reliability of the MT-by-SGMVapproach to be ascertained.

3D model

We consider now a 3D magma chambermodel and introduce also a 2D coastal effect inorder to better represent the expected situationin the Campi Flegrei area across the Gulf ofPozzuoli. A 100 Ωm homogenous rock environ-ment, laterally in contact with a 100 m thick sea-water stratum with resistivity of 0.3 Ωm, isassumed to host a 3D magma chamber, assimi-lated to a 4×4×4 km3 cubic body with resistivi-ty of 1 Ωm and the top side buried at 4 km of

Figure 2. A 2D model of magma chamber immersed within the substratum of a three-layer sequence,whose first layer characterises a sea water layer. Thicknesses of the layers and side dimensions of the2D prismatic body are expressed in km.

12


Figure 3a and 3b. Sea-surface MT and MT-by-SGMV apparent resistivity pseudosections for models1 and 2 of fig.2. The vertical scale is logarithm of frequency in Hz and the horizontal scale is distancein km.

Figure 3c. Sea-surface MT and MT-by-SGMV apparent resistivity pseudosections for model 3 of fig.2.The vertical scale is logarithm of frequency in Hz and the horizontal scale is distance in km.

depth below sea level. The cubic chamber isplaced in such a way as to lie partly below thesea-water layer, as in fig.4 which shows a plan(a) and section (b) view of this complex 3Dmodel. For computation, the horizontal sectionof the 2D model simulating the coastal scarpeffect (the first 100 m of the whole model) hasbeen subdivided into two sectors of 14×21 cellseach, by assigning a resistivity of 100 Ωm ineach cell of the left-hand land sector, and 0.3Wm in each cell of the right-hand marine sector,as depicted in fig.4c.

We have repeated for this 3D model thesame finite difference process used for the pre-vious 2D simulation. Before illustrating the per-formance of the SGMV method, we delineatethe behaviour of the standard MT methodapplied to such a complex situation. Fig.5 showsa sequence of horizontal slices at different peri-ods, where the standard MT apparent resistivitymaps in the more resolutive TM mode aredepicted, starting from 1 s up to 10,000 s. Inorder to better highlight the effect of the cubicchamber on the MT response, the imagesobtained without the cubic body are also illus-trated. It results that the presence of the magmachamber can possibly be appreciated looking attwo effects appearing in the left-hand land sec-tor. The first effect consists in an apparent dis-tortion of the isolines, starting from 10 s

upward, tending to isolate a closed anomalyreflecting the boundary of the cubic body,placed vertically beneath the resistive land sec-tor of the model. The second effect consists in adrop of the resistivity value of the isolines up toabout 37% in the same area where they tend toencircle the target anomaly.

Apparently, there is no signal comingfrom the right-hand marine sector. Actually, thissilence seems to be due to the fact that in themarine sector the apparent resistivity values areso very low as to be undistinguishable with theadopted scale for the isolines, which favour theleft-hand isoline pattern. In a next representa-tion, regarding a profile at sea parallel to theshoreline, the choice of a logarithmic scale forthe isolines will better focus the apparent resis-tivity pattern inside the marine sector.

The analysis of fig.5 allows a final com-ment to be made regarding the presence of thecoast lateral effect. The strong resistivity lateralcontrast, assumed to characterise the passagefrom land to sea, generates an intense crowdingof the isolines in correpondence of the shoreline.This effect propagates virtually with the sameintensity in all horizontal slices for both the sit-uations with and without magma chamber.

In order to visualise the above results aspseudosections, we consider two profiles on


13

Figure 4. Section (a) and plan (b) views of acomplex 3D model simulating the CampiFlegrei volcanic area (Naples). The cell grid-ding for the application of the finite differencealgorithm is shown (c). All distances areexpressed in km.

Figure 5. Standard MT TM mode apparentresistivity horizontal maps at different periodsfor the model of fig.4 with (right-hand column)and without magma chamber (left-hand col-umn). Tips along the sides of the slices areevery 1 km.

14


Figure 6. Standard MT TM and TE mode apparent resistivity pseudosections drawn across a profilerunning on land parallel to the shoreline at a distance of 2 km, with (right-hand column) and withoutmagma chamber (left-hand column). In all pseudosections, the vertical scale is logarithm of period ins, and the horizontal scale is distance in km.

Figure 7. Standard MT TM and TE mode apparent resistivity pseudosections drawn across a profilerunning on land parallel to the shoreline at a distance of 5 km, with (right-hand column) and withoutmagma chamber (left-hand column). In all pseudosections, the vertical scale is logarithm of period ins, and the horizontal scale is distance in km.

land parallel to the coast line, one distant 2 kmfrom the shoreline, placed over the continentalborder of the magma chamber (fig.6), and theother displaced 5 km on land from the shoreline(fig.7). Again the comparison of the MTresponses with and without magma chamber ismade. Moreover, the less resolutive TE mode isalso reported. In the former profile (fig.6), theTM signature of the magma body is very evi-dent and also its geometry appears well delin-eated, whereas in the latter profile (fig.7) the tar-get anomaly tends to become evanescent, asexpected.

We consider now the TM and TE pseudo-sections across a profile through the axis ofsymmetry of the model, perpendicular to theshoreline (fig.8). For the portion of the profile atsea, MT-by-SGMV data have been used (bottomline in fig.8). A comparison is also made withstandard MT TM and TE pseudosections for thecase without (top line in fig.8) and with magmachamber (middle line in fig.8). The MT-by-

SGMV image at sea is quite consistent with thecorresponding standard MT image. In the landsector, the boundary of the magma body is againvery well outlined in the correct lateral position,especially in the TM mode. Again, the distortionof the isolines in the top level of the pseudosec-tions at periods around 1 s, can likely be associ-ated with the presence of the coastal boundary.The sea-scarp effect is now well evident also inthe marine sector, but only in the TE mode, inaddition to the back-projected similar, but muchstronger effect appearing in the land sector,mainly in the TM mode.

Finally, we consider the MT-by-SGMVTM and TE pseudosections (top line in fig.9),across a profile running parallel to the shorelineand placed at a distance of 2 km over the marineborder of the magma chamber, compared withthe standard MT TM and TE pseudosections(bottom line in fig.9). In order to emphasise theapparent resistivity variations around values lessthan 2.5 Ωm, a logarithmic scale has been now


15

Figure 8. Standard MT TM and TE mode apparent resistivity pseudosections drawn across a profilerunning along the symmetry axis perpendicular to the shoreline without (top line) and with magmachamber (middle line). The bottom line shows the TM and TE pseudosections along the same profileobtained using MT-by-SGMV data in the portion at sea, for the case with magma chamber. In all pseu-dosections, the vertical scale is logarithm of period in s, and the horizontal scale is distance in km.

adopted for the isolines. Even though with a notcomplete coicidence of the isolines, the compar-ison between standard MT and MT-by-SGMVimages can again be considered satisfactory.The MT-by-SGMV pseudosections seem now topossess a slightly greater resolution of themagma body, which appears equivalent in bothTM and TE imaging modes.

4. Conclusion

We have studied the capability of theSGMV geophysical method to resolve 2D and3D prismatic bodies approximating a magmachamber placed beneath a sea-water layer, inview of an application to the Campi Flegreicaldera (Naples, Italy), in particular to the por-tion of the caldera extending offshore in theGulf of Pozzuoli. The modelling has been per-formed using a finite difference algorithm, andhas allowed a comparison to be made betweenstandard free-surface MT representations and anequivalent MT imaging retrieved by the SGMVapproach. In all cases, the modelling has con-firmed the general capability of the em induc-tion methods to resolve complex volcanic struc-tures and the comparison has shown the reliabil-ity of the SGMV method in simulating MT

soundings in marine environment. However, itmust be emphasised that, in real cases, this kindof results implies the need of disposing of accu-rate field data with small error bars in order fora conductive magma chamber, residing beneatha sea-water layer, to be detected as reliably aspossible.

Acknowledgements

This work was partially supported by the GNVthrough the Epot project.

References

Kaufman, A.A. and Keller, G.V., (1981). The magne-totelluric sounding method. Elsevier,Amsterdam.

Mackie, R.L., Madden, T.R. and Wannamaker, P.E.,(1993). Three-dimensional magnetotelluricmodeling using difference equations - Theoryand comparisons to integral equation solu-tions. Geophysics, 58, 215-226.

Patella, D., Mauriello, P. and Siniscalchi, A., (1999).A sea-to-ground magnetovariational method.Proceedings of the 1999 Offshore TechnologyConference, 845-850.

Patella, D. and Siniscalchi, A., (1994). Two-level16


Figure 9. MT-by-SGMV TM and TE pseudosections (top line) compared with standard MT TM andTE pseudosections (bottom line), drawn across a profile offshore parallel to the shoreline at a distanceof 2 km. The vertical scale is logarithm of period in s, and the horizontal scale is distance in km.

magnetovariational measurements for thedetermination of underground resistivity dis-tributions. Geophysical Prospecting, 42, 417-444.

Zelwer, R. and Morrison, H.F, (1972). Spatial char-acteristics of mid-latitude geomagneticmicropulsations: Journal of GeophysicalResearch, 77, 674-694.


17

Characterization of the Coherent EMNoise due to Moving Sources on

Magnetotelluric Data

Maria Giulia Di Giuseppe1, Zaccaria Petrillo2,Antonio Troiano1 and Domenico Patella1

1 Department of Physical Sciences, University FedericoII, Naples, Italy

2 National Institute of Geophysics and Volcanology,Vesuvian Observatory, Naples, Italy

AbstractThe magnetotelluric (MT) sounding

method includes as a fundamental step duringdata processing the correct estimate of theimpedance tensor elements on the ground sur-face. Soundings performed in areas of intenseurbanization often show a not negligible tensorinstability, which manifests in a given station aswidely differring apparent resistivity curvesbeyond any confidence limit, according to thedata vector subset used. As discussed in litera-ture, the reason for such instability stands on thenon-stationarity of coherent contributions fromelectromagnetic (EM) sources not approximableto a plane wave field (near-field). Away to over-come such a serious drawback is based on theuse of the multivariate technique of data analy-sis, which allows the details of the EM noisestructure to be fully investigated, and the esti-mate of the number of coherent sources to beascertained. In many instances, by such tech-nique, the MT useful signal can even be extract-ed from a complex mixing of the useful planewave field with coherent signals from nearsources. The multivariate technique is based ona robust analysis of multichannel data expandedin terms of empirical orthogonal functions. Inthis paper, we approach this problem usingEgbert’s robust multivariate errors-in-variables(RMEV) technique. We show some examples ofthe application of Egbert’s algorithm to the opti-mum estimate of MT apparent resistivity curves,using at first a synthetic data structure in orderto fix management criteria of the various stepsof the algorithm, and then a field dataset belong-ing to an MT sounding very recently carried outin the Campi Flegrei volcanic area. The per-formance of the RMEV technique on our fielddata is considered quite satisfactory at the pres-ent stage of the research.

Key words magnetotelluric sounding - RMEVtechnique - Campi Flegrei

1. Introduction

The most important step in magnetotel-luric (MT) data processing is the correct esti-mate of the surface impedance tensor, which isa difficult task in critical frequency bands forsoundings carried out in proximity of electricalrailroads [Egbert, 1997]. Sometimes, criticalityextends to the whole MT frequency band inareas of also intense urbanization [Qian andPedersen, 1991]. The non-stationarity of coher-ent noise can be an explanation of the differentbehaviour of MT sounding curves carried out indifferent periods in the same place by differentgroups [e.g. Di Maio et al., 1998; Manzella etal., 2000].

The structure of the electromagnetic (EM)noise is generally local (near-field), but with ascale reaching tens or more km and an ampli-tude comparable to that of the MT source[Fraser-Smith et al., 1978]. Its characterisationis a necessary step to extract the MT signal. Inparticular, the bias due to trains in the 0.001÷1Hz frequency band, which is the band withinwhich the deep crustal features of primary geo-physical interest can be explored, is a funda-mental problem for our research purposes.

After the introduction of the remote refer-ence [Gamble et al., 1979a, 1979b], by whichthe EM field at a local site is correlated with thehorizontal magnetic components recordedsimultaneously at a remote station, and theapplication of various robust data-adaptiveweighting tools [e.g. Huber, 1981; Jones andJodicke, 1984; Egbert and Booker, 1986; Chaveet al., 1987], the robust multivariate errors-in-variables (RMEV) estimator was at last pro-posed [Egbert, 1997], which allows the back-ground noise level to be estimated and the biasdue to coherent noise to be diagnosed.

The use of a multivariate technique ofdata analysis allows details of the EM noisestructure to be explored, including an estimateof the number of coherent series in the data vec-tor. In some cases it is also possible to extractthe MT signal, i.e. the two series relative to thetwo orthogonal polarizations of the plane wave,even out of a complicate mixing with near-fieldterms due to trains and electric powerlines in the0.001÷1 Hz and 1÷1000 Hz band, respectively.

The multivariate technique, borrowedfrom meteorology where it is also known asprincipal component analysis or spectral decom-position, is based on a robust analysis of multi-ple components recorded at multiple stations(multi-channels) and then represented as empir-ical orthogonal functions. Data vectors withanomalous distance from the mean value are


19

excluded from the statistical sample, and themost suitable norm is used according to theerror distribution. The algorithm estimates theeigenvectors of the spectral density matrix(SDM) constructed with all available channels(magnetic and electric channels are dealt with inthe same way) [Egbert, 1997]. A source is final-ly associated to each eigenvalue emergingabove the threshold of the incoherent noise. Thefundamental step within the theoretical appara-tus is the estimation of the level of the incoher-ent noise in each channel, in order to avoid foreigenvalues without any physical significance toemerge out of it. It can also be demonstrated thatusing the eigenvector representation it is possi-ble to extract all the linear relationships whichconnect channel to channel and group of chan-nels to group of channels, like e.g. the imped-ance tensor elements in the case of local mag-netic to local electrical channels, the magnetictransfer functions in the case of magnetic chan-nels of different sites, and the tipper in the caseof local magnetic channels. The prerequisite ofthe technique is the use of multiple records (twoor three complete simultaneous MT stations),since it is heavily conditioned by the coherentsources-to-channels ratio in case of finite timeseries. Practice suggests to use a number ofchannels which doubles the number of sources.A limit of the SDM analysis is, however, theinability to associate an eigenvector to a singlesource when, in a given band, two or moreeigenvalues are very close. In such a case, aneigenvector can be a linear combinations ofeigenvectors related to single sources.

In this paper, firstly we give a short out-line of the RMEV theory, then we assess theperformance of the RMEV algorithm on an EMsynthetic data structure upon which a high con-trol can be exerted, and finally export the expe-rience thus acquired to a real field case.

2. Outline of the RMEV technique

Following Egbert [1997], in the multivariateapproach the frequency-domain MT array datavectors Xi, where i=1,2,…,N with N being thetotal number of samples, can be put in matrixnotation as

Xi = Uββi + Vγγi + εεi (1)

where, indicating with Κ the total number ofchannels in the array, the columns of the Κ×2 Umatrix are complex vectors, representing themagnetic and electrical fields that would beobserved at all sites for idealized quasi-uniform

magnetic sources, linearly polarized in the N-Sand E-W directions, the columns of the Κ×L Vmatrix represent the L coherent noise sources,and the vector εεi represents the incoherent noise.The vectors ββι and γγι define the polarizations ofthe MT signal and coherent noise sources,respectively.

The impedance tensor Z for a site is givenin terms of the elements of U corresponding tothe x- and y-component of the electric and mag-netic fields observed at the local station in polar-isation states 1 and 2, as follows

(2)

Solving the generalized eigenvalue prob-lem

Su = λλΣNu (3)

where ΣN is the covariance matrix of the inco-herent noise and

is the spectral density matrix of the data, we canobtain the estimates of the eigenvalues λ.

3. The RMEV technique applied to syntheticdata

We illustrate at first the results obtainedusing Egbert’s RMEV algorithm to a syntheticdata structure. The target has been the discrimi-nation between a plane wave field source of sig-nal MTS and a moving near-field source ofcoherent noise MTN. The MTS datasets(Comdat Project) consist of five local channelsand two remote channels. Firstly, only the MTSdatasets have been processed in order to test thecomputer program and verify the hypothesis ofexistence of two eigenvalues. Once ascertainedthe good quality of the results come out fromthis preliminary check, we have passed to con-taminate the local channels by adding the coher-ent noise.

To simulate a moving near-field source(train), we have assumed that the effect of adipolar source turning around the local MT sta-tion can be represented by a MTN signal modu-lation on the electric (Ex and Ey) and magnetic(Hx and Hy) axes as follows

(4a)

20



21

(4b)

(4c)

(4d)

where i=1,2,....,N with N being the total numberof samples, and R is a random function with ele-ments normally distributed around a zero mean

value.In order to have an idea of what kind of

records we are dealing with, fig.1 shows the sig-nal and noise power spectra, relative, for sim-plicity, to only the Hx component. In particular,we let notice the relative noise level at differentperiods in the range 1-104 s.

Fig.2 displays the obtained diagrams ofthe eigenvalues of the relative SDM expressedin dB, plotted versus period. Three eigenvaluessignificantly greater than unity appear in theperiod range from 4 s to about 60 s. The thirdlargest eigenvalue is a clear evidence of theadded coherent noise. In full agreement with the

Figure 1. Power spectra of the magnetic x-component of a synthetic MT signal (dark grey line) and acoherent noise due to a mobile near-field source (light grey line).

Figure 2. Eigenvalues of the spectral density matrix, relative to the corrupted MT dataset analysed in fig.1.

noise power spectra of the coherent noise for alllocal channels (fig.1 shows only the Hx compo-nent), the third eigenvalue decreases as periodincreases, until at about 60 s it definitely fallsaround the zero level, i.e. the background inco-herent noise top level.

We have then analysed the polarization ofthe three main eigenvectors at different periodswithin four time windows corresponding to fourdistinct angular positions of the mobile noisesource in the range 0°-90°.

Fig.3 is a plot of the electric (dashed lines)and magnetic (solid lines) eigenvectors in theband T=20 s. Although the noise level is similarto the signal level (see fig.1), the first two eigen-

vectors appear very stable, as expected, beingrepresentative of the MT source, while the thirdeigenvector rotates following the MTN mobilesource. As period decreases the noise contribu-tion tends to become stronger and the eigenvec-tors become a linear combinations of the threesources, losing directivity.

Finally, fig.4 shows the apparent resistivi-ty and phase curves for the TM and TE modes,computed by the RMEV method using the syn-thetic MT dataset without and with coherentnoise, and assuming that the eigenvectors asso-ciated with the largest two eigenvalues of theSDM define the MT source.

Though a residual bias effect, indicative

22


Figure 3. Eigenvector polar diagrams, computed in the band T=20 s within four contiguous time win-dows, relative to the corrupted MT dataset analysed in fig.1.

Figure 4. Apparent resistivity and phase curves computed by the RMEV method using the MT datasetanalysed in fig.1, with only incoherent noise (a) and incoherent plus coherent noise (b).

of the participation of the coherent noise sourcein the estimate, is still present in both the appar-ent resistivity and phase curves in the high fre-quency band, the quality of the RMEV compu-tation algorithm can be retained quite satisfacto-ry, compared with other standard computationtools.

4. The RMEV technique applied to experi-mental data

We illustrate now the application of theRMEV analysis to experimental data relative toa two-station MT sounding carried out atAstroni (Campi Flegrei, Naples, Italy). In realfield cases, the application of Egbert’s techniqueis more complicated, since eigenvalues signifi-cantly greater than unity may not represent theMT source and/or result nearly equal, makingthe distinction between MT signal and coherentnoise problematic.

Fig.5 shows a plot of the SDM eigenval-ues obtained at Astroni using a 600 s time win-dow. We have evidence of a coherent noise atlow frequencies (2-30 s). In this case, the greaterangular stability of the eigenvectors associatedwith the second and third eigenvalues in theband T=6.4 s (Fig.6) allows us to assume thatthey are the representative eigenvectors of theMT source. The first eigenvector, which shows

changes of direction, is probably related to acoherent noise source due to trains. This conclu-sion is in agreement with the circumstance thatthe signal level associated with electrical rail-ways results higher than the MT signal levelwhen the distance between the MT site and therailroad is less than about 10 km.

Finally, fig.7 shows the apparent resistivi-ty and phase curves computed using the WLS(weighted least-square) and RMEV methods. Inboth cases the curves exhibit a distorted behav-iour in the period range 4-40 s. The apparentresistivity increases steeply and phases falldown to -90°. This behaviour is typical of anMT signal contaminated by non-uniform EMcultural noise sources [Mackie and Madden,1992; Qian and Pedersen, 1991]. This conclu-sion is in agreement with the number of domi-nant SDM eigenvalues (see fig.5) in the sameperiod range.

5. Conclusion

In this work we have tried to find a way todiscriminate the MT signal from coherent noisein order to reconstruct the actual apparent resis-tivity and phase curves. The strongest contribu-tion to the distortion of MT curves is likely dueto electric railroads, which generate coherentnoise extending up to tens of km.


23

Figure 5. Eigenvalues of the spectral density matrix, relative to a two-station MT field sounding atAstroni (Campi Flegrei, Naples, Italy) within a time window of 600 s and with a sampling rate of 64Hz.

24


Figure 6. Eigenvector polar diagrams, computed in the band T=6.4 s within five contiguous time win-dows each with duration of 600 s, relative to the MT sounding performed at Astroni (Campi Flegrei).

Figure 7. Apparent resistivity and phase curves computed by the WLS (a) and the RMEV (b) meth-ods, relative to the MT sounding performed at Astroni (Campi Flegrei).

We have shown that the RMEV methodallows an estimate of the number of coherentsources (signal and noise) to be obtained withindata vectors, but only in few cases the MT sig-nal to be easily extracted. The limit of theRMEV analysis is, in fact, the inability to asso-ciate a given eigenvector to a single source;eigenvectors related to near eigenvalues can belinear combinations of the specific eigenvectorsof the single sources.

By analysing the behaviour of theeigenvectors associated with synthetic data wehave been able to infer that a useful interpreta-tive element is the rotation of the vectors relatedto moving sources. This information, even iflimited to some period bands, can help to recon-struct the true MT impedance curves, using thenot rotating eigenvectors.

Acknowledgements

This research was supported in part by the Epotproject of the GNV.

References

Chave, A.D., Thomson, D.J., and Ander, M.E., 1987.On the robust estimation of power spectra,coherences, and transfer functions, Journal ofGeophysical Research, 92, 633-648.

Di Maio, R., Mauriello, P., Patella, D., Petrillo, Z.,Piscitelli, S., and Siniscalchi, A., 1998.Electric and electromagnetic outline of theMount Somma-Vesuvius structural setting,Journal of Volcanology and geothermalResearch, 82, 219-338.

Egbert, G.D., 1997. Robust multiple-station magne-totelluric data processing, GeophysicalJournal International, 130, 475-496.

Egbert, G.D., and Booker, J.R., 1986. Robust estima-tion of geomagnetic transfer functions,Geophysical Journal of the RoyalAstronomical Society, 87, 173-194.

Fraser-Smith, A.C., and Coates, D.B., 1978. Largeamplitude ULF electromagnetic fields fromBART, Radio Science, 13, 661-668.

Gamble, T.D., Goubau, W.M., and Clarke, J., 1979a.Magnetotellurics with a remote reference,Geophysics, 44, 53-68.

Gamble, T.D., Goubau, W.M., and Clarke, J., 1979b.Error analysis for remote reference magne-totellurics, Geophysics, 44, 959-968.

Huber, P.J., 1981. Robust statistics, J. Wiley & Sons,New York.

Jones, A.G., and Jodicke, H., 1984. Magnetotellurictransfer function estimation improvement by acoherence-based rejection technique, Paperpresented at 54th SEG annual meeting.

Mackie, R.L , and Madden, T.R , 1992. A magne-

totelluric survey around the Loma Prieta faultzone, EOS, Transactions of the AmericanGeophysical Union, 73, 99.

Manzella, A., Volpi, G., and Zaja, A., 2000. Newmagnetotelluric soundings in the Mt. Somma-Vesuvius volcanic complex: preliminaryresults, Annali di Geofisica, 43, 259-270.

Qian, W, and Pedersen, L.B., 1991. Industrial inter-ference magnetotellurics: an example from theTangshan area, China, Geophysics, 56, 265-273.


25

On the Localisation of Long-StandingSelf-Potential Sources at Vulcano (Italy)

by Probability Tomography

Boris Di Fiore1, Paolo Mauriello2 andDomenico Patella1

1Department of Physical Sciences, University Federico IIof Naples, Italy

2Department of Science and Technology for Environmentand Territory, University of Molise, Italy

AbstractWe consider 7 self-potential (SP) areal

surveys performed in the period 1991-1994 atVulcano and show the results of the applicationof the 3D SP probability tomography methodaimed at localising in the subsoil the presence oflong-standing sources of the SP anomalies. Thelong-standing character is associated to sourcesshowing the highest probability of residing infixed positions underground, during the 1991-1994 observation period. The most importantfeatures resulting from the application of the 3Dprobability tomography are: (i) the presence ofsources spread along the Piano and FossaCaldera rims located in a very shallow depthinterval, not extending below sea level; (ii) thepresence of a negative source at the eastern sideof Vulcanello, which shows the highest occur-rence probabilities in the depth range 0.1-0.3 kmbsl, with maximum occurring around 0.2 kmbsl; (iii) the presence of a negative source closeto Grotta Palizzi, which shows the highestoccurrence probabilities in a depth range notextending below 0.1 km bsl, with maximumoccurring around sea level.

Key words self-potential – probability tomog-raphy - volcano geophysics

1. Introduction

During the 1985-1995 volcanic unrest atthe island of Vulcano (Aeolian Arc, SouthernItaly) abnormal changes of physical and chemi-cal parameters were detected in the active areaof the Fossa Cone (see fig.1). Mostly, a remark-able increase of temperature (up to 650°C) andemission rate (up to 1395 tons/day) of the per-sistent fumaroles along the northern crater rimand slopes of the Fossa Cone was recorded,indicating an increase of flux of magmatic gases[Barberi et al., 1991]. A renewed awarenessabout the volcanic hazard in this touristic islandwas stimulated by these events and an intense

research and monitoring activity was conse-quently promoted by the Italian Civil DefenseAuthority.

Among the many geophysical studies thatwere proposed, a Self-Potential (SP) investiga-tion was included, consisted of an areal surveyrepeated 7 times in the period 1991-1994. Themotivation was the SP study might haverevealed the sites of polarised electrical charges,which in volcanic areas are assumed to corre-spond to pressure and/or heat sources [e.g. Reviland Pezard, 1998]. The resulting SP maps arereported in previous papers [Di Maio et al.,1996, 1997], where details of the data acquisi-tion technique are outlined.

In this paper, we reconsider the 7 SP sur-veys at Vulcano and show the results of theapplication of the 3D SP probability tomogra-phy method [Patella, 1997a,b], aimed at localis-ing in the subsoil the presence of long-standingsources of the SP anomalies. It is worth antici-pating that the long-standing character will herebe associated to sources showing the highestprobability of residing in fixed positions under-ground during the 1991-1994 observation peri-od. The probability tomography method hasalready been tested on SP field datasets collect-ed in the volcanic areas of Mount Vesuvius(Naples, Italy) [Di Maio et al., 1998; Iuliano etal., 2002] and Phlegraean Fields (Naples, Italy)[Di Maio et al., 2000].

2. Structural and volcanological outline ofVulcano

The arc of Aeolian islands is located in theTyrrhenian sea about 40 km north of Sicily(fig.1). The islands were formed since LatePleistocene (130000 y.b.p.) through a series ofalternating lava flows and pyroclastic fall andflow deposits, which originated typical strato-volcanoes. The Aeolian arc was formed on aNW-SE structural alignment, which marks thetransition from the westwards downdippingTyrrhenian basin to the eastwards uprisingApennines chain. The three-tip star-like shapeof the arc indicates the existence of radial frac-tures, which favoured magma outpouring[Keller, 1980].

Vulcano is one of the seven islands of thearc and is located at its southernmost edge(fig.1). It raises up to 1500 m above sea floor(500 m a.s.l.) with an extension of 22 km2. FromLate Pleistocene the main strato-volcano, calledPrimordial Vulcano, whose remnant is the PianoCaldera, was originated. Then, at the end ofPleistocene the Lentia Mountains were formed


27

and later, during Holocene, the Fossa Calderacollapse occurred where the present activeFossa Cone (391 m a.s.l.) resides. Since 183b.C. the formation of Vulcanello started as aseparate small island, which in 1550 a.C. joinedVulcano due to accumulation of sands filling thenarrow isthmus [Frazzetta et al. 1983].

In historical times, the Fossa Cone andVulcanello were the sites of frequent and vigor-ous eruptions; mostly those occurred in the 6thand 16th century at Vulcanello and that occurredin 1888-1890 at the Fossa Cone. Vulcanellomanifested intense fumarolic activity at leastuntil 1878, as testified by the abundant sul-phurous deposits around its slopes. The FossaCone is the present most active center, charac-terised by a persistent fumarole activity alongthe northern crater rim and slope, which wasparticularly intense in the period 1985-1995.

The volcanic history of the Fossa Coneincludes various cycles of activity with a typicaleruptive pattern. Frazzetta et al. [1984] firstlymaintained that in case of further eruption, avolume smaller than that emitted during the lastevent of 1888-1890 ought to be released from aneruptive centre displaced either to west or tonorth of the present crater, in an area of greaterstructural weakness due to the persistent fuma-role activity. Successively, Frazzetta and LaVolpe [1991] stated that nature and volume ofproducts emitted in the 1888-1890 event suggestthat no further eruption should occur, having the

Fossa Cone most likely concluded its evolution.The abnormal, alarming intensification of fuma-role activity started in 1985, culminated in 1995without eruption.

3. Presentation of the SP surveys at Vulcano

The 7 SP surveys were performed fromMay 1991 to December 1994, using a networkof interconnected circuits spread over the wholeisland (dots in fig.2a). The SP maps are shownin fig.2b through fig.2h [redrawn after Di Maioet al., 1997].

A low wavenumber and roughly NW-SEoriented SP dipolar anomaly dominates over thewhole island, subject to sign reversal, as e.g.from the map of fig.2f to the map of fig.2g.Superimposed on this field, high wavenumberanomalies are present, the most intense of whichappear along the Fossa Cone rim and the easternslopes of Vulcanello. Time migration and spaceshift of the local anomalies inside the FossaCaldera can also be observed. A noteworthyanomaly with intermediate wavenumberappears in the area of Grotta Palizzi, across theFossa Cone southern foothill and the FossaCaldera rim. It is quite evident in the maps offig.2f and fig.2h.

In order to enhance long-standing SP sig-nals correlatable with the sources of the persist-ent volcanic activity, the steady component of

28


Figure 1. Sketch map of the outcropping volcanic units at Vulcano (Aeolian Arc, Italy).

the SP time varying field has been drawn byassigning at each station the weighted time aver-age of the original SP values. Fig.3a shows thestationary SP map, in conjunction with thestructural map of Vulcano [Ventura, 1994]sketched in fig.3b. The most interesting featuresare:a) the chains of weak, short wavelength positive

and negative anomalies along the wholePiano Caldera rim and western portion of theFossa Caldera rim, both outlined in fig.3b;

b) two strong negative anomalies with higherwavelength, one located along the easternside of Vulcanello and the other along thesouthwestern slopes of the Fossa Conetowards Grotta Palizzi.

4. Outline of the 3D probability tomographytheory

In order to get information on the locationof the sources of the SP anomalies shown infig.3a, the 3D probability tomography (PT)

method [Patella, 1997a,b] has been applied. Anoutline of the 3D PT theory is given at first, asfollows.

Consider a Cartesian coordinate systemwith the (x,y)-plane placed at sea level and the z-axis positive downwards. Suppose to dispose ofN SP datasets, collected in different times overthe same grid of stations located at r≡≡(x,y,z)∈ S,where S is the survey surface defined by the ele-vation function z(x,y). Indicate withE(r)=<En(r)> the weighted time average of theN natural electric field vectors En(r) (n=1,2,..,N)over S, and assume that E(r) can be discretisedas [Patella, 1997a,b]

(1)

i.e. as a sum of partial effects due to Q sourcepoles. The qth pole located at rq∫(xq,yq,zq) isgiven an average source strength aq and itseffect at r is governed by the function

(2)


29Figure 2. (a) The circuit network used to obtain the SP maps reported in pictures (b)-(h).

Consider now the total signal power Λassociated with E(r) over S

(3)

which, using eq.1, can be expanded as

(4)

Take the generic qth term of eq.4 andapply Schwarz’s inequality (5)

from which, indicating with 2X and 2Y the sidesalong the x- and y-axis, respectively, of thesmallest rectangle containing the projection of Sonto the x,y-plane [Patella, 1997b], a long-standing charge occurrence probability functionη(rq) is defined as

(6)

where (7)

and

(8)

The η(rq) function, satisfying the condi-tion -1≤η(rq)≤+1, gives a measure of the aver-age probability, which a negative (ηn<0) or pos-itive (ηn>0) source pole obtain at rq as respon-sible of the average E(r) field.

The role of probability attributed to η(rq)is motivated as follows. In general, a probabili-ty measure P is defined as a function assigningto every subset g of a space of states G a realnumber P(g) such that [Gnedenko, 1979]

P(γ)≥0, for every γ, (9a)P(Γ)=1, (9b)if γ=α∪ β, with α∩β≡0, P(γ)=P(α∩β)=P(α)+P(β).

(9c)Assuming that the presence of a source at

rq is independent of the presence of a source atanother point, the function

P(rq)=

where V is a generic volume including all non-null values of |η(rq)|, can be defined as a proba-bility density, allowing a measure of the proba-bility to find a pole at rq to be made in agree-ment with axioms (9a,b,c).Actually, eq.6 differs from eq.10 only for anunknown constant factor, appearing at thedenominator of eq.10, and has the advantage ofgiving information on the sign of the sources.Therefore, η(rq) can conventionally be assumedas a measure of the charge occurrence probabil-ity.

5. Analysis of the SP tomography at Vulcano

Fig. 4 shows the result of the applicationof the 3D PT imaging method to the average SPsurface map, drawn in fig.3a. The horizontaltomoslices give a 3D representation of the η(rq)function. Without imposing a priori constraints,a structural pattern of the most probable loca-tions of electrical charge accumulations in theshallow part of the volcanic complex has thus

30


Figure 3. (a) The SP stationary map, obatainedas weighted time average of the SP surveysdrawn in fig. 2. (b) Schematic structural map ofVulcano.

(10)

been retrieved.The most important features are:

a) the sources of the weak anomalies spreadalong the Piano and Fossa Caldera rimsappear to be most probably located in a veryshallow depth interval, not extending belowsea level;

b) the intense anomaly at the eastern side ofVulcanello has a negative source, whichshows the highest occurrence probabilities inthe depth range 0.1-0.3 km bsl, with maxi-mum occurring around 0.2 km bsl;

c) the Grotta Palizzi large anomaly has also anegative source, which shows the highestoccurrence probabilities in a depth range notextending below 0.1 km bsl, with maximumoccurring around sea level.

6. Conclusion

We have shown the results of the applica-tion of the 3D SP probability tomographymethod to the weighted average SP survey, cal-culated from 7 SP surveys performed in the peri-od 1991-1994 at Vulcano, in order to highlightthe presence of long-standing SP sources infixed positions underground. The most impor-

tant result of this analysis has been the presenceof a negative source close to Grotta Palizzi,which is considered a place of great importanceto understand the volcanic structure and dynam-ics of the Fossa cone. This source shows thehigher occurrence probabilities in a depth rangenot exceeding 0.1 km bsl, with the maximumoccurring around sea level. The next step will bethe analysis of this SP source in the frameworkof the coupled flows theory, in order to establishif the SP anomalous and stable signal close toGrotta Palizzi is originated and fed by a stablepressure source.

Another important application will be theprobability tomography analysis using an ele-mentary dipole source scanner, in addition to thepole source scanner approach described in thispaper, in order to assess the possible existenceof zones where SP sources of electrochemicalnature occur [Revil et al., 2001] and to resolvepermeability boundary zones [Iuliano et al.,2002].

Acknowledgements

This work was supported by the Epot project ofthe GNV.

References

Barberi, F., Neri, G., Valenza, M. and Villari, L.,(1991). 1987-1990 unrest at Vulcano. ActaVulcanol., 1, 95-106.

Di Maio, R., Di Sevo, V., Giammetti, S., Patella, D.,Piscitelli, S. and Silenziario, C., (1996). Self-potential anomalies in some Italian volcanicareas. Ann. Geofis., 39, 179-188.

Di Maio, R., Mauriello, P., Patella, D., Petrillo, Z.,Piscitelli, S., Siniscalchi, A. and Veneruso, M.,(1997). Self-potential, geoelectric and magne-totelluric studies in Italian active volcanicareas. Ann. Geofis., 40, 519-537.

Di Maio, R., Mauriello, P., Patella, D., Petrillo, Z.,Piscitelli, S. and Siniscalchi, A., (1998). Electricand electromagnetic outline of the MountSomma-Vesuvius structural setting. J. Volcanol.Geotherm. Res., 82, 219-238.

Di Maio, R., Patella, D., Petrillo, Z., Siniscalchi, A.,Cecere, G. and De Martino, P., (2000).Application of lectric and electromagnetic meth-ods to the definition of the Campi Flegreicaldera (Italy). Ann. Geofis., 43, 375-390.

Frazzetta, G., La Volpe, L. and Sheridan, M.F.,(1983). Evolution of the Fossa Cone. J.Volcanol. Geotherm. Res., 17, 229-260.

Frazzetta, G., Gillot, P.Y., La Volpe, L. and Sheridan,M.F., (1984). Volcanic hazards at Fossa ofVulcano: Data from the last 6000 years. Bull.Volcanol., 47, 106-124.

Frazzetta, G. and La Volpe, L., (1991). Volcanic his-tory and maximum expected eruption at “La


31

Figure 4. The 3D probability tomography ofthe average SP survey map drawn in fig. 3a.

Fossa di Vulcano” (Aeolian Islands, Italy). ActaVulcanol., 1, 107-114.

Gnedenko, B.V., (1979). Kurs teorii verojatnostej.Mir, Moscow.

Keller, J., (1980). The Island of Vulcano. Rend. Soc.It. Miner. Petrol., 32, 369-414.

Iuliano, T., Mauriello, P. and Patella, D., (2002).Looking inside Mount Vesuvius by potentialfields integrated geophysical tomographies. J.Volcanol. Geotherm. Res., 113, 363-378.

Patella, D., (1997a). Introduction to ground surfaceself-potential tomography. Geophys. Prospect.,45, 653-681.

Patella, D., (1997b). Self-potential global tomogra-phy including topographic effects. Geophys.Prospect., 45, 843-863.

Revil, A. and Pezard, P.A., (1998). Streaming electri-cal potential anomaly along faults in geothermalareas. Geophys. Res. Lett., 25, 3197-3200.

Revil, A., Ehouarne, L. And Thyreault, E., (2001).Tomography of self-potential anomalies of elec-trochemical nature. Geophys. Res. Lett., 28,4363-4366.

Ventura, G., (1994). Tectonics, structural evolutionand caldera formation on Vulcano Island(Aeolian Archipelago, Southern TyrrhenianSea). J. Volcanol. Geotherm. Res., 60, 207-224.

32


New Magnetotelluric Response on the Mt. Etna Volcano

Annalisa Zaja1 and Adele Manzella2

1Dipartimento di Geologia, Paleontologia e Geofisica,Università di Padova,Via Giotto 1, 35123 Padova, Italy2CNR-Istituto di Geoscienze e Georisorse, Via Moruzzi 1,

56124 Pisa, Italy

AbstractDuring autumn 2001 some MT sound-

ings, in a remote-reference mode, were carriedout on the Mt. Etna volcano. Data were collect-ed with 3 Metronix acquisition systems, one unitwas located on the remote site in Calabria andthe others on the Mt. Etna volcano along a W-Eprofile centred at Rifugio Sapienza. Theobtained electrical resistivity section shows aconductive zone between 0 to 4000 m b.s.l. Thelowest resistivity values, of the order of 1 Ωm,has been detected in the western part of the sec-tion. The conductor is interpreted as being dueto magmatic intrusion at shallow depth. Thisintrusion was probably a remnant of the previ-ous eruption that took place few months beforethe fieldwork, which did not emptied the magmastored at shallow level. This hypothesis wouldbe also testified by the strong eruption startedone year after the MT survey.

Key words magnetotelluric sounding - 1Dresistivity section - Mt. Etna volcano

1. Introduction

In the last decade many geophysicalmethods have been applied to investigate thestructure of the Mt. Etna volcano. The seismicmodel of Sharp et al. [1980] and the modeling ofthe deformation of Mt. Etna during its 1991-1993 major eruption from radar interferometrymeasurements [Massonnet et al., 1995] hypoth-esised a large magma chamber located at depthof 15-25 km within a crust of continental thick-ness. Seismic data [Hirn et al.,1997] suggestedthe presence of a upwelling mantle, capped by alens of melt, located at a depth range of 15-20km below Mt. Etna. Murru et al., [1999], usingb-values of earthquakes recorded before 1997,suggested the presence of at least two majoractive magma reservoirs with radii less than 2and 5 km, respectively, one located WSW of thesummit at about 2km b.s.l., the other 2 km E ofthe summit at about 11 km b.s.l.

The structure beneath the volcano from

the surface down to 18 km depth has beenrecently defined from seismic tomographicmodeling [Chiarabba et al, 2000]. The mainstructural features defined by this recent seis-mic tomography consists of a high-velocitybody located beneath the central craters, whoselateral extension is about 12 km between 3 and9 km depth and about 6 km between 9 and 18km depth. At shallow depth this body appearssplit in two high-velocity anomalies, locatedbelow the summit craters and the eastern flank(Valle del Bove), respectively. This high veloci-ty body is interpreted as being due to solidifiedmagma intrusions. Within this broad body, theauthors hypothesise thin feeding systems below9 km and small sized magma storage at depthshallower than 9 km.

Loddo et al., [1989], using deep dipolegeoelectrics, excluded the presence of a shallowmagmatic chamber as suggested by the absenceof any geophysical markers down to about 3 kmb.s.l. Mauriello et al. [2000] suggested, from 1DBostick inversion of MT soundings, the exis-tence of a wide conductive zone, with resistivi-ties as low as few Ωm, located below the south-ern side of the volcano in the depth range 15-30km.

The whole set of geophysical data sug-gests that the shallow volcanic structure cannotbe considered in a static condition, and that thevery dynamic nature of the structure is reflectedby the clear and periodic change of physicalparameters at depth.

This paper describes the result of a mag-netotelluric (MT) survey on the southern flankof the volcano, with the aim of characterize themagmatic and still melted intrusion at depth.The conductive anomaly that has been definedis interpreted and discussed.

2. Data analysis

MT soundings were recorded with threeMetronix acquisition systems during autumn2001. One system recorded data in the remotesite of Verzino, located in Calabria, while elevensoundings were carried out on the southern sideof the Mt. Etna volcano, along a W-E profilecentred approximately at Rifugio Sapienza (site1). Figure 1 shows the location of the MTsoundings.

Data were recorded in the frequency bandof 40960 – 0.002 Hz. The high frequency bandswere acquired during the daytime, whereas thelower frequency band was acquired during thenight simultaneously on the volcano and theremote site.


33

Due to presence of radio and telephonetransmitters, MT data appeared affected bynoise, especially in the high frequency range.

In order to remove the noise, data were

processed using a robust code [Larsen et al.,1996]. Data could be processed in single-sitemode, and the noise could be removed from dataof all the sites except those recorded in the cen-tral part of the profile (site 1, 2 and 3 in Fig. 1)The obtained apparent resistivity and phaseresponse curves of the MT soundings are shownin Figs. 2 and 3. For some not yet clear reason,the data acquired in the remote site appears scat-tered and out of phase with the data acquiredsimultaneously on the Etna volcano, and couldnot be used.

Beside the very noisy central sites, theMT sounding curves show a low scattered dataand a regular behaviour for all soundings alongthe whole profile. These curves show highapparent resistivity values (500-1000 Ωm) athigher frequencies and low values (10 Ωm) atlower frequencies. This evidence suggests thatbelow a resistive cover the detected volcanicstructure is very conductive.

The use to plot data in the form of appar-ent resistivity and phase pseudosections helps toimage the structure along the profile at differentfrequencies. The calculated apparent resistivity

34


Figure 1. Location of the MT soundings on theMt. Etna volcano

Figure 2. Apparent resistivity and phase curves along N-S and E-W directions

and phase pseudosections in the N-S and W-Edirections are presented in Fig. 4 and Fig.5,respectively.

On both the apparent resistivity pseudo-sections, a very conductive area, for frequenciesbetween 1 and 0.01 Hz and a maximum of phaseanticipated for frequencies between 100 to 1 Hzis clearly visible on the western side of the pro-file. The very low values of phase, at very longperiods, are possibly due to the presence of

coherent noise on the recorded data which wasnot removed by a single site data processing.

To image the electrical volcanic structureat depth, data have been modeled using the 1DBostick and the layered inversions.

In the 1D interpretative resistivity sec-tion, presented in Fig.6, it is possible to recog-nize:

• a very resitive shallow layer ( ∼ 1000 Ωm).The highest resistivity values are detected on


35

Figure 3. Apparent resistivity and phase response curves along N-S and E-W directions

Figure 4. Apparent resistivity and phase pseu-dosections in the N-S direction

Figure 5. Apparent resistivity and phase pseu-dosections in the W-E direction

the western flank of the volcanic apparatus; • a very conductive layer (2-20 Ωm) at depthranging between 0-4000 m b.s.l. The highestresistivity values are detected on the westernside of the profile.

3. Discussion

The near surface resistive layer representsthe volcanic cover. Its resistivity agrees with theshallow resistivity defined by Loddo et al.[1989], and Mauriello et al. [2000]. The veryinteresting and new feature defined in this sur-vey with respect to those performed in the pastis the very conductive body at a depth of 0-4km, where previous survey indicated the pres-ence of high resistivity. This body is shallower,thicker and more conductive on the western sideof the investigated section. The conductiveanomaly can be interpreted as being due to amagmatic intrusions, in the shallow crust, with avery high fluid fraction. In order to understandwhy we define such a different structure withrespect to those defined in the past, we musttake into account the particular period of oursurvey. The measurements were carried out only3 months after the spectacular eruption of July2001, and one year before the very long eruptionof 2002-2003, which is still active at themoment. We hypothesise that the shallow mag-matic intrusion storage that fed the 2001 erup-tion was not totally emptied during the eruption,and that a large quantity of melted material waspresent at shallow level during our survey. Thishypothesis is proved by the fact that one yearafter the survey a new eruption started, and theamount of material that has been and is stillbeing erupted could have never been accumulat-ed in just one year.

4. Conclusion

The new MT soundings, collected duringautumn 2001, produced a resistivity sectionalong a W-E profile centred at the RifugioSapienza, on the southern side of the Mt. Etnavolcano. This section defines the resistivity dis-tribution of the volcanic structure down to thedepth of 8 km. It shows a very conductive areabetween 0 to 4000 m b.s.l. that indicate the pres-ence of melted material at shallow depth. Webelieve that the magma intruded at shallow levelin the crust, which was imaged by our survey,has been then erupted during the 2002-2003eruption. To support this interpretation, a repeti-tion of the MT soundings is planned in nextfuture. If the magma stored at shallow level hasbeen totally erupted during the eruption of2002-2003, the new resistivity section should becharacterized by higher resistivity values corre-sponding to the real values of the near surfacevolcanic formations of the area. This imagewould be comparable with the one depicted byMauriello et al. [2000]. This study testify thestrong potentiality of MT method in defining theshallow volcanic structure of Etna volcano, andfor monitoring the magmatic activity.

Acknowledgements

Metronix Company is acknowleged for provid-ing the three systems for the demo project, andin particular Bernhard Friedrichs for the techni-cal support during the survey. We thank NicolaPraticelli, Giampaolo Girardi and AlessandroMaretto for their help during the fieldwork. Thisresearch was financially supported by the GNVthrough the Epot project.

References

Chiarabba C., Amato A., Boschi E., (2000). Recentseismicity and tomographic modeling of theMount Etna plumbing system. Journal ofGeophysycal Research, Vol.105, No. B5,p.10,923-10,938.

Hirn A., Nicolich R., Gallart J., Laigle M., CernoboriL., ETNASEIS Scientific Group (1997).Roots of Etna volcano in faults of great earth-quakes.Earth and Planetary Science Letters,148, p.171-191.

Larsen J.C., Mackie R., Manzella A., Fiordelisi A.,Rieven S., (1996). Robust smooth magnetotel-luric transfer function.Geophys. J. Int., 124,p.801-819

Loddo M., Patella D., Quarto R., Ruina G.,Tramacere A., Zito G. (1989).Application ofgravity and deep dipole geoelectrics in thevolcanic area of Mt. Etna (Sicily). Journal of

36


Figure 6. 1D Resistivity Section

Volcanology and Geothermal Research , 39,p.17-39

Massonnet D., Briole P. And Arnaud A.(1995).Deflation of Mount Etna monitored byspaceborne radar interferometry. Nature,375, p.567-570.

Mauriello P., Patella D., Petrillo Z., Siniscalchi A.(2000) An integrated studies of M.te Etna vol-canic structure. Annali di Geofisica, 43, N.2,p.325-342.

Murru M., Montuori C., (1999). The location ofmagma chamber at Mt. Etna, Italy, mappedby b-values. Geophys. Res. Lett., vol.26,N.16, p 2553-2556.

Sharp A.D.L., Davis P.M.and F.Gray (1980). A lowvelocity zone beneath Mount Etna andmagma storage.Nature 287, p.587-591.


37

Electrical Modelling of the ShallowStructural Setting of the Cisternazza-

Montagnola Area (Mt. Etna)

Giuseppe Della Monica1, Rosa Di Maio2, RobertoScandone1, Gianpaolo Cecere3, Ciro Del Negro4,Prospero De Martino3, Francesco Santochirico2

1Dipartimento di Fisica, Università Roma Tre, Roma,Italy

2Dipartimento di Scienze Fisiche, Università di NapoliFederico II, Napoli, Italy

3Istituto Nazionale di Geofisica e Vulcanologia -Osservatorio Vesuviano, Napoli, Italy

4Istituto Nazionale di Geofisica e Vulcanologia – Sezionedi Catania, Italy

AbstractWe present the results of a study concern-

ing the definition of the main structural linea-ments and the dynamic processes characterisingthe shallower crustal portion of the south-east-ern sector of the Mt.Etna by electric-type geo-physical methods. At this end, using the self-potential and the geoelectrical techniques, ageophysical exploration was performed in atest-site (Cisternazza-Montagnola area) interest-ed by the eruption events of July-August 2001.In particular, a self-potential survey, in an areaof about 2 km2, and a geoelectrical tomography,along a profile 1200 m long, have permitted tomodel the buried volumes down to a depth ofabout 300 m below ground level. The presenceof low resistivity and high charge occurrenceprobability values in the central portion of theinvestigated area, to a depth of about 150 mb.g.l., seems to indicate the occurrence of a shal-low groundwater flow.

Key words applied geophysics - electric meth-ods - volcanology

1. Introduction

During the recent Etna eruption of July-August 2001, the vent at height of 2550 m a.s.l.had a moderate explosive activity probablycaused by magma-water interaction. On 19 July2001, two days after the beginning of the erup-tion, two pit craters opened at 2550 m a.s.l. onthe SE flank of Etna. The initial eruptive activi-ty was characterised by frequent explosion withthe emission of ashes which were dispersed tothe SE of the volcano in direction of Catania.Between 24 and 31 July the activity of thesecraters was characterised by strombolian explo-

sion and the emissions of several lava flows.The strombolian activity built an impressivescoria cone. The lava flows destroyed the upperstation of the cableway, and menaced the touris-tic settlement of Rifugio Sapienza. On the 31 ofJuly, in coincidence with the end of the lavaflow emission, there was a renewal of ash explo-sions. This activity slowly subsided with thegeneral trend of the eruption. Overall this activ-ity may be due to different degree of interactionbetween magma and water, depending on theheight of the magma head in the conduit.

As the main damages of the eruption werecaused by the ash dispersion coming from thisvent, it is necessary a better knowledge of themechanisms dominating this kind of Etneanactivity by the individuation, if any, of the shal-low groundwater circulation network. Since theelectric parameters are strongly dependent ontemperature and pressure, as well as on the pres-ence and abundance of mineral particles and flu-ids, a relevant role is played, in principle, by theelectric geophysical methods in investigatingvolcanic environments. Recent studies, per-formed in the main Italian volcanic areas [DiMaio et al., 1997, 1998a, 1998b, 2000], havedemonstrated that a joint use of high resolutiontomographic geoelectrical methodologies, inparticular of self-potential (SP) and dipolar geo-electrics (DG), seems capable of revealing themost important shallow-sited electrical chargepolarisation and resistivity variations, mostprobably caused by rock-water-magma interac-tions in active areas, and more generally, byinvasion and circulation of hot fluids in porousmedia and/or along permeable fracture systems.

Indeed, the analysis of the SP signals,observed on the surface with multi-channelacquisition techniques along profiles or by sen-sor areal distribution, can fruitfully put in evi-dence double layer like anomalies across frac-tures, particularly enhanced in presence of fluidflows through them. With an appropriate inte-gral transformation of the observed SP data(cross-correlation power analysis) according toa sectional tomographic representation, it is pos-sible to obtain the structural configuration of theelectrokinetic paths and further delineate theburied geometries, as well as to understand therole of water solutions and their interaction inthe deep dynamics of the fractured systems.

An important contribute to a better defini-tion of the structural features depicted by theabove mentioned SP prospecting is provided bythe DG tomography. Indeed, it is deputed togive a high-resolution image of the subsoilstructural pattern on the basis of the resistivitycontrasts characterising the various geologic


39

bodies in contact to each other inside the maxi-mum lateral and vertical investigation ranges.Besides this fundamental property, the DGtomographic approach, gets also useful informa-tion helping to understand the meaning of someSP anomalies, particularly those which are relat-ed to charge distributions along resistivity dis-continuity planes, induced by the SP primarysources.

In this paper, we present the results ofself-potential and geoelectrical measurementsperformed in the Cisternazza-Montagnola area,in the framework of a study concerning the def-inition of the main structural lineaments and thedynamical behaviour of the feeding and uprisingsystems characterising the shallower crustalportion of the south-eastern sector of the Mt.Etna.

2. Self-potential survey

The SP data were obtained by measuringthe potential difference existing between twogrounded copper rod electrodes, which werecontinuously displaced along the circuits report-ed in fig. 1b. The mutual distance between everytwo consecutive electrode positions was takenconstantly equal to 50 m. A total of 96 SP dropmeasurements, distributed over an area of about2 km2, were collected. Figure 2 shows the elab-

orated SP final map. Separation between nega-tive and positive SP anomalies is marked by theblack zero-valued thick line, which was drawnafter shifting the SP zero, originally attributed toan arbitrary reference station for the calculationof the initial set of SP mapping values, to allpoints corresponding to the average SP value ofthe initial set. For further details about the SPmeasuring system, survey technique and dataprocessing the reader is referred to a previouspaper [Di Maio et al., 1996].

From a qualitative point of view, the SPmap shows the investigated area characterisedby a low wavenumber regional trend with pre-vailing “negative” SP values in the western sec-tor and “positive” SP values in the central-east-ern sector. The demarcation band of this bipolarfield is defined by a crowding of the SP isolinesin the westernmost part of the surveyed area,along a nearly N-S direction. Superimposed onthis regional trend there appear high wavenum-ber local anomalies. It is interesting to note thepattern of the isolines in some transition zonesfrom positive to negative SP values, that soundscorrelated to the fracture systems, so as dis-played in fig.1a. Therefore, such a feature couldbe indicative of shallow electric charge accumu-lations along the structural discontinuity planes,where in primary electrokinetic fluid streamscould be the sources of the observed anomalies.Finally, the negative SP anomaly in the north-

40


Figure 1. (a) Schematic map of fractures and volcanic centres developed during the July-August 2001eruption of Mt.Etna (from Billi et al., 2003, modified). (b) Geophysical survey area. The dotted cir-cuits and the AA’ full line refer, respectively, to the self-potential survey and the dipolar geoelectricprofile. (c) Eruptive vent at 2550 m a.s.l. (from INGV-CT).

eastern part of the map, seems well delineate theborder of the Cisternazza caldera, interested byfluid circulation.

In order to elicit from the SP survey mapof fig. 2 the most quantitative information on thedepth location of the polarisation field sources,we have adopted a tomographic imaging proce-dure [Di Maio and Patella, 1994, Patella, 1997a]of the SP anomalies including topographiceffects [Patella, 1997b]. Briefly, the 3D tomo-graphic approach aims at the recovering of theunderground electric charge distributionsthrough a cross-correlation procedure betweenthe observed natural electric field and a theoret-ical scanner function, representing the syntheticSP response on surface of an elementary posi-tive charge with unitary intensity, located in anygeneric point of the subsoil. Then, by a normal-isation procedure of the cross-correlation opera-tor based on Schwarz’s inequality, it is possibleto define a charge occurrence probability func-


41

Figure 2. The self-potential survey map.

Figure 3. 3D self-potential probability tomography in the depth interval from 50 m to 300 m b.g.l.

tion (COP) [Patella, 1997a], constrained to varyinside the interval [-1,1]. Positive values are theresult of a major influence from positive chargeaccumulations, while negative values resultfrom negative charge concentrations. Finally, bya suitable 3D grid distribution of probabilityvalues in the investigated volume, the tomo-graphic image can be drawn for inspecting thepattern of the polarisation source centres in aprobabilistic sense.

Figure 3 shows the 3D tomographicinversion of the SP data displayed in the map offig. 2, and here reported again at the top of thefigure. The tomography refers to shallowimages between 50 m and 300 m below theground level (b.g.l.). As for the shallowest partof the underground investigated volume, it isinteresting to note, in the north-eastern sector ofthe first slice of the tomographic sequence, anegative charge accumulation, whose maximumCOP values are observed at depth of about 70 mb.g.l. According to our previous hypothesis, thisdepth indicates the bottom of the Cisternazzacrater.

Moreover, the E-W oriented dipolar field,already shown by the SP isoline pattern of fig. 2,now appears clearly evident. The charge accu-mulations have the highest absolute COP valuesin the range 100-150 m b.g.l. for both negativeand positive nuclei. The depth location andintensity of these clusters seem to outline astructural discontinuity characterised by a con-spicuous fluid circulation, very likely ascribableto the N-S fracture system (Fig.1a) developedon top of Mt.Etna during the July-August 2001eruption [Billi et al., 2003].

3. Geoelectrical tomography

In order to verify the occurrence of a sig-

nificant underground fluid circulation, as sug-gested by the results of the SP survey, a ultra-high resolution (u.h.r.) geoelectrical tomogra-phy [Worthington, 1984] has been carried outalong the profile indicated in fig.1b with theAA’full line. This technique is able to give anextremely detailed picture of the electric resis-tivity behaviour across the vertical planethrough the profile. In fact, followingWorthington [1984], the u.h.r. geoelectricalpseudosection can be classified as a first-ordertomography, for it can provide, in a truly objec-tive way and prior to any data inversion pro-gram, symptomatic resistivity anomaly imagesacross the investigated section. Indeed, sophisti-cated 2D and 3D inversion procedures appliedto many field examples have shown that thecomplex geometries of the interpreted modelsare closely reflected in the original pseudosec-tion images [see, e.g., Loke and Barker, 1995,1996; Turberg and Barker, 1996; Dahlin, 1996].

Figure 4 shows the DG apparent resistiv-ity pseudosection across the selected profile.The DG data were obtained with dipoles of 100m of length and the measured dipolar apparentresistivities were attributed at a pseudodepthequal to half the spacing between the centres ofthe emitting and receiving dipoles, along themedian axis through the line joining the twodipoles. Continuous displacement of the dipolesalong the selected profile of 1200 m of lengthprovided a very dense network of about 54experimental data points in the vertical pseudo-section.

Looking at the fig. 4, relatively highapparent resistivity values (higher than 1000Ωm) characterise the shallower portion of thepseudosection, very likely ascribable to frac-tured volcanics saturated with waters. In fact,the resistivity values describing dry volcanicmaterials generally exceed the observed values

42


Figure 4. DG apparent resistivity pseudosection along the AA’ profile shown in Fig. 1b.

of about two orders of magnitude. This hypoth-esis is in agreement with the Vp and Vp/Vs mod-els given by Patane et al. [2002]. The authors,indeed, observe in the shallower part of theinvestigated area low P-wave velocities andhigh Vp/Vs values, which they correlate to sedi-mentary rocks where water-filled pores andcracks exist. Moreover, very interesting appears,for the purposes of our study, the resistivityanomaly pattern in the deeper zone of the pseu-dosection: a resistive dyke-like configurationseems to intrude inside conductive walls. Theresistivity values characterising the conductiveblocks bring to hypothesise the presence of agroundwater flow, while the values describingthe resistive body seem to suggest the presenceof solidified lava, due to magma uprising whichoriginated the eruptive vent at 2550 m a.s.l..Therefore, the presence of a local water table,outlined by the electric investigation at a depthof about 150 m b.g.l, could justify a magma-water interaction [Taddeucci et al., 2002], whichconferred to the 2001 eruption an explosivecharacter.

4. Concluding remarks

We have presented and discussed theresults of an electric-type geophysical survey inthe south-eastern sector of the Mt.Etna(Cisternazza-Montagnola area). Self-potential(SP) and dipolar geoelectrics (DG) were used toinvestigate the shallower crustal portion of thearea site of July-August 2001 eruption.

As it concerns the SP method, the mainresult was the evidence of a roughly N-S frac-ture system (Fig. 3) to west of the vent openedduring the eruption at 2550 m a.s.l.. The succes-sive SP data analysis, through a tomographicimaging procedure, has been able to define thedepth of the fluid flow, which probably feeds theoutlined fracture system. Indeed, the occurrenceof electric positive and negative charge accumu-lations in the depth range 100-150 m b.g.l. (Fig.4), brought to hypothesise the presence of ashallow aquifer, responsible of the phreatomag-matic activity observed in some phases of theJuly-August 2001 eruption. This interpretationconforms to the result pointed out by the DGtomography, performed along a profile crossingthe quoted fracture system. The presence, infact, of a largely extended relatively low resis-tivity zone at a depth of about 150 m b.g.l.seems ascribable to a local water table, whichcaused magma-water interactions.

Noteworthy was also the evidence of ahigh-resistivity intrusive body in the deep cen-

tral portion of the DG pseudosection (Fig. 4).The pattern of this resistive anomaly lets foreseethe occurrence of the dyke that fed the activityof the vent.

Acknowledgements

We thank A. Bonaccorso for help provided torealise the measurement campaign and G.Macedonio who authorised personnel of theOsservatorio Vesuviano to participate in thegeophysical survey. Sincere thanks to S.Riccioli and P. Aloe for the invaluable help inthe field work. Study performed with financialsupport from INGV (Catania Section).

References

Billi, A., Acocella, V., Funiciello, R., Giordano, G.,Lanzafame, G. and Neri, M., (2003).Mechanisms for ground-surface fracturingand incipient slope failure associated with the2001 eruption of Mt.Etna, Italy: analysis ofephemeral field data. Journal of Volcanologyand Geothermal Research, 122, 281-294.

Dahlin, T., (1996). 2D resistivity surveying for envi-ronmental and engineering applications. FirstBreak, 14, 275-283.

Di Maio, R. and Patella, D., (1994). Self-potentialanomaly generation in volcanic areas. TheMt.Etna case-history. Acta Vulcanologica, 4,119-124.

Di Maio, R., Di Sevo, V., Giammetti, S., Patella, D.,Piscitelli, S. and Silenziario, C., (1996). Self-potential anomalies in some Italian volcanicareas. Annali di Geofisica, 39, 179-188.

Di Maio, R., Mauriello, P., Patella, D., Petrillo, Z.,Piscitelli, S., Siniscalchi, A. and Veneruso,M., (1997). Self-potential, geoelectric andmagnetotelluric studies in Italian active vol-canic areas. Annali di Geofisica, 40, 519-537.

Di Maio, R., Mauriello, P., Patella, D., Petrillo, Z.,Piscitelli, S. and Siniscalchi, A., (1998a).Etna: Self-potential, geoelectric and magne-totelluric measurements. In: Data related toeruptive activity, unrest phenomena and otherobservations on the Italian active volcanoes -1993-1995 (P.Gasparini, ed), ActaVulcanologica, 10(1), 187-193.

Di Maio, R., Mauriello, P., Patella, D., Petrillo, Z.,Piscitelli, S. and Siniscalchi, A., (1998b).Electric and electromagnetic outline of theMount Somma-Vesuvius structural setting.Journal of Volcanology and GeothermalResearch, 82, issue 1-4, 219-238.

Di Maio, R., Patella, D., Petrillo, Z., Siniscalchi, A.,Cecere, G. and De Martino, P., (2000).Application of electric and electromagneticmethods to the definition of the Campi Flegreicaldera (Italy). Annali di Geofisica, 43, 375-390.

Patane, D., Chiarabba, C., Cocina, O., De Gori, P.,Moretti, M. and Boschi, E., (2002).Tomographic images and 3D earthquake


43

locations of the seismic swarm preceding the2001 Mt.Etna eruption: Evidence for a dykeintrusion. Geophysical Research Letters, 29,135-1÷135-4.

Patella, D., (1997a). Introduction to ground surfaceself-potential tomography. GeophysicalProspecting, 45, 653-681.

Patella, D., (1997b). Self-potential global tomogra-phy including topographic effects.Geophysical Prospecting, 45, 843-863.

Taddeucci, J., Pompilio, M. and Scarlato P., (2002).Monitoring the explosive activity of the July-August 2001 eruption of the Mt. Etna (Italy)by ash characterization. GeophysicalResearch Letters, 29, 71-1÷71-4.

Turberg, P. and Barker, R., (1996). Joint applicationof radio-magnetotelluric and electrical imag-ing surveys in complex subsurface environ-ments. First Break, 14, 105-112.

Worthington, M.H. (1984). An introduction to geo-physical tomography. First Break, 2, 20-26.

44


Bouguer Correction for a SphericalEarth: Application to the Etna Data

Mariano Loddo and Domenico Schiavone

Dipartimento di Geologia e Geofisica, Università di Bari

AbstractThe procedures to perform complete

Bouguer corrections are a critical concern main-ly when rugged topographies and large investi-gation areas are interested. These correctionsgenerally include the simple slab and terraincorrections. In recent years it was recognizedthat a curvature correction is necessary also forexploration surveys. In order to standardize thecorrection parameters and to allow the joiningtogether of different data sets, the choice of anouter radius of 166.7 km was suggested for thecomplete Bouguer correction. This paper pres-ents an automatic procedure to perform theBouguer correction considering as reference thespherical surface through each gravity station.The terrain correction in the “outer zone” (from2.5 km to 166.7 km) is performed calculating,from gridded average elevation data, triangularpolyhedra with a face on the reference sphere.For the “inner zone” (station to 2.5 km) triangu-lar polyhedra are constructed by modelling thetopographic surface with a triangular facetedsurface resulting from the Delaunay triangula-tion of the digitized elevation data. An exampleof the application of the proposed procedure tothe Etna gravimetric data is shown.

Key words Bouguer correction - gravimetricdata - Mt. Etna

1. Introduction

As it is well known the Bouguer anomalyrepresents the residual values between theobserved gravity and the gravity componentsgenerated by a simple earth model ( the idealearth model). As stated by Chapin (1996) thegravity corrections, adopted for obtaining theBouguer anomalies, “attempt to make up for theincorrect assumptions made in the original earthmodel”. It was lengthy debated in the last tenyears in the scientific community on the proce-dures to carry out the corrections for prospect-ing targets, mainly as regards the earth model toadopt for the simple Bouguer correction ( a pla-nar model or a spherical one) and the limit towhich the terrain corrections should be applied[LaFehr, 1991a, 1991b, 1998; Talwani, 1998].

Following LaFehr (1998), if major changes inelevation occur between stations also for localsurveys a spherical cap with surface radius of166.7 km from a station must be consideredboth for the simple Bouguer correction and theterrain one. The selection of this distance,although arbitrary, is justified by the need ofstandardization in the correction procedures. Asa consequence of this choice it is (1) avoided theintroduction of fictitious elevation-dependentanomalies and (2) eliminated the occurrence ofmisties between independently conducted adja-cent or overlapping surveys [LaFehr, 1991a,1998].

We consider the argumentations ofLaFehr well founded and his standardizationrequirement to be observed for gravity surveysin a large part of the Italian territory.

In this paper we present a procedure forthe complete Bouguer correction with an exam-ple of application to the Etna field data.

2. Complete Bouguer correction

The classical complete Bouguer correc-tion is a three-step procedure [Bullard, 1936]:

• Simple Bouguer correction (Bullard A) – itis an elevation correction where the air in theFree-air correction is replaced by an infiniteslab filled with rock.• Curvature correction (Bullard B) – itattempts to correct the physically unaccount-able slab model of the earth making its shapemore realistic; it is not generally used.• Terrain correction (Bullard C) – it accountsfor the topography around the station out tothe maximum distance assumed to produce ameaningful contribution to the data values.


45

Figure 1. Sketch of the topographic surface andthe spherical cap (dashed area) in the meridianplane ZOΛ and geometrical relationshipbetween ellipsoidal coordinates and Cartesiancoordinates used for terrain correction.

2.1. Bullard A+B correction

The simple Bouguer correction and thecurvature one can be unified in a single stepconsidering directly a spherical cap. Fig.1shows, in a meridian plane, a sketch of the topo-graphic surface and the spherical cap around astation S. See LaFehr (1991b) for the algorithmsto calculate the attraction of a spherical cap.

2.2.Terrain correction

The procedure to correct gravimetric datafor the topographic relief around the stations isthe processing step more susceptible to intro-duce errors in the computed anomalies. Thisaccounts for the large number of papers on thissubject published in the last several decades.

Considering, for simplicity, only the com-pletely automated methods, the differenceamong them is the way the topographic surfaceis mathematically represented.

The starting point is a digital representa-tion of the topographic surface. The digital earthmodels (DEM or DTM) represent the surface atthe nodes of a regular grid through elevation ormean values. The used gridded data come fromdatabases, when available, or are specially con-structed for a study area.

Considering the inverse square distancelaw for gravitational attraction, an increasingaccuracy in the surface approximation is neces-sary, the distance from the station decreasing. Totake into account this requirement, moving outfrom the station the area is generally dividedinto different zones in which different strategiesare adopted for the correction. Thus, an inner ornear zone and an outer or distant zone are gen-erally considered. In some cases one or moreintermediate zones are introduced between theprevious ones [Blais and Ferland, 1984; Ma andWatts, 1994].

Fundamentally, for the inner zone, thegridded data are fitted with a mathematical sur-face – a set of Gaussian functions [Herrera-Barrientos et al. 1991], a multiquadric equation[Krohn, 1976], a triangle-based surface[Cogbill, 1990] – and interpolated values com-puted at a more dense grid points distribution[Blais and Ferland, 1984] or mean values calcu-lated in circular sectors similar to the Hammer’schart [Herrera-Barrientos and Fernandez, 1991].Once this is done, corrections are calculatedusing different approximations of the surface:flat-top prisms [Hammer, 1939], inclined-topcircular prisms [Olivier and Simard, 1981], dip-ping triangular elements [Zhou et al., 1990].

While for the distant zones a regular

structure of the data could be justified by datastorage needs in the framework of databasescovering large areas (at a regional, state or glob-al scale), the complex procedures adopted torepresent the topography in the area nearest astation seem to us unjustified for the nowadayscomputer memory and power capabilities.

Our reasoning is the following. The orig-inal digital terrain data are produced from mapsor aerial photographs by manual digitizing,semi-automatic line following or automaticraster scanning or provided by digital satelliteimageries. Whatever be the method to generatesurfaces from the data, the accuracy of thereconstruction cannot be better than the originaldata. Any other processing step applied to thedata is likely to misrepresent the terrain modeland to introduce errors in the terrain correction.Besides, with reference to the application of thesurface modelling to gravity data correction, wemust consider that hardly the position of thegravity stations coincide with the nodes of aDTM, requiring a supplemental approach tointroduce them into computation [Ma andWatts,1994]. Hence, a method directly using the irreg-ular distribution of the original data is, to ouropinion, more suitable to perform, at the maxi-mum accuracy contained into the elevation dataand in a simpler way, the modelling of thetopography.

Triangulated Irregular Networks (TINs)represent a data structure that directly relies ondata. Terrain models are consequently represent-ed by triangular faceted surfaces. Triangulatedsurface models are the most widely used inmany different application domains, includingcomputer graphics, geographic data processing,computer vision and computer aided design.The advantage of this method is the possibilityof including surface features and on the simplic-ity of the topological structure. In the frame-work of digital terrain modelling, triangle-basedmodels allow for the variable resolution con-nected with different topography behaviours.Thus, TINs succeed in representing a surface ata certain level of accuracy using a smalleramount of data.

Among the methods for triangulating aset of irregularly spaced points in 2-D and 3-Dspaces, the Delaunay one satisfies some opti-mality criteria. In particular, the method gener-ates triangles that are as much equiangular aspossible [Lawson, 1977; Preparata and Shamos,1985], thus avoiding thin and elongated triangu-lar facets, it minimizes the maximum circumcir-cle [D’Azavedo and Simpson, 1989] and themaximum contained circle [Rajan, 1994] ( thelast two conditions can be equivalently

46


expressed as follows: considering any fourpoints, such points do not belong to the samecircle).

Using the triangulation method, the ter-rain correction can be carried out through trian-gular prisms [see, for example Zhou et al. 1990].

3. Terrain correction method

Fig. 2 shows the scheme adopted for theterrain correction. The inner zone is defined asthe 5 km2 square region centred at each station.In this zone the height field is approximatedfrom digitized 1:25000 topographic mapsthrough Delaunay triangulations.

There are many Delaunay triangulationsalgorithms with different computer speed andmemory requirements [see, for example: Barberet al. 1996; Bourke, 1989; Renka, 1984;Shewchuk, 1996, 1997, 2002]. Among thefreely available computer routines we have pre-ferred the Triangle program by Shewchuk(1996) for its efficiency and computationalspeed. Fig. 3 shows an example of digitizedpoints and the resulting triangulations. Fordrawing clarity it is represented only the 1 km2

area surrounding the station.In the distant zone, between the inner one

and the circular, 170 km radius, outer edge thetopography is approximated by 7.5”x 10” grid-ded data representing mean elevation values.The gravity effect of the topography both in theinner and outer zones is evaluated consideringtriangular polyhedra. The relationships forhomogeneous polyhedral bodies by Okabe(1979) are used. The faces of the polyhedra are the triangular facets in the inner zone and three

neighbouring grid values in the outer zone, onthe topographic surface, and their geocentricprojections on the reference sphere, respective-ly. To apply the Okabe’s formulae transforma-tions from ellipsoidal to plane coordinates areneeded. In particular, from figure 1, assumingthe local sphere at each station to approximatethe ellipsoid, a station S, a generic point P on thesurface and its projection on the sphere U, haveellipsoidal coordinates S(r0,ϕ0,λ0), P(r,ϕ, λ) andU(r0,ϕ,λ), respectively; where OT=OV=R0 isthe mean earth radius, TS=h0 and VP=h are theheights above the mean sea level of the stationand the point, respectively, r0=R0+h0 andr=R0+h. ϕ0 and ϕ are the ellipsoidal latitudesand λ0 and λ the ellipsoidal longitudes of thetwo points, respectively. For simplicity, Fig. 1shows the points S and P in the same meridianplane.

Considering a Cartesian coordinate sys-tem with origin in S, the plane XY tangent to the


47

Figure 2. Definition of the inner and outer zonefor topographic correction and grid spacingused to represent the topography in the outerzone.

Figure 3.Method used to approximate the topo-graphic surface in the inner zone; a) example ofdigitized elevation points around staz1 and b)resulting Delaunay triangulations.

local sphere in S, X axis northward, Y axis east-ward and Z axis toward the centre of the sphere,the coordinates of the points P and U become:

4. Application to Etna data

The method previously described wasused for reprocessing the gravity data surveyedfor the study of the Mt. Etna volcano [Loddo etal. 1989]. The Bouguer anomaly shown in thecited paper was obtained performing the topo-graphic correction with a manual chart methodover a distance of 28 km from each station andusing the 1930 International Gravity Formula.For the new processing step the original datawere standardized using the IGSN71 system[Morelli et al., 1974] and the Italian First OrderGravity Network [Marson and Morelli, 1978].Besides, the Geodetic Reference System 1980[Moritz, 1984] was applied and the data correct-ed for the spherical cap and the topography outto 166.7 km. In order to numerically comparethe old and the new processing procedures, theinfinite slab and the old topographic correctionswere applied to the transformed data.

Fig. 4 shows the approximate area over

which the topographic corrections of all theEtna data were carried out. The Sicily mountainchains are completely contained in the areatogether with a large part of the calabrianApennines. Besides, large sea-covered surfacesare present. For these last zones, the 7.5”x10”mean elevation gridded data were computed bydigitizing the bathymetric maps. The obtaineddatabase was connected to the existing one forinland zones.

Considering the elevation values of theEtna stations, the maximum difference betweenthe infinite slab and the spherical cap amountsto about 2-3 mGal. On the contrary, differenceslarger than 10 mGal result for the effect of thetopography as figs. 5 and 6 indicate. The mapsare constructed using a mass density of 2650kg/m3.

The differences between the completeBouguer corrections obtained with the new pro-cessing method and the older one are mapped infig. 7. As it was expected, the differencesincrease with the elevation resulting in substan-tial changes in the Bouguer anomalies.

To our knowledge, there are few papersthat take into account the topographic effect outto 170 km [Krohn, 1976; Banerjee, 1998] andjust one that shows, with a field example, thedifferent contributions to the corrections by thetopography in the first 20 km range and by therest of the 170 km range area [Banerjee, 1998].The survey presented in the last cited paper, car-ried out in an area with very large elevationchanges, shows results similar to ours as regardsthe contribution of the elevation changes to theterrain correction. In particular, it was con-

48


Figure 4. Approximate extent of the 167 km radius area considered for the computation of the terraineffect on the Etna data.

firmed the increase with the elevation risingboth of the terrain correction and of the contri-bution to the total terrain correction, by theregion between 20 km and 170 km from thegravity station.


We have presented an automatic methodto perform the complete Bouguer correction ona spherical earth considering the effect of thetopography out to 170 km from the stations. For

the zone nearest the station (the inner zone),where the topography have the largest influenceon the accuracy of the corrections, the earth sur-face is approximated by a TIN structure gener-ated by digitized height values. The method issimple and does not introduce further approxi-mations to the original elevation data.

Our results show that the contribution ofthe topographic correction to Bouguer anom-alies changes with the elevation of the stationresulting in a different effect over short dis-tances. Besides, the influence of the distanttopography cannot be ignored when largechanges in elevation among stations exist. Asstandard the processing steps to obtain theBouguer anomalies should include the effect ofthe earth curvature and of the terrain out to 170km from the station.

Acknowledgments

This research was supported by the NationalInstitute of Geophysics and Volcanologythrough the EPOT project.

References

Banerjee, P., (1998). Gravity measurements and ter-rain corrections using a digital terrain modelin the NW Himalaya. Comput. And Geosci.,24 (10), 1009-1020.

Barber, C.B., Dobkin, D.P. and Huhdanpaa, H.T.,(1966). The quickhull algorithm for convexhulls. ACM Trans. on Math. Software, 22 (4),469-483.

Blais, J.A.R. and Ferland, R., (1984).Optimization in


49

Figure 5. Topographic effect for the Etna sta-tions evaluated with the manual chart methodout to 28.8 km from each station. Contour linesin mGal.

Figure 6. Topographic effect for the same sta-tions of Fig. 5, computed through our process-ing method. Contour lines in mGal.

Figure 7. Difference in mGal between the com-plete Bouguer corrections for the Etna dataresulting from the old and the new processingmethod.

gravimetric terrain corrections. Can. J. EarthSci., 21, 505-515.

Bourke, P., (1989). Efficient triangulation algorithmsuitable for terrain modelling. In: Pan PacificComputer Conference, Beijing, China, 1989.

Bullard, E.C., (1936). Gravity measurements in EastAfrica. Phil. Trans. Roy. Soc. London, 235,486-497.

Chapin, D.A., (1996). The theory of the Bouguergravity anomaly : a tutorial. The LeadingEdge, 15, 361-363.

Cogbill, A.H., (1990). Gravity terrain correctionscalculated using digital elevations models.Geophysics, 55 (1), 102-106.

D’Azavedo, E.F. and Simpson, R.B., (1989). Onoptimal interpolation triangle incidences.SIAM Journal on Scientific and StatisticComputing, 20 (6), 1063-1075.

Hammer, S., (1939). Terrain corrections for gravi-metric stations. Geophysics, 4, 184-194.

Herrera-Barrientos, J. and Fernandez, R., (1991).Gravity terrain corrections using Gaussiansurfaces. Geophysics, 56 (5), 724-730.

Krohn, D.H., (1976). Gravity terrain correctionsusing multiquadric equations. Geophysics, 41(2), 266-275.

LaFehr, T.R., (1991). An exact solution for the grav-ity curvature (Bullard B) correction.Geophysics, 56 (8), 1179-1184.

LaFehr, T.R., (1991). Standardization in gravityreduction. Geophysics, 56 (8), 1170-1178.

LaFehr, T.R., (1998). On Talwani’s “Errors in thetotal Bouguer reduction”. Geophysics, 63 (4),1131-1136.

Lawson, C.L., (1977). Software for C1 surface inter-polation. In: Mathematical Software III (J.R.Rice, ed.), pp. 161-194. Academic Press Inc.,New York.

Loddo, M., Patella, D., Quarto, R., Ruina, G.,Tramacere, A. and Zito, G., (1989).Application of gravity and deep dipole geo-electrics in the volcanic area of Mt. Etna(Sicily). J. Volcanol. Geotherm. Res., 39, 17-39.

Ma, X.Q. andWatts, D.R., (1994). Terrain correctionprogram for regional gravity surveys.Comput. And Geosci., 20 (6), 961-972.

Marson, I. and Morelli, C., (1978). First ordergravity net in Italy. 8th Meeting of the inter-national gravity commission, Paris, 12-16Sept. 1978, 660-689.

Morelli, C., Gantar, C., Honkasalo, T., McConnel,R.K., Tanner, I.G., Szabo, B., Uotila, U. andWhalen, C.T., (1974). The internationalgravity standardization net 1971 (IGNS71).International Association of Geodesy, IUGG,Spec. Publ. n° 4.

Moritz, H., (1984). Geodetic Reference System 1980.Bullettin Géodésique, 58, 388-398.

Okabe, M., (1979). Analytical expressions for gravi-ty anomalies due to homogeneous polyhedralbodies and translations into magnetic anom-alies. Geophysics, 44 (4), 730-741.

Olivier, R.J. and Simard, R.G., (1981). Improvementof the conic prism model for terrain correc-tion in rugged topography. Geophysics, 46(7), 1054-1056.

Preparata, F.P. and Shamos, M.I, (1985).Computational geometry: an introduction.

Springer Verlag, Berlin.Rajan, V.T., (1994). Optimality of the Delaunay tri-

angulation in Rd. Discrete and ComputationalGeometry, 12, 189-202.

Renka, R.J., (1984). Algorithm 624, Triangulationand interpolation at arbitrary points in aplane. ACM Trans. On Math. Software, 10,440-442.

Shewchuk, J., (1996). Triangle: Engineering a 2Dquality mesh generator and Delaunay trian-gulator. In: First Workshop on AppliedComputational Geometry, May 1996,Philadelphia, Pennsylvania, pp. 124-133.

Shewchuk, J., (1997). Delaunay refinement meshgeneration. Ph. D. Thesis, Technical ReportCMU-CS-97-137, School of ComputerScience, Carnegie Mellon University,Pittsburg, Pennsylvania, 18 May 1997.

Shewchuk, J., (2002). Delaunay refinement algo-rithms for triangular mesh generation.Computational Geometry: Theory andApplications, 22 (1-3), 21-74.

Talwani, M., (1998). Errors in the total Bouguerreduction. Geophysics, 63 (4), 1125-1130.

Zhou, X., Zhong, B. and Li, X., (1990). Gravimetricterrain corrections by triangular-elementmethod. Geophysics, 55 (2), 232-238.

50



51

Data Concerning MagneticSusceptibility Changes in Powdered

Rock Induced by Temperature.Results from Mount Etna and Ustica

Island Specimens

Antimo Angelino1, Ciro Del Negro2,Alberto Incoronato3, Rosalba Napoli2 and

Pasquale Tiano3 *

1 CNR-IAMC Istituto per l’Ambiente Marino Costiero,Napoli, Italy

2 Istituto Nazionale di Geofisica e Vulcanologia, Sezionedi Catania, Italy

3 Dipartimento di Scienze della Terra, Università diNapoli, Italy

AbstractThe variation of the magnetic susceptibil-

ity with temperature of volcanic samples col-lected at Etna, and Ustica Island have beeninvestigated and possible explanations of themagneto-mineralogical changes have been sug-gested. The magnetic susceptibilities of pow-dered specimens have been measured duringheating in air, from room temperature up to 700°C, and subsequent cooling. The continuoussusceptibility curves (k-T curves) are generallynot reversible and appear to be sensitive to themagnetic mineralogy. Although, two maingroups of behaviours have been distinguished(A and B groups), it is shown that very signifi-cant variations of the magnetic susceptibilitiescan occur even as a result of a temperatureincreasing of some hundred degrees aboveambient temperature.

Keywords Etna – Ustica - magnetic suscepti-bility - temperature

1. Introduction, apparatus and measure-ments

Generally low field magnetic susceptibil-ity, k, measured at room temperature is used ininterpreting magnetic anomalies. However it isknown that k can change with temperature sig-nificantly. Samples from Mount Etna and UsticaIsland have been collected (Fig.1) in order toprovide information on these changes.Variations in air of k with temperature of pow-dered specimens were measured, in theLaboratorio di Paleomagnetismo e Magnetismodelle Rocce of Dipartimento di Scienze della

Terra of Università degli Studi di Napoli“Federico II”, using a Bartington apparatus (Fig.2) consisting in:1) Magnetic susceptibility meter MS2. It works

on the principle of a.c. induction.2) Water jacketed sensor type MS2W30. This

has a 30 mm internal diameter sample cavityand the passage of water within the probescreens it from extremes of temperaturewhich may be present within the sample cav-ity.

3) Furnace type MS2WF. This comprises a non-inductively wound platinum wire furnacewith a maximum operating temperature of900 °C and a maximum sample capacity of15 mm diameter.

4) Power supply type MS2WFP. This unit sup-plies electrical power to the furnace and pro-vides either preset thermostatic control oftemperature or slowly varying linear increas-ing or decreasing of temperature.

The heating or cooling cycle is selected on thefront panel of the power supply unit MS2WFP.The initial, maximum and final temperature val-ues, the rate of heating and cooling, the meas-urement steps are selected via software. TheMS2WFP unit is computer controlled and con-nected to both the heating unit MS2WF and tothe susceptibility meter unit MS2. The latter isconnected to the water cooled MS2W30 sensorwithin which the specimen is located. The driftis corrected by taking two background measure-ments at the beginning and at the end of process.

All the powdered specimens, 5 cm3

each, were heated up to 700 °C, starting from35 °C, and cooled down at a constant rate of 8°C/min and the measurements were carried outwith 5 °C step.

2. Discussion

The variations of k with temperature, nor-malised with reference to the value measured atthe start of the heating, kstart, are plotted in fig-ures 3 and 4. The value of k for each untreatedspecimen of standard size (cylinder: 2.54 cm,diameter, x 2.20 cm, height) are also indicated.The variations of k with temperature can begrouped into 2 main groups calledA (Fig. 3) andB (Fig. 4) respectively.

The behaviour of type A specimens (Fig.3) during heating is generally similar to thatexhibited during cooling. However, the value ofthe magnetic susceptibility at the end of cooling,kend, is much lower than the value measured at

* To whom correspondence should be addressed, e-mail: [email protected]

the start of the heating, kstart. The overall behav-iour during the entire heating-cooling processsuggests that the dominant magnetic carrier ismagnetite and/or Ti-poor titanomagnetite[Goguitchaichvili et al., 2001; Orlicky, 1990;Tarling, 1983].

The lower value of k observed during thecooling can be the result of partial transforma-tion occurred above 500 °C of the main magne-to-mineralogical phase into a new phase charac-terised by an higher Curie temperature, TC, andlower k, such as hematite [Dunlop and Özdemir,1997; Tarling, 1983; France et al., 1999].Differences of behaviour exhibited by A typespecimens during heating can related to differ-

ent magnetic grain sizes. In fact, specimenscharacterized by predominant SD magnetic car-rier exhibit variations of the k values that inapproaching the TC can be 35 to 40 % higherthan kstart. In fact, according to Thompson andOldfield [1986] MD carrier are characterized bya much smaller increasing of k values.

The behaviour of type B specimens(Fig.4) during heating is generally characterisedby increasing of kstart of 40 to 50% in the range100-200 °C.

Generally a rapid and significant decreas-ing of kstar, even 70 to 80%, follows in therange 250 to 300 °C. Such low values areretained until the end of treatment although few

52


Figure 1. Sites location maps of Ustica Island and Mount Etna.

Figure 2. Bartington apparatus for measuring variation of k during heating and cooling (Redrawnfrom Bartington manual).


53

Figure 3. Normalised magnetic susceptibility (k/kstart) versus temperature (°C) of Etna and Usticaspecimens (Group A, see text). The value of k of each untreated specimen of standard size (see text) isalso indicated. Thick (thin lines) indicate heating (cooling) curves. Etna specimens labels: LF = lavaflows, DK = dykes, A =Alc.antara, M = Moio/Motta S.A., D = Mt. Dolce, PP = Provenzana-Pernicanafracture system. Ustica specimens labels: C. Site location in Fig.1.

specimens exhibit further increasing anddecreasing (however much smaller than the pre-vious ones) between 400 and 500 °C. Thebehaviour of k during the cooling is very similarfor almost all the specimens. In fact, k increasesbetween 600 and 500 °C and keeps either con-stant or lowers very little as cooling proceeds. Infew cases, the sharp increasing during the early

stages of the cooling is followed by a smallerone that ends at about 250-200 °C after which itdecreases. The observed behaviours can beascribed to Ti-rich titanomagnetite, charac-terised by TC of about 250 °C, that at about 400°C changes into maghemite, possibly [Özdemir,1987; King, 2000]. In many cases it is evidentthat further changes, into hematite, occur at

54


Figure 4. Normalised magnetic susceptibility (k/kstart) versus temperature (°C) of Etna and Usticaspecimens (Group B, see text). Specimens labels as in Fig. 3.

about 450 °C [Özdemir, 1987; King, 2000]. Thepresence of hematite is clearly detected from theinitial path of the cooling curves in all cases.However, the steep increasing of the k valuebetween 550 and 500 °C can be clearly be asso-ciated to Ti-poor titanomagnetites [Thompsonand Oldfield, 1986; Orlicky, 1990]. Howeverthese titanomagnetites could only form duringthe very late stages of the heating. The bell typeshape exhibited around 300 °C can be ascribedto MD Ti-rich titanomagnetites [Thompson andOldfield, 1986; Shcherbakova and Shcherbakov,2000; Day et al., 1977; Radhakrishnamurty etal., 1977]

3. Conclusion

The study of the variations of k with tem-perature carried out on Ustica Island and MountEtna specimens has allowed to highlight 2 maingroups: A and B. As far as type A specimens areconcerned, their k values during heating aremuch higher than those during the cooling. Onthe contrary, B type specimens show k valuesduring heating that are lower than those duringthe cooling, except the 200-250 °C interval wherethe Ti-poor titanomagnetite contribution prevails.It must be stressed that during the heating k val-ues increase significantly. In B type specimenssuch increasing occurs up to 200-300 °C while inA type specimens they last even up to 500 °C.The magnitude of these variations may be ofinterest in interpreting magnetic anomalies involcanic areas, particularly when the modellingeffects active volcanic areas.

Acknowledgements

This work was developed in the frame of theGeomagnetism Laboratory of INGV-CT.

References

Day, R., Fuller M. and Schmidt V.A., (1977).Hysteresis properties of titanomagnetites:grain size and compositional dependence.Phys. Earth. Plan. Int., 13, 260-267.

Dunlop, D.J. and Özdemir Ö., (1997). RockMagnetism: Fundamentals and frontiers.Cambridge University Press. pp. 573.

France D., Hu Y., Snowball I, Rolph T., Oldfield F.and Walden, J., (1999) Additional rock mag-netic measurements. In: EnviromentalMagnetism: a practical guide. (J. Walden, F.Oldfield and J.P. Smith, eds.), QuaternaryResearch Association, Technical Guide, No.6., London, 197-211.

Goguitchaichvili, A., Morales J., Urrutia-FucugauchiJ. and Soler A.M., (2001). On the use of con-tinuous thermomagnetic curves in paleomag-netism: a cautionary note. Earth Planet. Sc.Lett., 333, 699-704.

King, J. G. and Williams W., (2000). Low-tempera-ture magnetic properties of magnetite. J.Geophys. Res., 105, N. B7, 16,427-16,436.

Orlicky, O., (1990). Detection of magnetic carriersin rocks: results of susceptibility changes inpowdered rock samples induced by tempera-ture. Phys. Earth. Plan. Int., 63, 66-70.

Özdemir, Ö., (1987). Inversion of titanomaghemites.Phys. Earth. Plan. Int., 46, 184-196.

Radhakrishnamurty, C., Likhite S.D. andSahasrabudhe P.W., (1977). Nature of magnet-ic grains and their effect on the remanentmagnetization of basalts. Phys. Earth. Plan.Int., 13, 289-300.

Shcherbakova, V.V. and Shcherbakov V.P., (2000).Properties of partial thermoremanent magne-tization in pseudosingle domain and multido-main magnetite grains. J. Geophys. Res., 105,N. B1, 767-781.

Tarling, D.H., (1983). Palaeomagnetism – Londonand New York, Chapmann & Hall. pp 379.

Thompson R. and Oldfield F., (1986). EnviromentalMagnetism – London, Boston and Sydney,Allen & Unwin. pp 227.


55

Exploring the Time Dynamics ofGeoelectrical and Geomagnetical Signals

Marianna Balasco, Gerardo Colangelo,Vincenzo Lapenna and Luciano Telesca

Istituto di Metodologie per l’Analisi Ambientale del CNR,Tito Scalo (PZ)

AbstractFractal tools have been used to investi-

gate the time dynamics of hourly geomagneticand geoelectrical data, recorded during the year2000 and 2001 respectively, by a monitoringnetwork located in the seismic area of Irpiniaand in the volcanic area of Etna, both in south-ern Italy. Scaling behaviour has been revealedby means of different statistics: the LombPeriodogram method, the Detrended FluctuationAnalysis and the Higuchi analysis. The valuesof the scaling exponents estimated by means ofthese methods indicate that the temporal fluctu-ations of the geoelectrical signals are not typicalof purely random stochastic processes (i.e.white noise), but evidence the presence of long-range correlations.

Keywords electromagnetic time series - fractalmethods

1. Introduction

The dynamics underlying tectonicprocesses could be directly revealed by theinvestigation of the temporal fluctuations ofself-potential signals, which may be useful tomonitor and understand many seemingly com-plex phenomena linked to seismic and volcanicactivity [Park, 1997; Johnston, 1997]. Self-potential field variability may be induced bystress and fluid flow field variability [Scholz,1990], therefore, the analysis of these inducedfluctuations could contribute to gain informa-tion on the governing geophysical mechanismscharacterizing normal as well as intense vol-cano-seismic activity. In this context, in thiswork we investigate the dynamical properties ofgeoelectrical signals, as they can be detectedfrom observational time series.

Self-potential signals are the result of theinteraction among very heterogeneous and notwell known mechanisms which can be influ-enced by the particular structure of the moni-tored zone [Patella et al., 1997]. This means thatlocal features can be mixed to the general onesso increasing the difficulty of rightly character-

ising and interpreting the signal time variations.In addition, as occurs for many environmentalsignals, observational data are made even moreerratic by the presence of anthropic phenomena:electrical signals coming from anthropic sourcesmay be added, e.g., to the natural signal so mak-ing harder its dynamical characterization[Cuomo et al., 1998].

In a previous paper Cuomo et al. [1998]analyzed the geoelectrical daily means in orderto give information about the statistical featuresof the geoelectrical background noise and theinner dynamics of geophysical processes pro-ducing the electrical phenomena observed onearth surface in seismic areas. They discussedthe statistical analysis of dynamical systemsbased on the estimation of their degree of pre-dictability, distinguishing randomness fromchaos and providing a parsimonious representa-tion in terms of autoregressive models of obser-vations, by means of the only information com-ing from the time series itself.

In the study of seemingly complex phe-nomena, as those generating self-potential sig-nals, methodologies able to capture the dynami-cal peculiarities in observational time series areparticularly useful tools to obtain informationon the features and on the causes of signal timevariability. In particular, fractal techniques,developed to extract qualitative and quantitativeinformation from time series, have been appliedrecently to the study of a large variety of irregu-lar, erratic signals and by now have demonstrat-ed to be very useful to reveal deep dynamicalfeatures. Cuomo et al. [2001] detected scalingbehaviour in the power spectra of geoelectricaltime series, revealing the antipersistent charac-ter of the self-potential fluctuations. Telesca etal. [2001] proposed a new approach to investi-gate correlation between geoelectrical signalsand earthquakes, analyzing the time variationsof the fractal parameters, characterizing theirdynamics. Balasco et al. [2001] found that self-potential measurements seem to be featured bylong-range correlations with scaling exponentswhich indicate that the underlying geophysicalprocess is characterized by stabilizing mecah-nisms.

In the frame of the EPOT project the maincontribute of this Research Unit concerned thedevelopment of innovative and robust methodsto explore the time dynamics of geoelectricaltime series measured in seismic areas. Firstly,techniques to denoise time series have beendeveloped, and software packages to removeclimatic and cultural noises from geoelectricaltime series have been designed. In particular,great attention has been devoted to the analysis


57

of the influence of data missing, that is a typicalsituation in the framework of geophysical mon-itoring activities. To overcome the problemrelated to the application of conventional FFTanalysis, we applied the Lomb PeriodogramMethod. Fractal techniques have been appliedfor searching scaling invariance laws in the timeseries.

The algorithms have been designed andvalidated using the data-base of geophysicaltime series available at Geophysical Lab ofIMAA, in a second step these techniques havebeen successfully applied to extract quantitativedynamics from time series recorded by means ofthe magnetic network of Etna volcano.

2. Methods

To quantitatively characterize geoelectri-cal signals, we need to use techniques able toextract robust features hidden in these complexfluctuations.

Various methods for analyzing the corre-lation properties of a time series are available,and many techniques have been developed todetect and quantify fractal features in experi-mental and observational data.

The spectral analysis represents the stan-dard method to evaluate the presence of purelyrandom fluctuations in time series. Signals,whose samples are uncorrelated among them,are characterized by a flat power spectrum(white noise); while signals, whose samples arelong-range correlated, are characterized by apower spectrum decreasing with the frequency,S(f)∝ f-α, where α indicates the degree of corre-lation (coloured noise). For unevenly sampledtime-series the power spectrum can be calculat-ed by means of the Lomb Periodogram method[Lomb, 1976]. Denoting as xn the datum meas-ured at instant tn, the Lomb Periodogram isdefined by the following formula:

(1)

where ω=2πf is the angular frequency and τ isgiven by

(2)

The slope of the line fitting the log-logplot of the power spectrum by a least squaremethod in the linear frequency range gives the

estimate of the spectral index α.A more stable estimate of the spectral

exponent can be performed by the calculation ofthe fractal dimension of the signal using theHiguchi method [Higuchi, 1988; Higuchi,1990]. In the literature, many papers have beendevoted to find methods capable of giving stableestimations of the power-law spectral index.Burlaga and Klein [1986] presented a method tocalculate stable values of the fractal dimensionD of large-scale fluctuations of the interplane-tary magnetic field; the relationship between thefractal dimension D and the spectral exponent αis given by Berry’s expression D=(5-α)/2[Berry, 1979], for 1<α<3. They defined thelength LBK(τ) of the B(t) curve as

(3)

where

denotes the average value of B(t) between t=tkand t=tk+τ. This length is a function of τ, and forstatistically self-affine curves, the length isexpressed as LBK(τ)∝τ -D. Using this relation,the value of D can be estimated, as the slope ofthe log-log plot of the length LBK(τ) vs. the timeinterval τ. Then, using Berry’s, the spectralexponent estimation can be estimated.

Another method which also gives a stablevalue of the fractal dimension has been present-ed by Berry [1979]. A new time-series is con-structed from the given time series X(i), (i=1, 2,...., N),

(4)where [ ] denotes Gauss’ notation. The length ofthe curve is defined as

(5)

The average value <L(t)> over t sets ofLm(τ) is defined as the length of the curve forthe time interval τ. If <L(τ)> ∝τ -D, within therange τmin ≤ τ ≤ τmax then the curve is fractalwith dimension D in this range. He examinedthe relationship between the fractal dimension Dand the power law index α, by calculating thefractal dimension of the simulated time serieswhich follows a single power-law spectrumdensity. Even in this case, the spectral exponentestimation could be carried out using Berry’sexpression.

Recently, the method of Detrended58


Fluctuation Analysis (DFA) has been developedto reveal long-range correlation structures inobservational time series. This method was pro-posed by Peng et al. [1995], and it avoids spuri-ous detection of correlations that are artifacts ofnonstationarity, that often affects experimentaldata. Such trends have to be well distinguishedfrom the intrinsic fluctuations of the system inorder to find the correct scaling behaviour of thefluctuations. Very often we do not know the rea-sons for underlying trends in collected data andwe do not know the scales of underlying trends.DFA is a well-established method for determin-ing the scaling behaviour of data in the presenceof possible trends without knowing their originand shape [Kantelhart et al., 2001]. The method-ology operates on the time series x(i), wherei=1,2,...,N and N is the length of the series. Withxave we indicate the average value

(6)

The signal is first integrated

(7)

Next, the integrated time series is dividedinto boxes of equal length n. In each box a least-squares line is fit to the data, representing thetrend in that box. The y coordinate of thestraight line segments is denoted by yn(k). Nextwe detrend the integrated time series y(k) bysubtracting the local trend yn(k) in each box.The root-mean-square fluctuation of this inte-grated and detrended time series is calculated by

(8)

Repeating this calculation over all boxsizes n, we obtain a relationship between F(n),that represents the average fluctuation as a func-tion of box size, and the box size n. If F(n)behaves as a power-law function of n, data pres-ent scaling:

F(n)∝ nd. (9)

Under these conditions the fluctuationscan be described by the scaling coefficient d,representing the slope of the line fitting log F(n)to log n. The values of exponent d may representa range of processes. For example d=0.5 meansthat the signal samples are uncorrelated or short-range-correlated variable. An exponent d≠0.5 ina certain range of scales n suggests the existenceof long-range correlations. If d=1.0 the temporalfluctuations are of flicker-noise type; if d=1.5the temporal fluctuations are of Brownian type.The DFA scaling exponent d and the spectralexponent α are related to each other asdescribed in Buldirev et al. [1994] and Havlin etal. [1988] by the following equation:

(10)

3. Data analysis and results

Fig. 1 shows a typical power spectrum ofa geoelectrical signals, calculated by means ofthe Lomb Periodogram method. The time seriesshows a very clear scale-invariance, denoted bythe power-law behaviour of the spectrum versusfrequency, with the scaling exponent α indicat-ing that the temporal fluctuations of the signal


59

Figure 1. Lomb Periodogram of one geoelectrical time series measured in Giuliano station (southernItaly) during 2001.

are not purely random (flat spectrum), but pres-ent long-range correlations.

Fig. 2 shows the results of the Higuchianalysis performed on one of the four geoelec-trical time series measured by Tito station. Theplot evidence scaling behaviour with scalingexponent D approximately 1.8. A divergencefrom the linear behaviour is present at largertimescales; this could be due to edge effect, thatgives rise to an increase of the <L(τ)> at thosescales.

Fig. 3 shows the results of the DetrendedFluctuation Analysis performed on the geoelec-trical time series measured by Marsico station.The scaling behaviour is apparent with scalingexponent d approximately 1.3.

We analysed the time dynamics of one

time series of geomagnetic data measured dur-ing 2000 by one station installed on the Etna(southern Italy). Fig. 4 shows the hourly signalvariation.

Fig. 5 shows the Lomb periodogram: it isevident the scaling behaviour, characterized bya flicker-noise-type dynamics of the temporalfluctuations, indicated by the unitary value ofthe spectral exponent α. This 1/f-like behaviouris mainly due to solar-terrestrial interaction,which is the external origin for the fluctuationsof the magnetic field until periods of monthlyorder.

Fig. 6 shows the results obtained applyingthe Detrended Fluctuation Analysis to the CSRgeomagnetic signal; it is clear the appearance oftwo different scaling regimes, with different val-

60


Figure 2. Higuchi analysis of one of the geoelectrical time series measured in Tito station (southernItaly) during 2001.

Figure 3. Detrended Fluctuation Analysis of the geoelectrical time series measured in Marsico station(southern Italy) during 2001.


61

Figure 4. Hourly time variability of geomagnetic signal measured during 2000 at the station CSRlocated on Mount Etna (southern Italy).

Figure 5. Lomb Periodogram of the geomagnetic signal measured by station CSR.

Figure 6. Detrended Fluctuation Analysis performed on the CSR geomagnetic signal.

ues for the scaling exponents, with a crossoverlocated approximately at 24 hours. Thiscrossover effect indicates that different dynam-ics govern the same geophysical phenomenon atsmall and long timescales. The crossover can beassociate to the diurnal variation, induced bypressure and temperature.

4. Conclusions

We have shown that the time dynamics ofthe geoelectrical and geomagnetic time seriesmeasured in a seismic and volcanic active areasof Southern Italy are not realizations of a purelyrandom stochastic process. The power spectrahave the power-law form typical of colored-noise with the spectral exponent measuring thedegree of correlations in the signals, this indi-cating the presence of memory effects in thegeophysical system generating geoelectrical andgeomagnetic signals. The spectral results areconfirmed by applying fractal methods of analy-sis. The Higuchi analysis has revealed that thesignals present typical features of fractal curveswith scaling exponents D consistent with thespectral indices. The DFA has shown the pres-ence of long-range correlations in the data, char-acterizing the temporal fluctuations of the sig-nals as persistent.

Acknowledgements

The authors are grateful to Ciro Del Negro forproviding us of the geomagnetic data. Thisresearch was supported in part by the Epot proj-ect of the GNV.

References

M. Balasco, V. Lapenna and L. Telesca, (2001). 1/fαfluctuations in geoelectrical signals observedin a seismic area of southern Italy.Tectonophysics, 347, 253-268.

Berry, M.V., (1979). Diffractals. J. Phys. A Math.Gentile., 12, 781-792.

Buldyrev, S.V., Goldberger, A.L., Havlin, S., Peng,C.-K. and Stanley, H.E., (1994). Fractals inbiology and medicine. In: Fractals in Science(A. Bunde and S. Havlin S, eds). Springer-Verlag.

Burlaga, L.F. and Klein, L.W., (1986). Fractal struc-ture of the interplanetary magnetic field. J.Geophys. Res., 91, 347-351.

Cuomo, V., Lapenna, V., Macchiato, M., Serio, C.and Telesca, L., (1998). Linear and non lineardynamics in electrical precursory time series:implications with earthquake prediction.Tectonophysics, 287, 279-298.

Cuomo, V., Di Bello, G., Heinecke, J., Lapenna, V.,Martinelli, G., Piscitelli, S. and Telesca, L.,(2001). Investigating the temporal fluctua-tions in geoelectrical and geochemical signalsjointly measured in a seismic area of southernapennine chain (Italy). Annali di Geofisica,44, 179-191.

Havlin, S., Selinger, R., Schwartz, M., Stanley, H.E.and Bunde, A., (1988). Random multiplicativeprocesses and transport in structures withcorrelated spatial disorder. Phys. Rev. Lett.,61, 1438-1441.

Higuchi, T., (1988). Approach to an irregular timeseries on the basis of the fractal theory.Physica D, 31, 277-283.

Higuchi, T., (1990). Relationship between the fractaldimension and the power-law index for a timeseries: a numerical investigation. Physica D,46, 254-264.

Kantelhardt, J.W., Koscienly-Bunde, E., Rego,H.H.A., Havlin, S. and Bunde, A., (2001).Detecting long-range correlations withdetrended fluctuation analysis. Physica A,295, 441-454.

Johnston, M.J.S., (1997). Review of electric andmagnetic fields accompanying seismic andvolcanic activity. Survey in Geophysics, 18,441-475.

Lomb, N.R., (1976). Least-squares frequency analy-sis of unequally spaced data. Astrophyisicsand Space Science, 39, 447-462.

Park, S.K., (1997). Monitoring resistivity change inParkfield, California: 1988-1995. J. Geophys.Res., 102, 24545-24559.

Patella, D., Tramacere, A. and Di Maio, R., (1997).Modelling earth current precursors in earth-quake prediction. Annali di Geofisica, 40,495-517.

Peng, C.-K., Havlin, S., Stanley, H.E. andGoldberger, A.L., (1995). Quantification ofscaling exponents and crossover phenomenain nonstationary heartbeat time series.CHAOS, 5, 82-87.

Scholz, C.H., (1990). The mechanics of earthquakesand faulting. Cambridge University Press, 439pp.

Telesca, L., Cuomo, V., Lapenna, V. and Macchiato,M., (2001). A new approach to investigate thecorrelation between geoelectrical time fluctu-ations and earthquakes in a seismic area ofsouthern Italy. Geophys. Res. Lett., 28 ,4375-4378.

62


Non-Stationary Analysis of GeomagneticField Variations for the Identification

and Characterisation ofVolcanomagnetic and Seismomagnetic

Events

Maurizio Fedi and Mauro La Manna

Dipartimento di Scienze Della Terra, Università di Napoli

AbstractSome geomagnetic variations, termed

volcanomagnetic (VM) and/or seismomagnetic(SM) effects, are linked to volcanic and seismicactivity. Here, we analyse real geomagnetic timeseries to detect the VM and/or SM effectscaused by historical volcanic and/or seismicevents. We apply to geomagnetic signals twosignal processing techniques, called CWTSA(Continuous Wavelet Transform SingularityAnalysis) and TVANS (Time-Variant Analysisof Non Stationary Signals). Both techniques arevery effective in identifying the geomagneticvariations at the time instants linked to volcanicand/or seismic activity. The main feature of themethods is that they work inherently in a localsense, i. e. they do not need time averaging andare not global estimates on time windows, likeFourier spectral techniques. But CWTSA mayalso work in a global sense, which gives in prac-tice similar results to conventional spectralanalysis. We tested these methodologies on seis-momagnetic real data to which we added fivetheoretical singularities in order to simulate geo-magnetic anomalies due to a piezomagneticeffect from a seismomagnetic model of a faultrupture. CWTSA and TVANS were then appliedto real geomagnetic time sequences recorded inNorth Palm Springs during the seismic event of8 July 1986. The results evidence a good agree-ment between detected and known event.

Key words non-stationary analysis – geomag-netic anomalies - North Palm Springs

1. Introduction

It is known that volcanic activity and/orseismic events can cause time variations of thegeomagnetic field of a few nT. They are termedseismomagnetic (SM) and volcanomagnetic(VM) effects. A clear relation between SM andVM effects and volcanic and seismic events isoften discussed in literature. [Davis et al. 1983,Johnston et al. 1981, Johnston et al. 1987,Johnston 1997, Zlotnicki & Le Mouel. 1988,

Zlotnicki et al. 1998].The SM and VM effects can be caused by

several physical phenomena. The most commonmechanisms are the piezomagnetism and ther-momagnetism, but also other mechanisms playa very important rule to generate geomagneticvariations: electrokinetic effects and resistivityvariations in the rocks. Moreover, other phe-nomena can generate important geomagneticvariations in volcanic area, like the removal ofmagnetized materials [Johnston et al. 1981] andthe interactions between the eruptive shockwaves and Earth’s ionosphere [Zlotnicki 1995].

To understand the possible duration of theSM and VM effects it is very important to knowthe origin of these. It is known that they canaccompany the volcanic and seismic events butalso they can precede and follow these ones.The events with a duration very quick (hours)are associated to piezomagnetic effects, whilethose very intense, in volcanic areas, are usual-ly caused by thermomagnetic effects. Instead,the long period effects are related to electroki-netic effects [Zlotnicki et al. 1998].

Actually, in several volcanic and seismicareas in the world are installed geomagnetic net-works of surveillance that continuously monitorthe geomagnetic field variations (SM and VMeffects). Some of these are located along SanAndreas fault system in California (USA), onthe Mt. S. Helens (USA), on the Merapi(Indonesia), on various volcanoes in Japan, onthe Mt Etna (Italy), etc. Usually, the variationsof the geomagnetic field are studied consideringthe simultaneous difference between the magni-tudes of the geomagnetic fields measured in twoor more stations which are often spaced severalkilometres apart. This primary operation aims atremoving or reducing the slow variations of themain and transient magnetic fields due to theinner and external part of this one respectively.Instead, it is very difficult the reduction of theirregular transitory variations due to anomalousresistivity variations in the rocks. Actually, theusual method applied to reduce of 1-2 nT theirregular transitory variations is based on thehourly and daily mean values of the differenceof the magnetic fields [Del Negro et al.. 1997,Del Negro et al. 2002, Zlotnicki et al. 1998].

Here, we propose two methodologies ofanalysis to study the real geomagnetic timesequences recorded in stations of geomagneticnetworks. The first one is based on the continu-ous wavelet transform (CWT), it allows thedetection singularities of the signal; the secondone, instead, is based on a time-varying adaptivepredictor which provides information about“innovation” events in the time. We do not only


63

consider the difference between more signalsbut we try to analyse the separated signals.

These methodologies were first tested onseismomagnetic real data where we simulatedthe geomagnetic variations adding theoreticalsingularities. Then, just like example, weapplied them to real geomagnetic time seriesrecorded during the North Palm Springs earth-quake. We found a good correlation among his-torical data and the seismic event detected byour signal processing techniques. In the follow-ing sections we describe two techniques ofanalysis which allow the detection of geomag-netic time variations linked to possible volcanicand/or seismic activity.

2. Non-stationary analysis

2.1 CWTSA analysis of non-stationary signalsinstead than conventional Fourier analysis

The first technique, called CWTSA(Continuous Wavelet Transform SingularityAnalysis), is based on the computation of con-tinuous wavelet transform of a signal. The con-tinuous wavelet transform allows for a localizeddecomposition of measured physical quantities(as well logs or field data) into their multiscaleconstituents.

This obviously is more able to studymuch more complexity of geophysical data thanthat we can deal with other techniques, such asFourier analysis. In practice, the scaling behav-iour of a real process carries over the local scal-ing properties of its wavelet coefficients[Gonçalves et al., 1998]. Fourier analysis isinadequate to describe the local behaviour of agiven signal, since it refers to a global and notlocal scale. The only way to make more local aconventional spectral analysis is to partition thesignal and compute the power-law scaling expo-nent local for any sub-interval [Zhou and Thybo1998]. But this has well known disadvantagesand, in any case, it is a not inherently justifiedway to deal with a local problem. For instance,global analysis, like Fourier spectral analysis,gives all the information required to assess thefractal nature of a signal, but does not help tofind and classify the singularities in a localsense.

Wavelet analysis, instead allows an inher-ent locally-posed analysis. Moreover, it may bealso used to perform a global analysis, ifrequired, as for instance using the Legendretransform and the related singularity spectrum.For a comparison between second order statis-tics (Fourier spectra) and wavelet analysis, see

[Fedi 2002]. The continuous wavelet transformof f(t) ∈ L2 ( ) at scale s and time t0 is

(1)

where the kernel function Ψto,s(t) = 1/(s)-1/2Ψ[(t- t0)/s] is the analysing wavelet.

It provides a partition of the signal in thetime-scale plane and it allows the detection ofthe rapid changes (usually steps, jerks, etc) pres-ent into the signal. These quick variations aredefined singularities. Some theorems [Mallatand Hwang, 1992] prove that the wavelet trans-form is an optimal tool to define the local regu-larity of a function. The regularity can be esti-mated by the study of the local maxima of themodulus of the continuous wavelet transform,or as a whole, in a region of the time-scale planecalled cone of influence by the continuouswavelet transform coefficients. The wavelettransform modulus maxima lines (WTMML)are the lines interconnecting the maxima of themodulus of the wavelet transform within thecone of influence and across the time-scaleplane. They emanate from the abscissas wherethe singularities are located. The partitioning ofthe time-scale plain with WTMML provides anefficient measurement procedure of the localHolder exponents associated with singularities,through the slope of the WTMML at smallscales [Mallat and Zhong 1992, Mallat 1998,Hermann 1997].

CWTSA is suitable to detect both isolatedand not-isolated singularities. Obviously, it isknown that real geomagnetic time sequences, asall real data, are very often characterized by not-isolated singularities.

2.2 TVANS analysis of non-stationary signals

The second technique, called TVANS(Time-Variant Analysis of Non-StationarySignals), is based on time-variant analysis and itis based on a predictive analysis. This methoddeals with the general problem of estimation inwhich a sample of each of the several measuredsequences is predicted, in adaptive way, from aweighted linear combination of past samplesfrom other sequences. The mutual correlationbetween the signals can then be estimated.Considering that the phenomenology of theprocess is time-variant, a non-stationaryapproach is more useful to describe the physicalprocesses tied to volcanic and seismic dynam-ics. For this reason it also has been utilised an

64


approach of adaptive type. In the non-stationaryanalysis all the variables are time-varying.Therefore also the weight vector of predictionwill depend on time, as well as the cost function(least squares error). The technique of analysisconsists in a set of adaptive mutual predictorstrained on a sliding time-window that, via a“forgetting” mechanism, tracks the changingstatistical characteristics of the observed timeseries [Haykin, 1996]. The TVANS uses anadaptive algorithm (RLS) that allows the detec-tion of some time intervals where important sta-tistical variations of the signal occur. These vari-ation are termed “non-stationarity zones” andthey could be associated to zones where SM andVM effects occur.

3. Application of the techniques to seismo-magnetic signals from a fault rupture model

The CWTSA and TVANS have been test-ed on two real seismomagnetic signals to whichwe added singularities in order to simulate geo-magnetic anomalies from a seismomagneticmodel of a fault rupture, figure 1 and table I.

The INGV- Catania has developed aMatLab code VMM (Volcano MagneticMonitoring) that allows the building of seismo-magnetic and volcanomagnetic models. Weused this code to build our seismomagneticmodel based on a fault rupture. Then we consid-ered two real seismomagnetic signals at whichwe added five theoretical singularities to simu-late the geomagnetic variations due to a piezo-magnetic effect caused by a fault rupture of a 10km length. The five singularities added arecharcterized by different Holder exponents suchas α1= 0.2, α2= -1, α3= 0, α4= 0.5 and α5= -0.5.For the first sequence (station 1) we added thefive singularities with a 10 nT amplitude, whilefor the second sequence (station 2) the ampli-tude was 11 nT.

First, we verified in which way the timeaverages applied to the signals affected theresults. The differences of the geomagnetic sig-

nals at the two stations either before adding thefive singularities (a) and then adding them (b)are shown in figure 2. It is clear that the differ-ences are similar. Only for the singularity withan Holder exponent α3=0 a different behaviouris clearly visible. The diagrams, in (b) and in(d), indicate the time average of the difference,with a window of 6 points, without singularitiesand adding them, respectively. These two dia-grams evidence that only the singularities withα3=0 is distinguishable while the informationabout the others is dramatically lost. In practice,the time average only detect the singularitiesassociated to step function (α3=0).

Subsequently, CWTSA and TVANS havebeen applied to the difference of the signals andto the signals themselves, respectively. We con-sidered two cases: without the five theoreticalsingularities and with them. In figure 3 the CWTof the difference of the geomagnetic time serieseither without singularities (a) or adding them(b) is shown. It is clear that the wavelet trans-form detects well the time instant where the the-oretical singularities are added. A net changebetween the two diagrams occurs. In fact, theCWT allows the detection of singularities dif-ferent from the case (a). TVANS, instead, hasbeen applied directly to the station signals.


65Table I - Physical parameters of the fault of the model.

Figure 1. Seismomagnetic Model. Simulationof geomagnetic variation due to a piezomagnet-ic effect for a fault rupture of 10 Km.

TVANS evidences some intervals where a sta-tistical “innovation” occurs. Figure 4 shows theresults of the time-variant analysis applied to thesignals either in the case without the singulari-ties (a) and (b) or in that where we added them(b) and (d). For the signal recorded in station 1the five theoretical singularities are detectedwell. In the diagrams the least square minimumerrors (LSME) of the signal 1 predicted byitself, by the signal 2 and by both, evidence thatnew non stationarity zones (b) occur, withrespect to the TVANS before adding the singu-larities (a). The same thing happens for the sig-nal 2 in (c) and (d).

In conclusion, the CWTSA and TVANS

are very effective to identify well the geomag-netic variations ( i.e. singularities).

4. Real geomagnetic time series recordedduring the North Palm Springs earthquake.

Real seismomagnetic signals have beenmeasured by two proton magnetometers of ageomagnetic networks of surveillance placed atdistances of 3 km and 9 km from the epicentreof the North Palm Springs earthquake occurredon July 8 1986, magnitude 5.9, along SanAndreas fault system, approximately 12 km NWof North Palm Springs, California, at 0921 UT

66


Figure 2. In (a) the difference of the geomagnetic fields measured in stations 1 and 2 without theoret-ical singularities is shown; black arrows indicate the positions where the singularities will be succes-sively added. In (c) the difference of the geomagnetic fields shown in (a) after adding the singularities.In the diagram (b) the time average of the difference (a) performed on 6 points is shown. In (d) thesame time average adding the singularities is visualized. The double arrow indicates the unique iden-tified singularity α3=0.

Figure 3. CWT of the geomagnetic field difference for stations 1-2 without the singularities. Thearrows indicate the positions in the CWT where the singularities will be successively added (a) andadding them (b).


67

Figure 4. TVANS of the geomagnetic signal recorded in station 1 without theoretical singularities (a)and adding them (b). In (a) and (b) in order from top to bottom: signal 1, least square minimum error(LSME) of the predictor 1, LSME of the predictor 1-2, LSME del of the predictor 1-1-2. of the geo-magnetic signal recorded in station 2 without theoretical singularities (c) and adding them (d). In (c) e(d) in order from top to bottom: signal 2, LSME of the predictor 2, LSME of the predictor 2-1, LSMEof the predictor 2-2-1. The arrows in the diagrams (a) and (c) indicate the positions before adding thetheoretical singularities, while those in (b) and (d) indicate the positions of the singularities added.Vertical axes refer to adimensional quantities.

Figure 5. (a) CWT of the difference of the geomagnetic time series measured at stations (OCHM –LSBM). The LSME of the predictors 1-2 e 2-1 are shown in (b) and (c).

[Johnston et al., 1987]. Two stations, OCHMand LSBM, have been sampling and transmit-ting data every 10 minutes through a 16-bit dig-ital telemetry system to Menlo Park, California.

The length of the analysed geomagnetictime sequences is two months (June-July 1986).

CWTSA was directly applied to the dif-ference of geomagnetic time series without per-forming time averages. In figure 5a the CWT ofthe difference is visualized. Several cones ofinfluence detect some singularities. The mostevident cones are four; the first one around theJune 28, the second one on July 8, the other twoon July, 21 and 24 respectively. According to thesingularity analysis, we observe a sharp varia-tion of the signal (singularity) at the point ofabscissa t0, where the cones of influence begins.

Then, TVANS was applied to two geo-magnetic time sequences recorded in OCHMand LSBM stations. They are indicated with x1and x2 respectively. In the diagram (b) theLSME of the predictor 1-2 is visualized. In dia-gram (c ), instead, the LSME of the predictor 2-1 is shown. The most important statistical varia-tions of the sequences are evident: around June28, around July 8 and between July 21 and 24.

Summarizing, the comparison of theresults of CWTSA and TVANS show in agree-ment some important time intervals whereimportant geomagnetic variations occur. Thefirst around June 28, the second around July 8and the third between July 21 and 24.

It is not possible, for the North PamSprings data set, to correlate the results withother geophysical data because actually thesewere not available.

5. Conclusions

Some important magnetic variationsoccur during volcanic and seismic activity.Usually, the amplitude of the geomagnetic vari-ations are very small, ranging 1-2 nT, so that itis very difficult to detect them.

In this work, two methodologies of non-stationary analysis, CWTSA and TVANS, havebeen applied to study geomagnetic time series.These methodologies, tested to seismomagneticreal data from a seismomagnetic model of afault rupture, have shown a remarkable ability todetect simulated time variations. Such tech-niques, inherently superior to the usual second-order statistics methods (like Fourier spectra)may operate on either a local or a global scale.Fourier power spectra or other common tech-niques, like time averages, do not have this localperformance: for instance, using different kinds

of singularities, we have verified that the tech-nique based on time averages is effective to evi-dence only singularities with α=0.

CWTSA and TVANS have been appliedto real geomagnetic time sequences. In particu-lar, CWTSA has been applied to the differenceof geomagnetic series while the TVANS hasbeen applied to single station signals. Theresults have shown that these techniques have agood ability to detect geomagnetic variationsthat could be associated to SM and/or VMeffects. Comparing the results from both tech-niques is evident a substantial agreement for theevent relative to seismic activity recorded atNorth Palm Springs. Moreover, these two tech-niques allowed other particular temporal inter-vals to be detected, where the statistical charac-teristics of the signal change. In conclusion, theresearch has provided good results: using local-ized techniques of analysis, like CWTSA andTVANS, one may not only obtain the sameresults than conventional techniques like timeaveraging, but may also study other features ofthe signal, which are completely lost with con-ventional analysis. The characterization of thesingular events is another potential feature ofour approach and will be described in a differentpaper.

Finally, we note that while the CWTSAcan be applied to the difference of geomagnetictime series, TVANS can be also applied to morestations. This technique is therefore potentiallyvery interesting, since may allow to studyingsimultaneously time series recorded in multi-stations, as typically occurs for a geomagneticnetworks of surveillance.

Acknowledgements

This research was supported in part by the Epotproject of the GNV.

References

Davis, P.M. and Johnston, M.J.S. (1983). Localisedgeomagnetic field changes near active faultsin California 1974-1980, Journal ofGeophisycal Research, 88, No B11, 9452-9460.

Del Negro C., Ferrucc, F. and Napoli, R. (1997).Retrieval of large volcanomagnetic effectsobserved during the 1981 eruption of Mt.Etna, Annali di Geofisica, vol. XL, 2, 547-56.

Del Negro, C., and Currenti, G. (2002).Volcanomagnetic signals associated with the2001 flank eruption of Mt. Etna (Italy),accepted by Geophysical Research Letters.

Fedi, M. (2002). Global and Local Multiscale

68


Analysis of Magnetic Susceptibility Data.Pure Appl. Geophys., in press.

Gonçalvès P., Riedi R., Baraniuk R. (1998). A simplestatistical analysis of wavelet-based multi-fractal spectrum estimation, in Proc. 32ndConf. On Signals, System and Computers,(Asilomar, Pacific Grove, CA), Nov 1998.

Haykin,S. (1996). Adaptive filter theory, Info. andSys. Scie. Ser. Prentice Hall, T. Kalaith editor,pp. 365-572.

Johnston, M.J.S., Mueller, R.J. and Dvorak J. (1981).Volcanomagnetic observations during erup-tions, May-August 1980, US Geol. Sr. Prof.Pap. ,1250, 183-189.

Johnston, M.J.S. and Mueller R.J. (1987).Seismomagnetic observation during the 8 July1986 magnitude 5.9 North Palm Springsearthquake, Science, 237, 1201-1203.

Johnston, M.J.S. (1989). Review of magnetic andelectric field effects near active faults and vol-canoes in the U.S.A., Earth Planet. Sci. Lett.,57, 47-63.

Johnston, M.J.S. (1997). Review of electric and mag-netic fields accompanying seismic and vol-canic activity, Survey in Geophysics, 18, 441-475.

Mallat S. (1998). A Wavelet Tour of SignalProcessing, Academic Press.

Mallat S. & Hwang W.L. (1992). Singularity detec-tion and processing with wavelets, IEEETransactions an Information Theory, 38, no 2,617-643.

Mallat S. & Zhong S. (1992). Characterization ofsignals from multiscale edges, IEEETransactions on Pattern an MachineIntelligence, 14, no 7, 710-732.

Zhou, S. and Thybo, H. (1998). Power spectra analy-sis of aeromagnetic data and KTB susceptibil-ity logs, and their implication for fractalbehavior of crustal magnetization, Pure Appl.Geophys., v. 151, 147-159.

Zlotnicki, J. and Le Mouel, J.L. (1988).Volcanomagnetic effects observed on Piton deLa Fournaise volcano (Réunion island):1985-1987, Journal of Geophysical Research,93, 9157-9171.

Zlotnicki, J. (1995), Monitoring active volcanoes,strategies, procedures and techniques, editedby Mc Guire, C Kilburn & J. Murray, UCLPress.

Zlotnicki, J. and Bof, M. (1998). Volcanomagneticsignals associated with the quasi-continuosactivity of the andesitic Merapi volcano,Indonesia: 1990-1995, Physics of the Earthand Planetary Interiors, 105, 119-130.


69

Nonlinear Identification and Modelingof Geomagnetic Time Series at

Etna Volcano

Annamaria Vicari1,2, Gilda Currenti1,2,Ciro Del Negro1, Luigi Fortuna2 and

Rosalba Napoli1

1Istituto Nazionale di Geofisica e Vulcanologia - Sezionedi Catania, Italy

2Università di Catania – Dipartimento di IngegneriaElettrica Elettronica e dei Sistemi, Italy

AbstractGeomagnetic fluctuations observed on

the ground are closely interrelated to externalmagnetic fields of ionospheric and magnetos-pheric origins. Theoretical studies have shownthat the magnetosphere belongs to the class ofdissipative chaotic systems. Assuming that themagnetosphere evolves in a coherent and organ-ized way, a low-dimensional analogue modelwas studied to understand its dynamics.Following on from this description of the mag-netosphere, we propose an innovative methodfor chaotic dynamical system identificationfrom measured data. We firstly applied a non-linear time series analysis to examine the behav-ior of geomagnetic signals and to obtain usefulinformation about the internal deterministiccomponent of magnetic time series from vol-canic areas. We describe geomagnetic activity interms of a relatively simple nonlinear dynamicalanalogue model, whose parameters are deter-mined in such a way that the simulated outputsignal synchronizes with the data acquired fromthe magnetic monitoring network at Etna vol-cano. Finally, once a possible dynamic of thesystem has been evaluated, we make an estimateof possible external deterministic forces of thesystem.

Key words geomagnetic fluctuations - chaoticdynamical system - Etna volcano

1. Introduction

A wide variety of techniques have beendeveloped to reconstruct dynamics from geo-magnetic time series, and to characterizedynamics in terms of predictability or dynami-cal invariants such as the correlation dimensionor spectrum of Lyapunov exponents. The truenature of geomagnetic variations is unknown[Barraclough and De Santis, 1997]. Variations

in the Earth’s magnetic field over different timescales are tied to different causative physicalprocesses. The temporal variations in the geo-magnetic field have extremely wide timescales,corresponding to a rich collection of physicalmechanisms. We turn our attention to geomag-netic variations within shorter periods (fromminutes to months). On these time scales, natu-ral geomagnetic variations are due to secondaryfields induced in the Earth by ionospheric andmagnetospheric current systems. They intro-duce dissipativity and non-linearity, which aretwo necessary conditions for the existence ofchaotic dynamics [Pavlos et al., 1994; 1999].When the observed phenomenon is not obvious-ly governed by some simple law, it is commonpractice to assume random behaviors. Startingfrom this assumption, statistical and spectralanalyses are usually applied. Unfortunately, astatistical approach provides information onlyon the mean aspect of the geomagnetic field,and a conventional spectral analysis is not ableto distinguish chaos from random signals sinceboth have continuous broadband power spectra.These investigations are not able to detect anydeterministic behavior, especially when theunderlying process is expected to be chaotic. Inthe last decades different analyses have beendevoted to reveal the presence of the chaoticmotion in geomagnetic time series [Klimas etal., 1996], with particular attention to the behav-ior of magnetospheric processes [Vassiliadis,1990]. The hypothesis of low-dimensionalchaotic behavior of magnetospheric dynamicswas examined and it was observed that magne-tospheric data analysis highlighted an organizedevolution. It appears that a relatively small num-ber of magnetospheric state variables dominatethe evolution. The tools of nonlinear time seriesanalysis and chaos theory can be used with con-fidence in order to obtain useful informationfrom apparently very irregular time series suchas the geomagnetic sequences collected on Etnavolcano. With this in mind, we firstly appliedtwo different algorithms to detect determinismin the geomagnetic signal and then we proposea novel method for chaotic dynamical systemidentification using a procedure based on a mas-ter-slave synchronization approach. In thismethod, the complex geophysical system is con-sidered as an autonomous one that evolvesspontaneously. Nowadays, several studies haveclaimed that the magnetosphere can be handledas a non-autonomous system, indicating the sig-nificative role of the solar wind driver as exter-nal forcing [Horton et al., 2001; Doxas et al.,1999]. Therefore, we investigated the reliabilityof a possible non-autonomous model of the geo-


71

magnetic signal, taking the solar wind data fromWIND satellite observations.

2. Detecting Determinism

Our purpose is to detect the presence ofchaotic dynamics in geomagnetic time series. Awide variety of methods are often applied toexperimental or real datasets to evaluatewhether the signals are consistent with a lowdimensional deterministic or stochastic mecha-nism. Particularly, we apply two different tech-niques: Kaplan Test and Local LinearForecasting. These analyses allow us to examinethe presence of deterministic dynamics and dis-tinguish randomness from chaos.

We analyze 10-minute mean values ofgeomagnetic total intensity from the magneticnetwork on Mt. Etna during the period betweenJanuary, 1999 and December, 2000. Each monthis separately analyzed.

2.1 Kaplan Test

When deducing dynamics from a timeseries, continuity is often the only safe assump-tion one can make about a possible determinis-tic mechanism for a time series. To test for thecontinuity of the underlying system, a valuabletechnique involves examining all pairs of pointszj, zk in terms of the distance δj,k=|zj-zk| and thedistance between their images εj,k=|zj+1-zk+1|[Kaplan, 1994].

It is useful to compute ε(s) that is givenby the average of the values εj,k with correspon-ding δj,k<s, where s sets the width of the ‘bins’.The behavior of ε(s), as s tends to zero, is eval-uated. If

it is supposed that the process is governed by a

deterministic mechanism, otherwise a stochasticbehavior is expected.

To explain the concept described above,the results of this test, applied on some randomgenerator, are shown. It is worth noting that theε(s) never reaches zero value, maintaining val-ues above 0.2 (Figure 1.a). Applying the Kaplantest to the geomagnetic time series, the resultsshow that ε(s) value goes down to zero value foreach period as s decreases, revealing a possibledeterministic behavior of the time series ana-lyzed. In Figure 1.b the application of Kaplantest during August 2000 is reported.

2.2 Local Linear Forecasting

Sugihara and May [1990] developed arobust technique applied to real data. It employsa local linear forecasting in order to verifywhether a time series is chaotic or not. The ideabehind using prediction as an evidence of chaosis very intuitive. The limited predictive abilityof a chaotic dynamical system is due to its sen-sitivity to initial conditions. Therefore it isexpected that chaos is characterized by adecrease in the correlation between predictedand actual values as prediction time increases[Tsonis and Elsner, 1990]. If the system ischaotic, then the decrease in predictive abilitywith prediction time is equivalent to the pres-ence of a positive Lyapunov exponent. Thisproperty can be used to distinguish chaoticbehavior from randomness. In fact, for a randomsignal, it is expected that the forecasting proper-ty doesn’t depend on the prediction interval.

The algorithm is based on predicting thefuture value of a data point by considering thefuture values of points, which are nearby in thereconstructed phase space.

The first step of the proposed algorithm isto choose an appropriate time delay and anembedding dimension in order to construct

72


Figure 1. Kaplan test results for several random signals (a) and geomagnetic time series (b).

delay vectors in the phase space (1), using theembedding theorem by Takens [Takens F.,1981]. Given a time series x(t), the reconstruct-ed delay vector is represented by:

X(tn)= [x(tn), x(tn-τ), x(tn-2τ),…, x(tn-(E-1)τ)] (1)

where τ is the time delay and E is the embeddingdimension.

In order to predict a time L ahead of tn, aneighborhood is selected around the point X(tn).For all points belonging to this neighborhood,that is, all points closer to X(tn) in the recon-structed phase space, the future values at timetn+L are evaluated. The finally accepted predic-tion is the average of all these individual predic-tions. For each prediction all past points in thereconstructed phase space are considered, theyare tested for closeness and most of them arerejected as too far away. The search of neigh-borhood must be repeated at each step in time topredict the future value. The correlation coeffi-cient between predictors and true data is used toquantify the predictive ability. The correlation

coefficient is dominated by the chaotic diver-gence of initially close trajectory and its rapiddecay in relation to prediction time interval L isa strong signature of chaos.

The procedure to reconstruct the orbits inthe pseudo-phase space is associated with theappropriate choice of the embedding dimensionand the time delay. We use two methods, whichare most common in nonlinear dynamics, theaverage mutual information (AMI) and the falsenearest neighbors (FNN) methods [Abarbanel,H. D. I., 1995]. Since the AMI rapidly decays(Figure 2.a), the time delay cannot be deter-mined choosing the first minimum of AMI, as isusually performed. Analyzing the AMI plot, atime delay τ=10 samples (1 sample correspondsto 10 minutes) seems to be a reasonable choice.In Figure 2.b the percentage of false nearestneighbors, as a function of the embeddingdimension, is shown. The shape of FNN plotindicates an embedding dimension of about 3-4.These results have to be interpreted with greatcare, because of finite sets of noisy measure-ments. The embedding theorems mentioned pre-


73

Figure 3. Correlation coefficient versus the prediction-time interval.

Figure 2. AMI plot for determining time delay (a) and FNN percentage versus Embedding dimension(b).

viously assume that the observations are avail-able with arbitrary precision. Consequently, sev-eral authors have investigated what happens tothe embedding procedure when noise is presentand the sequence is of finite length. For theembedding procedure, noise seems to be thedominant limiting factor [Schreiber, T., 1999].

Having chosen the time delay and theembedding dimension, the nonlinear forecastinganalysis is applied over the reconstructed phasespace. The results show a quick decrease of thecorrelation coefficient as the prediction-timeinterval increases for both E=3 and E=4 (Figure3). It is worth noting that the correlation coeffi-cient strongly depends on the prediction timeinterval, revealing the unpredictability of futurevalues for long time steps that is the most strik-ing characteristic of chaotic behavior.

3. Nonlinear Identification

It is well known that the famous Lorenz3-dimensional dynamical system is derivedfrom the Navier-Stokes equations for studyingthe flow in fluids. If the magnetospheric systemis considered as a magnetized fluid, the Navier-Stokes equations are to be generalized takinginto account Maxwell’s equations and the vari-ables related to electromagnetic field [Armeroand Simo, 1996]. Therefore a similarity existsbetween the Lorenz system and the magnetos-pheric one [Bhattacharjee, 1987].

With this in mind, we investigated if thestate variables of the Lorenz system are able tofollow the geomagnetic trajectories by oppor-tunely setting its control parameters.

Recently, the search for synchronizationhas moved to chaotic systems. For a chaoticdynamical system, the evolution sensitivelydepends on the initial conditions. So, two trajec-tories starting from two different, but close ini-tial conditions separate exponentially in thecourse of time. This is a relevant practical prob-lem, in so far as experimental initial conditionsare never known perfectly. By a synchronizationapproach, two (or many) chaotic systems (eitherequivalent or non-equivalent), starting fromslightly different initial conditions, adjust agiven property of their motion to a commonbehavior, due to coupling or forcing. In order toidentify the control parameters of Lorenz sys-tem, we applied a combined method using asynchronization approach and GeneticAlgorithm (GA) [Manganaro et al., 1999]. Thesynchronization can be obtained through differ-ent methods. After testing some of these, weprefer the Pecora-Carroll approach [Pecora and

Carrol, 1990; 1991], based on coupling of twosystems: the first one, the master, is independentfrom the other one, the slave, while the evolu-tion of the second depends on the first, as illus-trated in Figure 4. This arrangement is calledmaster-slave configuration. In the Pecora-Carroll approach the u master system is parti-tioned into two subsystems, w and v. A slavesystem w’ is created by duplicating the w systemand replacing the set of variables v’ by their cor-responding v.

In this way the w’ is forced by the u sys-tem by means of the v variables. As time tendsto infinity, if w’ tends to w then the master andslave are synchronized. Our chaotic system

identification, based on Pecora-Carroll cascadedsynchronization, has been applied to identify theparameters of a Lorenz system, whose equationsare reported in (3), in such a way that it syn-chronizes with the geomagnetic time series.

(3)

Our geomagnetic signal, whose dynamicshave to be estimated, is considered as a mastersystem and is used to drive the Lorenz model,acting as a slave. The slave system responds tothe driving signal in function of its parameters,which must be changed in order to minimize thedifference between the geomagnetic sequenceand the slave’s state variable. To quantify thisdifference we define a performance index as:

(4)

where M is the length of data and p is the vectorparameters to be identified.

The master and slave will be synchro-nized when the performance index has reachedits global minimum. Therefore the synchroniza-tion problem can be formulated as an optimiza-tion problem, which can be solved by GA.When a genetic algorithm is used to solve an

74


Figure 4. Mastaer-slave configuration.

optimization problem, the performance indexmust be opportunely chosen to obtain the bestsolution. Initially, the genetic algorithm will cre-ate a population of solutions based on providedsample data structure (Genome or phenotype).

The genetic algorithm then operates onthe population to evolve to the best solution.The σ and λ parameters of Lorenz model repre-sent the GA phenotype (p variables of I(p)index), whereas the r parameter is fixed at 8/3value. Figure 5 shows the modeling scheme set-

up for identification of Lorenz parameters.At each step of GA, the system of differ-

ential equations (3) is solved by a fourth-orderRunge-Kutta algorithm with a time step of 0.01.It is important to note that Runge-Kutta algo-rithm receives the geomagnetic signal as inputtoo. If the max number of generation is notreached, Runge-Kutta’s output is compared withthe geomagnetic signal to produce the perform-ance index I(p). This process continues until I(p)goes down a threshold value (global minimum).

3.1 Results

The used data set represents a time seriesof 10-minute mean values from magnetic sta-tions on Mt. Etna during the months of June1999 (Figure 6a) and March 2000 (Figure 6b).The mean values are removed from the timeseries.

Each monthly data set of geomagnetictotal intensity is analyzed separately and intro-duced as the driving signal in the master-slaveconfiguration, therefore the number of data M is4320 samples. The initial values of x, y, and z inEquation (3) are chosen arbitrarily because asynchronization approach is used. In particular,we have found that the best synchronization,


75

Figure 5. Modeling scheme.

Figure 6. Time series of the geomagnetic field during June 1999 (a) and March 2000 (b).

Table I - Setting parameters of GA for two different simulations.

that is the minimum I(p), is obtained when the xstate variable of slave Lorenz system is driven.Two of the ‘simple’ and ‘steady-state’ ones, car-ried out varying the GA parameters, are writtenup here to show the major factors of impact.

The parameters of the Lorenz system,associated to the optimum value I(p), are report-ed in table II. In order to evaluate the results ofthe identification, the geomagnetic signal andthe output signal obtained with the estimated

76


Figure 7. Geomagnetic data in dot-dash line and the x state variable of Lorenz model in solid line dur-ing June 1999 (a) and March 2000 (b).

Figure 8. Synchronization error during June 1999 (a) and March 2000 (b). The STD values are respec-tively 4.97 and 2.98.

Figure 9. Geomagnetic data vs. reproduced signal of Lorenz model during June 1999 (a) and March2000 (b). Data are normalized into [-1,1] interval.

parameters have been superimposed in Figure 7.The associated synchronization errors areshown in Figure 8.

The quality of the synchronization can beappreciated by observing Figure 9, which showsthe geomagnetic signal versus the output-simu-lated signal, after they have been normalized. Inan ideal synchronization, we should see astraight line. But in real data applications, this isnever going to happen owing to noise. Toimprove the results, we could filter the geomag-netic data by using a low-pass filter. We haven’tapplied any pre-processing procedure on thedata to avoid losing useful information on thesignal.

Although the input signal changes, ourfindings clearly reveal that the value of sigmaand lambda always remains in the same rangesin which the Lorenz system shows the well-known butterfly attractor. Therefore, it permitsus to not exclude the presence of a commondynamics, characterized by the obtained param-eters.

4. Forcing Method

Once a possible dynamics of the geomag-netic signal has been estimated, we overcomethe hypothesis of an autonomous model, and wesuppose that the geophysical system can bemodeled as a non-autonomous system[Lundstedt, 1997], namely one that evolvesunder the influence of some external determin-istic forces. So, the question is: how to detectthe external force? It is necessary to make somerelevant considerations.

The analysis of geomagnetic series in thefrequency domain reveals a composite spectrumthat can be split into two parts: a sum of period-ic terms (power concentrated in a discrete set offrequencies) and a continuous broadband spec-trum (a continuous distribution of power overthe whole frequency range). The broadenedlines reveal the presence of harmonics with theirfundamental oscillations, and a deterministicchaotic component in addition to noise (thebroadband background) (Figure 10).

To fit regular variations, we justly choosea sinusoidal forcing with periodicity determined

by the fundamental oscillations of the spectrum,while the irregular geomagnetic external varia-tions are given an account of solar wind veloci-ty. Therefore the excitation (sinusoidal excita-tion and solar wind) is expressed by a linearcombination of terms, as follows:

(5)

where:

is the solar wind component;

is periodic components as:

(6)

a, b, ci, with i = 1…4, are weight coefficientsand Ω is the fundamental pulse.

The interaction between geomagneticvariations and the excitations is expressed byweight coefficients that are the GA phenotype.The term makes the system non-autonomous: in such a way, we obtain an esti-mate of a possible external dynamic of the sys-tem. The external excitation is introduced in theLorenz equation and best results are obtainedwhen x-driven configuration is used:

(7)

As is shown in Figure 11, the modelingscheme is modified with respect to the previousone. At each step of GA, the system of differen-tial equations (7) is solved by a fourth-orderRunge-Kutta scheme with a time step of 0.01,but there are two considerable differences:


77

Table II - Lorenz’s parameters and I(p) valueobtained for two different geomagnetic sequences.

Figure 10. Power spectrum of geomagnetictime series.

1. the phenotype of GA is composed of sys-tem parameters and the weight coefficientsof the external forcing;2. Runge-Kutta algorithm receives only solarwind velocity as input regardless of the geo-magnetic signal.

4.1 Results

We consider one of the geomagnetic datasets, used in the previous method, namely June1999 (Figure 6). The external forcing is repre-sented by the 10-minute mean measurementsfromWIND satellite observations for solar windvelocity during the same period (Figure 12).

The setting parameters of GA are thesame as reported in Table I. The parameters ofboth the external forcing and the Lorenz system,in correspondence to the minimum value I(p),are reported in Table III. The geomagnetic sig-

nal and the output signal, obtained with the esti-mated parameters, have been superimposed inFigure 13 in order to estimate the results of theidentification. The related identification error isshown in Figure 14.

It should be remarked that Lorenz‘sparameters, achieved by forcing approach, aresimilar to those computed by the synchroniza-

78


Figure 11.Modeling scheme with external forc-ing.

Figure 12. Solar Wind velocity from Windsatellite observations during June, 1999.

Figure 13. Geomagnetic data in dot-dash lineand the x state variable of Lorenz model in solidline during June, 1999.

Figure 14. Modeling errors during June 1999.The standard deviation of error is 6.2.

tion method. This result lends support to thehypothesis that these parameters are related tothe dynamics of the system. Instead, the weightcoefficients quantify the interaction between thesignal and the external forcing.

5. Conclusions

Nonlinear time series analysis and chaot-ic identification methods were employed todetect determinism, non-linearity and sensitivityto initial conditions for geomagnetic time series.These three properties are a necessary conditionfor a time series to be chaotic. The Kaplan testresults permit us to not exclude that a determin-istic dynamics of the system leading the geo-magnetic variations exists. Furthermore, using anonlinear forecasting approach, the limited pre-dictive ability has been tested, revealing a strongsensitivity to initial conditions. The dependenceon initial conditions represents a difficulty whenan analogue model describing the geomagneticvariations should be derived. We have over-come this problem by using the synchronizationapproach as a tool for chaotic identification. TheLorenz system synchronizes well with the geo-magnetic time series, when its control parame-ters are chosen in the range where the dynami-cal behavior is chaotic. A possible external forc-ing dynamic of the system has also been intro-duced. The preliminary results are sufficientlygood, but new forcing components must beintroduced to obtain better ones. Certainly, thestrong coupling between solar wind parameters,magnetosphere and ionosphere constitutes themost significant state variables, which deter-mine the dynamical behavior. Since in the shortperiod band (i.e. less than a month) the geomag-netic field spectrum is essentially led by exter-nal contributions (from magnetosphere and ion-osphere), we concluded that those external sys-tems are in a nonlinear possibly chaotic state.This is possible and reasonable, but this resultcould have been affected by using data from avery anomalous site such as a volcano. In vol-canic areas both magnetization and conductivityare very anomalous, and a significant effect ofelectromagnetic induction (magnetizationaffects mostly the ‘static -or more slowing-part’, while the conductivity affects the ‘chang-ing part’ at different periods) is also present in

the signal investigated. In conclusion, one can-not completely exclude that the nonlinearities(or some of them) come from nonlinear induc-tion effects. However, the results obtained are aclear evidence of the presence of chaos in mag-netic data from volcanic areas. It should benoted that models of the geomagnetic field havealready been studied. Our method has theadvantage that the system parameters are deter-mined directly from measured data rather thanfrom preconceived notions of the processes gov-erning the geomagnetic system.

Acknowledgments

We are indebted to all personal ofGeomagnetism Laboratory of INGV-CT whoguarantee the regular working of the permanentmagnetic network on Etna volcano. Thisresearch was supported by project EPOT of theGruppo Nazionale per la Vulcanologia of theINGV, and developed in the frame of theTecnoLab, the laboratory for the technologicaladvance in geophysics organized by DIEES-UNICT and INGV-CT.

References

Abarbanel, H. D. I., (1995). Analysis of observedchaotic data. Springer Verlag.

Armero, F., Simo J. C., (1996). Long-term dissipativ-ity of time-stepping algorithms for an abstractevolution equation with applications to theincompressibile MHD and Navier-Stokiesequations. Comput. Methods Appl. Mech.Engrg. 131, 41-90.

Bhattacharjee, J. K., (1987). Convection and chaosin fluids.World Scientific, Singapore.

Barraclough, D. R. and De Santis, A., (1997). Somepossible evidence for a chaotic geomagneticfield from observational data. Phys. EarthPlanet. Inter. 99, 207-220.

Currenti, G., Del Negro, C., Fortuna, L., Vicari, A.,(2002). Nonlinear identification of complexgeomagnetic models: An innovativeapproach. Nonlinear Phenomena in ComplexSystem. In print.

Doxas, I., Horton, W., Smith, J. P., (1999). A physicsbased nonlinear dynamical model for thesolar wind driven magnetosphere-ionospheresystem. Phys. Chem. Earth. 24, no. 1-3 67-71.

Horton, W., Weigel, R. S., Sprott, J. C., (2001).Chaos and the limits of predictability for thesolar-wind-driven magnetosphere-ionospheresystem. Phys. Plasmas. 8, 6 2946-2952.


79

Table III. Lorenz parameters and weight coefficients for the minimum value of I(p).

Kaplan, T., (1994). Exceptional events as evidencefor determinism. Physica D, 73, 38-48.

Klimas, A. J., Vassiliadis, D., Baker, D. N., Roberts,D. A., (1996). The organized nonlineardynamics of the magnetosphere. J. Geophys.Res. 101, no. A6 13089-13113.

Lundstedt, H., (1997). Solar wind magnetospherecoupling: predicted and modeled with intelli-gent hybrid systems. Phys. Chem. Earth. 22,no. 7-8 623-628.

Manganaro, G., Arena, P., Fortuna, L., (1999).Cellular Neural Networks: Chaos,Complexity and VLSI Processing. Springer-Verlag.

Pavlos, G. P., Diamantidis, D., Amopoulos, A.,Rigas, A. G., Daglis, I. A., Sarris, E. T.,(1994). Chaos and magnetospheric dynamics.Nonlin. Proc. Geophys.1, 124-135.

Pavlos, G. P., Athanasiu, M. A., Diamantidis, D.,Rigas, A. G., Sarris, E. T., (1999). Commentsand new results about the magnetosphericchaos hypothesis. Nonlin. Proc. Geophys. 6,99-127.

Pecora, L. M., Carrol, T. L., (1990). Synchronizationin chaotic systems. Phys. Rev. Lett, Vol.64,pp. 821-824.

Pecora, L. M., Carrol, T. L., (1991). Driving systemswith chaotic signals. Phys. Rev. A, Vol.44, pp.2374-2383.

Sugihara, G. and May, R. M., (1990). Nonlinear fore-casting as a way of distinguishing chaos frommeasurement error in time series. Nature,Vol.344, pp.734-741.

Schreiber, T., (1999). Interdisciplinary application ofnonlinear time series methods. PhysicsReports,Vol.308, pp. 1-64

Takens F., (1981). Detecting strange attractors inturbulence. In Lecture notes in mathematics.Ed. by D. A. Rand and L. S. Young,Springer,Berlin, Vol. 898 pp. 366-381.

Tsonis, A. A. and Elsner, J. B., (1992). Nonlinearprediction as a way of distinguishing chaosfrom random fractal sequences. Nature,Vol.358, pp. 217220.

Tsonis, A. A., Triantafyllou G. N., Elsner J. B.,(1994). Searching for determinism inobserveddata: a review of the issue involved. Nonlin.Proc. Geophys.1, 12-25.

Vassiliadis, D. V., Sharma, A. S., Eastman, T. E.,Papadopoulos, K., (1990). Low-dimensionalchaos in magnetospheric activity from AEtime series. Geophys. Res. Let. 17, no. 111841–1844.

80


Inverse Modelling of Piezomagnetic andElectrokinetic Data in Volcanic Areas

Giuseppe Nunnari1 and Ciro Del Negro2

1Dipartimento di Ingegneria Elettrica, Elettronica edei Sistemi, Università di Catania

2Istituto Nazionale di Geofisica e Vulcanologia,Sezione di Catania

AbstractThe inversion problem dealt with is the

identification of the parameters of a volcanicsource causing observable changes in magneticdata recorded in volcanic areas. To study theinverse problem, synthetic data was generatedby considering two different types of volcanicsources: the traditional Mogi, whose mainadvantage is the limited number of parametersinvolved and the Okada type source that seemsmore realistic to interpret eruptive phenomenain volcanic areas such as Mt. Etna. Two types ofmagnetic effects were considered, namely thepiezomagnetic and the electrokinetic effects.The considered inversion problem was formu-lated following two different schemes: an opti-misation approach based on the use of GeneticAlgorithms (GAs) and a neural network basedapproach based on Multi-layer perceptrons(MLPs). A regular grid centred on the summitvolcano area was defined and it was hypothe-sised that measurements of the magnetic anom-alies are performed at the vertices of the grid.Then the two inversion schemes were consid-ered to compute the inverse solution associatedwith a given set of source parameters and theaccuracy of the solution was studied.Appropriate indexes were defined to give anobjective measure of the accuracy for eachparameter of the source. The results obtainedshow that both the Mogi and Okada models canbe unambiguously inverted. The accuracyobtained by using the GAs based approach isusually higher than that obtained with the neuralapproach. However, the neural approach ismuch faster and the accuracy for each individualmodel parameter is better than 10% in terms ofnormalised mean absolute error even in pres-ence of data affected by a level of gaussian noiseup to 30%.

Key words inverse modelling – piezomagneticphenomena – electrokinetic effects

1. Introduction

Clear correlations between volcanicactivity and changes in the local geomagneticfields have been observed in numerous volcanicareas. Several scientists [Johnston and Stacey,1969; Johnston, 1989; Yukutake et al. 1990;Tanaka, 1993; Del Negro et al. 1997 and 2000]have investigated the physical mechanismsinvolved with the observed magnetic anomaliesand it seems that they are mainly due to thermaldemagnetisation of rocks, to piezo-magneticeffects induced by the stress field generated bythe incoming magma and to electrokineticeffects induced by the circulation of ionised flu-ids. Since the expected changes can be comput-ed in the order of some nano Tesla (nT), veryaccurate instruments are required to recognisethese anomalies from electromagnetic noise.However, accurate instrumentation is not theonly ingredient to allow a practical use ofrecorded geomagnetic measurements. Goodnumerical methods to model data are of para-mount importance also. In particular, this paperdeals with the inverse modelling of geomagnet-ic data, i.e. with the problem of identifying theparameters of a volcanic source that is supposedto generate the changes observed in terms ofmagnetic data. The main aim of the paper is toassess the feasibility of the inversion problem.Moreover, the accuracy of the solution is stud-ied versus the number of measuring points andthe level of noise data. Two different types ofvolcanic sources were taken into account: thetraditional Mogi source [Mogi, 1958], whosemain advantage is the limited number of param-eters involved and the Okada type sources,which seem more realistic to interpret eruptivephenomena in volcanic areas such as Mt. Etna,where eruptions have their origin in dykes open-ing from a certain depth toward the surface. Twotypes of magnetic effects were considered,namely the piezomagnetic and the electrokinet-ic effects.

In order to provide the necessary infor-mation for studying the inverse problem, thedirect modelling problem was preliminaryaddressed based on the original formulas pro-posed by [Sasai 1991] for the Mogi model andby [Utsugi et. al. 2000] for the Okada source.The electrokinetic effects were computed byusing expressions provided by [Murakami,1989] and [Fitterman, 1979 and 1981].

In this study two different inversionapproaches were considered to solve the inverseproblem, namely the MLP Artificial NeuralNetworks (ANNs) and the Genetic Algorithmsoptimisation approach. MLP neural networks


81

have already been successfully applied to theinversion of seismic waveforms [Roth andTarantola, 1996], [Langer et. al. 1996] and forthe integrated inversion of geophysical data[Nunnari et al. 2001].

2. Direct Modelling

For the purposes of the applicationdescribed in this paper, synthetic data genera-tion is performed in order to provide a largeenough data set to represent the population ofthe possible models within the model space. Thetwo considered types of sources are schemati-cally represented in Fig 1 and Fig. 2 respective-ly.

The basic equations for the direct model-ling of piezomagnetic effects are the following.Let us indicate by ∆J the incremental stressinduced magnetisation, by W the associatedmagnetic potential and by H and B the magnet-ic field and magnetic induction respectively,then the following equations hold:

(1)

The piezomagnetic field associated with aMogi model has been investigated by Sasai(1991) who provided the following expressionsfor the components of the piezomagnetic poten-tial W:

(2)

if (H>D)

if (H<D)

(3)

if (H>D)

if (H<D)

where (x0, y0, z0) represents the observationpoint, C is the moment of the strain nucleus, λand µ are the Lamè’s constants,

(i=1,2,3),

and D1=D- z0 ;.D2=2H-D - z0 ;D3=2H-D - z0 .

Under the condition that the radius a issufficiently small as compared with f, themoment C is given by C = -1/2a3 ∆P, being ∆Pthe hydrostatic pressure. Differentiation of thepiezomagnetic potential with respect to x,y andz gives the components of the geomagnetic fieldchanges respectively. In table I the average

82


Figure 1. Mogi’s source: a hydrostaticallypumped pressure source in a homogeneous andisotropic elastic half-space with a uniformly mag-netised upper layer centred at (0,0,f) with radiusa. The Curie point isotherm is at a depth H.

Figure 2. The Okada source: a fault occurringin a homogeneous and isotropic elastic half-space with a uniformly magnetised upper layer.H is the depth of the Curie point isotherm.Depth is the distance between the origin O andthe upper edge of the fault; Strike is the orien-tation of the fault with respect to the North; Dipis angle of the fault plane with respect the hor-izontal plane; Rake is the angle of the strike-slip displacement; Length and Width are thelength and width of the fault respectively; Slipis the module of the strike-slip displacement;Opening is the module of the tensile displace-ment.

model parameters that have been used in thisstudy together with the corresponding ranges ofrandom fluctuation are reported.

For the Okada model, the piezomagneticeffects are due to fault motions that are sup-

posed to occur in a homogeneous and isotropicelastic half space with a uniformly magnetizedupper layer with a constant piezomagnetic stresssensitivity (see Fig. 2). Here a semi-infiniteelastic medium occupies z<0 and the magne-tised region is limited to the layer 0≤z≤H, whereH is the depth of the Curie point isotherm. Thepiezomagnetic potential W due to a finite faultcan be obtained by integrating the elementarypiezomagnetic potential over the fault plane.Analytical solutions for the piezomagneticpotentials for strike-slip, dip-slip and tensile-opening fault motions with arbitrary dip andstrike angles were derived [Utsugi et al., 2000].These solutions, despite being expressed as thecomposition of elementary functions, look likerather complicated non-linear expressions andare not reported here for the sake of simplicity.In table II the average model parameters used inthis study, together with the correspondingranges of random fluctuation, arereported.Electrokinetic effects in a faulted halfspace were computed by Fitterman [1981] and[Murakami, 1989] who obtained analytical solu-tions for the magnetic fields generated by aninclined electrokinetic source (see Fig. 3).

Inside the rectangular region the sourceintensity is expressed by S = (C1-C2) P, and isconsidered a constant; outside this region thesource intensity is zero. P is the pore pressure;

on the upper side of the contact, the electric con-ductivity is σ1 and the streaming potential coef-ficient is C1. On the lower side the properties areσ2 and C2, respectively. The depth of the sourceis a; the length and the width are L and W (=(b-

a)/sin(Dp)) respectively and the dip angle of thesource is indicated by Dp. The boundaries of theelectrocinetic source are: L/2 ≥ X0 ≥ -L/2, y2 ≥Y0 ≥ y1, b ≥ Z0 ≥ a.

The magnetic field (with components Bx,By and Bz) produced by the inclined electroci-netic source described is represented by the fol-lowing equations:

(4)

where:

(5)


83

Table I. Ranges for Mogi’s model parameters.

Table II. Ranges for the Okada’s model parameters.

Figure 3. Geometry of the Murakami inclinedmodel.

(6)

(7)

Here µ is the magnetic permeability, Xs,Ys, Zs are the source coordinates and σ isexpressed by σ = σ1 σ2 / (σ1 + σ2).

(8)

where

(9)

(10)

(11)

(12)

(13)

3. Inverse modelling with ANN

Consider a nonlinear input-output map-ping described by the functional relationship:

(14)

where x and d are the input and output vectorsrespectively. The vector-valued function f ( ⋅ )can be considered to be unknown, but it isassumed that a set of pairs (xi, di), referred to asexamples or learning patterns in typical neuralnetwork terminology, describing our knowledgeabout the function f ( ⋅ ) are given.

A typical way of approximating staticsystems using the popular single-hidden-layerMulti-layer Perceptron (MLP) is the following:

(15)

where yk (x) is the k-th entry of the approximat-ed function, ϕ ( ⋅ ) represents the sigmoid func-tion (i.e. ϕ ( z ) = 1 / ( 1+e-αz ), x ∈ ℜ d is the

MLP input vector, wj is a vector of coefficients(weight of the connections), and cj, tj are addi-tional adjustable coefficients.

The approximation problem has aninverse that consists of constructing a systemthat produces the vector x in response to the vec-tor d. The inverse system may thus be describedby

(16)

where the vector-valued function f –1 denotesthe inverse of f. The theoretical aspects concern-ing the use of MLPs for function approximationlie in the so-called Universal ApproximationTheorem [Cybenko 1989], which can beinvoked to prove that an MLP with a single hid-den layer is sufficient to compute a uniformapproximation with a prefixed degree of accura-cy. Further results about these aspects can befound in [Barron 1993].

Below, the vectors relating to the data setsand source parameters will be referred to as Dand P respectively. As the vector P varies in thespace of model parameters the data set D isobtained. The data can be measured or, as donehere, generated synthetically. It is therefore pos-sible to produce a population of pairs (D, P) thatrepresent the whole “data space” observed. Thispopulation will be used as the learning set forthe neural network. Identifying the sourcemodel on the basis of the data observed using aneural approach thus means finding an approxi-mated function of f –1 as indicated by

f –1(D) → P (17)

below.

4. Experimental Framework and Results

The experimental framework was formu-lated as follows. A regular grid 10 by 10 Kmwide centred on the summit volcano area wasdefined and it was hypothesised that piezomag-netic and electrocinetic magnetic anomalies arecomputed at the vertices of the grid (direct mod-elling) by using an appropriate software toolthat implements the models mentioned in theprevious section. Then a MLP neural networkwas trained to learn the inverse solution associ-ated with a given set of source parameters.Several trials were performed with a differentnumber of training patterns and distancebetween the grid vertices in order to characterisethe accuracy of the inverse solution in varioustmeasuring conditions. Appropriate indexes were

84


defined to give a measure of the accuracy foreach parameter of the source (i.e. for the solu-tion of the inverse problem). For the Mogimodel, only piezomagnetic data were consid-ered since for this type of source no electroci-netic effects are expected. Moreover, since themagnetic potential for this kind of sourcedepends on the product a3∆P (a and ∆P beingthe source radius and the hydrostatic pressurerespectively), it does not make sense to invert aand ∆P individually since the inverse problembecomes undetermined.

Before making the model inversion byusing ANN, an inversion approach based on theuse of Genetic Algorithms (GAs) was studied.GAs is one of the most powerful optimizationstrategies available and hence a high accuracyof the inverted parameters is guaranteed. Onehundred models uniformly distributed in thespace of parameters were inverted hypothesiz-ing a grid with 21x21 vertices (i.e. 441 measur-ing points). The results obtained for the Mogimodel are shown in Table III. The meaning ofthe performance indexes considered is describedin the Appendix. From these results it is possibleto recognize that the Mogi inverse problem canbe solved with very high accuracy by usingGAs. The Okada model involved ten parametersas described in Table II. The framework consid-ered for the inversion problem is similar to theone described for the Mogi model. One hundredmodels were inverted by using the GAs opti-mization approach and the results obtained aresummarized in the following Table IV.

Also in this case it is possible to recognisea high level of accuracy for all the considered

parameters demonstrating that the inverse prob-lem can be unambiguously solved. The maindrawback with the GAs inversion scheme is therelatively high computation effort required.

In order to overcome this drawback theMLP approach is proposed. As described in theprevious section, inversion methods based onMLP aim essentially to approximate the func-tion f –1 thus allowing to speed up the computa-tion of the source parameters that best matchesthe observed data. The availability of this func-tion allows to avoid searching for the minimum,as happens with a traditional optimisation algo-rithm such as GAs. As traditional optimisationalgorithms cannot “learn”, i.e. they cannot ben-efit from solutions obtained previously for sim-ilar problems, each new inversion requires thewhole search procedure to be re-iterated. Inorder to avoid the use of MLP with a large num-ber of inputs, the number of grid vertices wasdrastically reduced from 441 to 9. Moreover, inorder to have a more realistic data set, syntheticdata was corrupted by using various levels ofgaussian noise up to 70%. The results obtainedby using the MLP based approach are synthe-sised in the following figures. In particular, inFig. 4 the NMAE% obtained for some of theparameters of the Okada model for differentnumbers of learning patterns is shown. It is pos-sible to recognise that using MLP a larger num-ber of learning patterns usually leads to moreaccurate solutions. However, since the learningprocess requires an increasing computationaleffort with a larger number of learning patterns,then a compromise must be found. The accura-cy obtained for each parameter of the Mogi and


85

Table III. Performance indexes of the Mogi inverse model obtained by using GAs. The symbol Xsand Ys represents the x, y coordinates of the source. Evaluating the BIAS, MAE and RMSE for theproduct a3∆P it is necessary to consider that the order of magnitude for this parameter is 1011.

Table IV. Performance indexes of the Okada inverse model obtained by using GAs.

Okada sources for increasing levels of gaussiannoise is shown in Fig. 5 and Fig. 6 respectively.The neural approach proves less accurate than

the GAs optimisation approach, but it is possibleto appreciate that all the parameters are estimat-ed with an accuracy, in terms of NMAE%, thatis better than 10% even in presence of a noiselevel up to 30%. On the other hand, it must bestressed here that the neural inversion approachis based on a considerably lower number ofmeasuring stations (only 9 compared with the441 used for the GAs approach).

5. Conclusions

In this paper the problem of invertingmagnetic data of piezomagnetic and electroci-netic type has been addressed. The results showthat in spite of the high nonlinearity of the con-sidered inverse problems they can be unambigu-ously solved. The inversion scheme was set upbased on two different techniques: the GAs opti-mization approach that guarantees high accura-cy but requires a considerable computationeffort, and the MLP neural network approach

86


Figure 4. NMAE% obtained by using the neural inversion approach with different number of trainingpatterns.

Figure 5. Accuracy obtained for the two inverted parameters of the Mogi model by using the neuralapproach. Different levels of gaussian noise were considered.

Figure 6. NMAE% obtained by using the neural inversion approach for the Okada model.

that once appropriately trained assures very lowcomputation efforts and acceptable accuracyeven in presence of noise data and limited num-ber of stations. Future work is still required tomake the experimental framework more realis-tic. In particular, since the considered inversemodel refers to single sources, which might notbe realistic, we plan to consider the presence ofmultiple sources.

Acknowledgements

This work was supported by the Italian GNV(Gruppo Nazionale per la Vulcanologia) underthe coordinate project EPOT (TechnologicalInnovation and Automation in IntegratedApplication of Electromagnetic Methods andPotential Fields in Volcanic Active Areas).

References

Barron A. R., (1993). Universal ApproximationBounds for Superposition of a SigmoidalFunction, IEEE Trans. on InformationTheory, vol. 39, pp. 930-945.

Cybenko G., (1989). Approximation by SuperPrecision of a Sigmoidal Function Math ofcontrol signals & systems, Springer, NewYork, vol. 2, pp. 303-314.

Del Negro C. , Ferrucci F. ,Napoli R. (1997). ThePermanent Network for MagneticSurveillance of Mt, Etna: Changes in theGeomagnetic Total Intensity Observed in1995, Acta Volcanologica, no. 9, pp 1-7.

Del Negro C., Ferrucci F., Napoli R., 2000, A reviewof the volcano-magnetic effects observedbetween 1981 and 1995 on Mount Etna(Italy), Phys. Chem. Earth, 25, 725-730.

Fittermann D.V. (1979). Theory of electrokinetic-magnetic anomalies in a faulted half-space, J.Geophys. Res., vol. 84, pp. 6031–6040, 1979.

Fittermann D.V. (1981). Correction to theory of elec-trokinetic-magnetic anomalies in a faultedhalf-space, J. Geophys. Res., vol. 86, pp.9585–9588.

Johnston M.J.S., Stacey F. D., (1969). Volcano-mag-netic effects observed on Mt Ruapehu, NewZealand, J. Geophys. Res., 74, 6541-6544.

Johnston M.J.S, (1989). Review of magnetic andelectric field effects near active faults and vol-canoes in the U.S.A., Earth Planet Sci. Lett.,57, 47-63.

Mogi, K., (1958). Relations between the eruptions ofvarious volcanoes and the deformations of theground surfaces around them, Bulletin ofEarthquake Research Institute, Univ. Tokio.

Murakami H., (1989) Geomagnetic fields producedby electrokinetic sources, J. Geomagn.Geoelectron., vol. 41, pp. 221–247.

Nunnari G., Bertucco L., Ferrucci F., (2001). ANeural Approach to the Integrated Inversionof Geophisical Data Types, IEEE Transactionon Geosciences and Remote Sensing, Vol. 39,

N. 4, pp 736-748, April 2001.Okada, Y., (1992). Surface deformation due to shear

and tensile faults in a half-space, Bulletin ofSeismological Society of America.

Röth G., Tarantola A., (1996). Neural Network andInversion of Seismic Data,. J. Geoph. Res. 99,pp. 6753-6768.

Langer H., Nunnari G., Occhipinti L. (1996),Estimation of Seismic Waveform GoverningParameters with Neural Networks. J.Geophys. Res., vol. 101, pp. 20109-20118.

Sasai, Y., (1991). Tectonomagnetic modeling on thebasic of the linear piezomagnetic effect,Bulletin of Earthquake Research Institute,Univ. Tokio.

Tanaka Y., (1993). Eruption Mechanism as inferredfrom geomagnetic changes with special atten-tion to the 1989-1990 activity of Aso volcano,J. Volcan. Geitherm. Res., 56319-338.

Utsugi, M., Nishida, Y. And Sasai, Y, (2000).Piezomagnetic potentials due to an inclinatedrectangular fault in a semi-infinite medium,Geophys. J. Int..

Yukutake T., Utada H., Yoshino T., Watanabe H.,Hamano Y., Sasai Y., Kimoto E., Otani K.,Shimomura T., (1990). Changes in geomag-netic total intensity observed before the erup-tion of Oshima Volcano in 1986, J. Geomagn.,Geolectr., 42, 277-290.


87

Appendix A – Performance Indexes

88


AGraphical Computer Program forModeling of Volcanomagnetic Fields: a

Case Study Mount Vesuvius

Rosalba Napoli1, Gilda Currenti1,2,Ciro Del Negro1, Takeshi Hashimoto3,

and Annamaria Vicari1,2


2Dipartimento di Ingegneria Elettrica, Elettronica e deiSistemi – Università di Catania, Italy

3Institute of Seismology and Volcanoly Graduate Schoolof Science, Hokkaido University, Japan

AbstractA graphical computer program for vol-

canomagnetic modeling, called VMM, has beendeveloped. It is applicable to a variety of vol-canomagnetic problems concerning piezomag-netic, thermomagnetic, and electrokineticeffects. The capability and limitation of the pro-gram are presented. We applied this tool forcomputing the volcanomagnetic fields expectedto accompany eruptions at Mount Vesuvius. Weconsidered the piezomagnetic and electrokineticeffects due to a regional fault located on thewestern flank of volcanic edifice, which playsan important role in relation to the activity of thevolcano. Relatively intense changes are seenonly around both tips of the fault: the ampli-tudes of calculated piezomagnetic anomaliesrange from 5-6 nT in the case of tensile-opening(1 m) to 2-3 nT in the case of dip-slip, while theelectrokinetic anomalies are less than 1 nT

Key words magnetic modeling - magnetic mon-itoring - volcanomagnetism - Mount Vesuvius

1. Introduction

In real volcanic fields a variety of situa-tions are expected with regard to the manifesta-tion of geomagnetic changes accompanying vol-canic activities. Volcanoes are a kind of heat-transfer system from the depths to the groundsurface, and hence, in an active period they arefrequently accompanied by subsurfacehydrothermal convection, which causes changesin temperature, pressure, and fluid motion with-in the edifice. In addition faults or fissures,which frequently affect volcanoes, give rise tothe geomagnetic fields due to piezomagnetic orelectrokinetic processes. The correct identifica-tion and interpretation of the observed anom-alies is crucial to obtain a comprehensive under-

standing of physical processes taking placebeneath the volcanoes and, as such, it is impor-tant to distinguish which of them is the mosteffective for each volcano and for each stage ofits activity. However, attempts of modelingmagnetic fields expected to accompany volcaniceruptions often involve a great deal of effort,since [i) the solutions are scattered throughoutthe literature; (ii) they may have only limitedapplicability to certain locations and regimes;and (iii) are found using algorithms that are fre-quently complex and iterative. This can be espe-cially frustrating because forecasting and moni-toring of volcanic activity requires short-termdecision-making.

The need for the development of a vol-canology oriented software is thus derived fromthe desire of being able to model many kinds ofvolcanomagnetic signals in a way that couldmatch software monitoring standard. That is thesoftware should at least enable users to have auser-friendly tool to calculate and visualize awide spectrum of volcanomagnetic fieldsthrough a mouse-click operation, and to have anoption to generate image files in commonlyavailable formats, which could be easily export-ed for the purpose of exchange of data in a visu-alized form. With this in mind, we have collect-ed several theoretical solutions of geomagneticanomalies into a unified computer program. Thesoftware, named VMM (Volcano MagneticModeling), has been released recently to thepublic domain, especially offered to the vol-canological community. In the present paper wefirstly illustrate the capability of this programand its graphical user interface. Secondly, weapply this toolbox for estimating the magneticanomalies expected to accompany eruptions atMount Vesuvius (southern Italy). Finally, wealso suggest an adequate configuration of themagnetic station arrays for magnetic monitoringpurposes.

2. Summary of physical mechanisms

The volcanomagnetic fields rely uponthree main endogenous causes. The first is thatuprising melt may heat the superficial rocks to atemperature above the Curie point, with a con-sequent decrease in the intensity of the totalfield. Due to the thermal inertia of the rocks andthe generally small dimensions of magmaticintrusions at shallow depths, this phenomenon isprobably (i) slow and (ii) restricted to a limitedarea. The other two causes of volcanomagnetictransients bring into play the piezomagnetism ofrocks and streaming potentials. Anomalies of


89

this type show modest maximum values butthey are fast, with respect to thermomagneticchanges. The comprehension of the differentmechanisms, which can generate volcanomag-netic signals, has advanced considerably sincefirst observations of the phenomena. Severaltheoretical studies for tectonomagnetic and vol-canomagnetic modeling have been elaborated.

The main frame of the piezomagneticmodeling was established by Stacey [1964] andStacey et al. [1965], who demonstrated the seis-momagnetic and volcanomagnetic effects usingthe volume element method. Based on theirbasic theory, subsequently, Davis [1976],Johnston [1978] and Oshiman [1980] investigat-ed more realistic models. A series of theoreticalstudies elaborated by Sasai [1979, 1980, 1983,1991a, 1991b] allow to obtain analytic solutionsfor the piezomagnetic field due to a point-pres-sure source and to a strike-slip and tensile-open-ing vertical rectangular fault. Recently, Utsugiet al. [2000] extended Sasai’s analytic solutionto cases of an inclined fault including dip-slip.

There has also been theoretical progress inthe research field of the electrokinetic effect.Nourbehecht [1963] was the pioneer of such astudy formulating the basic theory of electroki-netic phenomena based on irreversible thermo-dynamics. Mizutani et al. [1976] proposed thepossibility of an electrokinetic field produced byunderground water-flow for the origin of thegeomagnetic variation accompanying theMatsushiro earthquake swarm. While Ishido andMizutani [1981] provided fundamental data ofthe parameters for the electrokinetic couplingthrough laboratory experiments, a series of stud-ies elaborated by Fitterman [1978; 1979; 1981]demonstrated analytic and semi-analytic solu-tions for the electric and magnetic fields due toelectrokinetic sources in horizontally-layeredand vertically-faulted half-space. Murakami etal. [1984; 1987] and Murakami [1989] extendedFitterman’s solutions to the case of inclinedfault using Edwards’ [1974] approximation.

When we consider the thermomagneticeffect, we sometimes take a rather simpler cal-culation approach compared to the other twoeffects mentioned above. Namely, we assign thetemperature distribution and the thermomagnet-ic property of the ground a priori. In many casesthe simplest approximation is adopted: the mag-netized host rock with some completely demag-netized sources within. Magnetic anomalies dueto thermal demagnetization with arbitrary shapecan be calculated by integrating dipole sources.We can also utilize some semi-analytic solutionsto reduce the dimension of volume integral suchas those proposed by Talwani [1965] and

Bhattacharyya [1980]. However, in many casesa point-source or spherical-source approxima-tion practically works in application to volcanicfields as a model of demagnetized source belowthe volcano, implying that the heterogeneity ofthe magnetized media is not crucial in the caseof thermomagnetic effect.

3. Capability of the VMM software

Although there are several numerical andanalytic solutions for volcanomagnetic model-ing in the literature, they are rarely user-friend-ly for those not familiar with the research fields.In order to improve the efficiency of volcanomonitoring, we have implemented some ofthese works in a unified toolbox with the aid ofgraphical user interface under MatLab (TheMathWorks, Inc.), which is a general purposeprogramming system with extensive libraries offunctions for any programming task. Here wecall this procedure VMM (Volcano MagneticModeling). The VMM toolbox consists of a col-lection of MatLab m-files that are distributed assource code. It is designed in a modular fashionso that different components can be combinedas necessary, depending on the specific meas-urements available and parameters desired.MatLab is available on a wide variety of operat-ing systems and platforms and it is widely usedin the scientific community. In addition, the vec-torized nature of MatLab lends itself to a moretransparent presentation of the underlying algo-rithms. The toolbox structure is designed tofacilitate quality-control checks at intermediatestages in the processing of a particular data set.

The VMM basically consists of four mod-ules for computing the volcanomagnetic fields.The first is for the piezomagnetic effects due toa fault based on the analytic solutions by Sasai[1991b] and Utsugi et al. [2000]. Computationsfor strike-slip, dip-slip, and tensile-opening of arectangular fault with an arbitrary dip angle areavailable. The second is for the piezomagneticeffects due to a point pressure source (Mogimodel in volcanology) based on the analyticsolutions proposed by Sasai [1991a]. The thirdis for the electrokinetic effects due to a rectan-gular fault using the analytic solutions byMurakami [1989]. The fourth is for the thermo-magnetic effects due to a spherical body usingthe analytic solution of a magnetic dipole. As anoption, the displacement and stress fields, whichare based on the analytic expressions of Okada[1992], are also available. In the present versionof VMM all fields are calculated in the plane ofthe ground surface. We have also installed the

90


VMM code on Website of our GeomagnetismLaboratory for remote applications via Internet(the address is: http://maglab.ct.ingv.it).

VMM is characterized by a high automa-tion level and development flexibility. Forinstance, if you want to add a new process codeto the library, all you need to do is to write asimple code. An example of the two input datawindows of VMM configuring the fault param-eters is shown in Fig. 1.

In the geometry fault window (Fig. 1a)we can define the length, width, burial depth,dip and strike angles of the fault. Calculation ofthe magnetic field will be done with the param-eters here as well as with others (length and typeof dislocation) given in the main menu.Visualization of the fault shape is realized in 3-D manner in the right-hand side of the figure. Inthe physical parameters window (Fig. 1b) it ispossible to configure the physical properties ofthe media. Here you can define the rigidity,Poisson’s ratio, and piezomagnetic stress-sensi-

tivity of the media as well as the geomagneticinclination, declination, average magnetizationof the media, and the depth of Curie pointisotherm, below which the media is assumed tobe completely demagnetized. Figure 2 displaysexamples of piezomagnetic fields of Bx (north-ward), By (eastward), Bz (downward), and Bt(total force) due to a rectangular fault withstrike-slip. It is also possible to compute a casefor multiple sources. For example, in the physi-cal property menu we can define both of thepiezomagnetic and electrokinetic properties ofthe ground as shown in Fig. 1b. Thus we canobtain a superposed field of the two as demon-strated in Fig. 3 (fields can be displayed in 3-Dexpression).


91

Figure 1. An example of input data windows of VMM: (a) the geometry fault window and (b) thephysical properties window.

4. Application to Mount Vesuvius

The last eruption at Vesuvius volcano tookplace in March 1944. Since then the volcano hasbeen in a state of complete quiescence and noparticular indication suggesting a renewal ofactivity has been observed. Nevertheless,Vesuvius must be considered an extremely haz-ardous volcano because in the course of its longeruptive history, it has often shown long periodsof quiescence, sometimes protracted for cen-

turies, which are followed by even more violentrenewals.

From a tectonic point of view there seemsto be an indirect connection between Vesuvius’eruptive activity and the dynamics of theCalabrian arc. Vesuvius is situated on a NE-SWregional fault [Finetti and Morelli, 1974;Cassano and La Torre, 1987], which crosses allthe recent formations and fed various eruptions[Scandone et al., 1991]. The existence of theregional fault is obvious both in gravimetric

92


Figure 2. An example of piezomagnetic field due to a rectangular fault with strike-slip calculated withVMM. The components Bx (northward), By (eastward), Bz (downward), and Bt (total force) of piezo-magnetic fields produced by an inclined strike-slip fault trending NE-SW direction are shown.

Figure 3 - An example of multiple-source fields of piezomagnetic and electrokinetic effects. Fields aredisplayed in 3-D expression in this case.

data on land [Florio et al., 1999; Cassano and LaTorre, 1987] and submarine seismic profiles[Finetti and Morelli, 1974]. In particular, theseismic profiles imply the presence of volcanicevents along this fault. Two historic fissureeruptions of Vesuvius in 1794 and 1861occurred along its inland continuation. Thisfault belongs to the tectonic system trendingperpendicular to the Apennines (NE-SW) andarranges the tensile tectonic field along the NW-SE direction due to the backward retreat of theCalabrian arc. The movement of the arc pro-duces strain variations propagating in the bor-dering areas. From a volcanological viewpoint,the arrival of an impulsive tensile strain in theVesuvian area sets off the movement of magma,which is in an unstable equilibrium at the vol-canic base [Marzocchi et al., 1993]. Under suchan extensional tectonic field, the region betweenVesuvius and Campi Fregrei shows a kind ofgraben structure composed of a group of normalfaults. The fault on the NW flank of Vesuviusforms the SE boundary of this graben systemand hence dipping to SW direction.

Taking these features of Vesuvius intoaccount, magnetic transients due to electrofiltra-tion and piezomagnetic effects associated withfault activity are more important than slowervariations due to the thermal demagnetizationprocess. Hence here we focus on the formereffects, for which it is easy to imagine a stronglink. At Vesuvius, these two causes of magneticanomalies can co-exist. Here we first examinethe piezomagnetic effects due to a tensile-open-ing (dike-intrusion) and a dip-slip along thefault. Secondly, we calculate the electrokineticeffects due to the same fault.

Magnetic properties

Total magnetization of volcanic rocks canbe calculated from laboratory measurements ofthermoremanent magnetization and magneticsusceptibility. Magnetic susceptibility values ofthe main samples of Vesuvius range between 1and 3x10-2 SI for solid rocks and between 0.3

and 2x10-2 SI for ejecta [Pierattini, pers. com.].1x10-2 SI is adopted as a representative value.Intensity of remanent magnetization is extreme-ly variable: practically nil for sedimentemplaced at low temperatures; it can exceed 5A/m in intrusive bodies. Despite the strong vari-ability of this parameter, it is believed that 2A/m constitutes a representative value.Therefore the remanent component is the mainagent of the total magnetization. For the compu-tation of the magnetic anomaly, we neglectedthe induced magnetization and used only theremanent component, which is considered uni-form and equals 2 A/m. Generally, the directionof natural remanent magnetization is the sameas that of the present mean field in accordancewith recent age (20-25 ky) of emitted products[Santacroce, 1987]. We assume the geomagnet-ic inclination and declination as 54 and 1degree, respectively.

Piezomagnetic field

Magnetic changes associated with a NE-SW tensile-opening and dip-slip faulting areshown in Fig.4. The values of the parametersused for the computation of the anomaly withVMM are indicated in table I. Parameters con-cerning the fault shape are based on the result ofseismic and gravimetric studies [Cassano andLa Torre, 1987; Finetti and Morelli, 1974].Relatively intense changes are seen only aroundboth tips of the fault: the amplitudes of calculat-ed anomalies range from 5-6 nT in the case oftensile-opening (Fig. 4a) to 2-3 nT in the case ofdip-slip (Fig. 4b).

These anomalies are intense enough todistinguish them from the normal variations ofthe Earth’s magnetic field, but their shapes areso similar that it will be difficult to distinguishto each other. We should also be careful in thatpiezomagnetic effect due to a fault is quite sen-sitive to the position of the edges of the fault.The large values of geomagnetic variation arelimited to small areas in the vicinity of the tips.This fact implies that we do not detect anything


93Table I. Fault parameters used for the piezomagnetic and electrokinetic calculation in Fig. 4.

significant if we lose the position of the tips.Accordingly, it is strongly recommended toinvestigate the position of the fault beforeinstalling magnetometers. Attention must alsobe paid to the possibility that a fault we are mod-eling is not always uniform throughout thedimension. In many cases, a large fault consistsof some patches within. Geomorphologically agroup of such small patches are considered asthe parts belonging to a single fault system. Insuch cases, piezomagnetic anomalies willappear at each edge of these patches.Considering such situations it is preferable todeploy magnetometers as densely as possiblealong a fault system.

Electrokinetic field

Electrokinetic phenomena require themovement of fluids within the volcanic edifice.Fluid motion in the vicinity of a boundary sepa-rating regions with different streaming-potentialcoefficients can produce an external magneticfield. The electrokinetic field is related tochanges in the stress field and to thermal orchemical changes of fluids within the intercon-nected crack and fissure nets [Nourbehecht,1963]. Explosive sequences of Vesuvius are

characterized by deposits whose compositionand structure show an interaction with aquifersduring the early stage of the eruptions. Manystudies have revealed the presence of aquifers atsome depths inside the Vesuvian substratum,both in the carbonate basement as well as in thevolcanic covering [e.g. Marzocchi et al., 1993].Therefore, the volcanic edifice is plausibly thesite of water circulation and any modification ofthe circulation regime might induce local distur-bances of the geomagnetic field.

To estimate an order of magnitude and theshape of a possible electrokinetic magnetic fieldat Vesuvius, we calculated the electrokineticfields due to the fault using the VMM. The faultgeometry is hypothesized the same as the caseof piezomagnetic effect and with source intensi-ty S equal to 1 V (equivalent to the over-pres-sure of 10 bar for 0.1 V/bar of the streamingpotential coefficient). We assumed the conduc-tivity of the ground as uniform with a value of0.005 S/m (200 Ωm). The calculated anomaly isshown in Fig. 5 displaying the amplitude lessthan 1 nT. Also the greatest component of thisfield, orientated parallel to the strike of theanisotropy structure, shows relatively smallmaximum values (< 1 nT). As is the case inpiezomagnetic effect, we observe that anomalies

94


Figure 4. Piezomagnetic fields in total force due to a tensile-opening fault (left panel) and a dip-slipfault (right panel) in Vesuvian area. Parameters used in the calculation are shown in table I. Units arein nanoteslas. The thick line shows the location of the fault.

are centered at both ends of the fault. We have tomention that the intensity of electrokinetic fieldis proportional to the conductivity of the ground.Thus we expect more intensive electrokineticfield if the ground is more conductive. We cal-culated here assuming the conductivity of theground is homogeneous. Although the value of0.005 S/m used here seems reasonable for atleast the superficial layer of Vesuvius, we expecta more conductive layer below. The magneticfield should be greater than those demonstratedabove if we take such a conductive layer intoaccount.

5. Concluding Remarks

In order to facilitate the identification andinterpretation of the sources of a wide spectrumof magnetic signals, we have implemented agraphical computer procedure for modelingmagnetic fields associated with volcanic activi-ty. It is applicable to the variety of problems forpiezomagnetic, thermomagnetic, and electroki-netic effects with user-friendly interfaces. Weapplied this tool to Mount Vesuvius. We consid-ered the piezomagnetic and electrokineticeffects due to a regional fault, which lies on thenorthwestern flank of Vesuvius. The outcomesof our study show that moderate-scale magneticanomalies of a few nanoteslas should be expect-ed to accompany the volcanic activity. Theintensity of the theoretical anomalies proved tobe above the minimum level of detection, orrather, volcanomagnetic fields are intenseenough to claim the possibility of distinguishingthem from the environmental magnetic noise. Inthe light of the volcanological history of theVesuvius, which mainly experienced explosive

eruptions, this possibility may be relevant fordetecting the modifications within the volcanicedifices of the stress field or of the thermody-namic state forerunning future eruptiveepisodes.

Finally, regarding the diversity of the spa-tial pattern of these magnetic anomalies, andneglecting the time scales of phenomena, com-putation of synthetic anomalies may be usefulfor the advance planning of the configuration ofmeasurement devices oriented to the detectionof eruptive forerunners. Considering the results

demonstrated above, we can now propose adesirable configuration of instruments aiming todetect geomagnetic variations associated withpossible activity of Vesuvius as shown in Fig. 6.

As was seen above, the dominant effectexpected in this area is the piezomagnetic fielddue to a tensile-opening fault that lies on thewestern flank of the volcano. Accordingly, it ispreferable that we deploy the instruments in par-allel alignment to the fault. In addition, consid-ering the possibility of summit activity, some ofthem are to be deployed in a N-S alignmentacross the summit.

Acknowledgments

This research was carried out in the frameworkof the project EPOT, which is supported byGruppo Nazionale per la Vulcanologia of theINGV.


95

Figure 5. Electrokinetic magnetic fields due tothe same fault as Fig. 4. Units are in nanoteslas.

Figure 6. A desirable configuration of geomag-netic monitoring at Vesuvius. The thick linerepresents the fault while the solid circles showthe points of observation.

References

Bhattacharyya, B. K., (1980). A generalized multi-body model for inversion of magnetic anom-alies. Geophys., 45, 255-270.

Cassano, E. and La Torre, P., (1987). Geophysics. In:R. Santacroce (Editor), Somma-Vesuvius,CNR Quad. Ric. Sci., 114, vol. 8, 175-192.

Davis, P.M., (1976). The computed piezomagneticanomaly field for Kilauea volcano, Hawaii, J.Geomag. Geoelectr., 28, 113-122.

Edwards, R.N., (1974). The magnetometric resistiv-ity method and its application to the mappingof a fault, Can. J. Earth. Sci., 11, 1136-1156.

Finetti, I. and Morelli, C., (1974). Esplorazione sis-mica a riflessione nei golfi di Napoli ePozzuoli, Boll. Geofis. Teor. Appl., 16, 175-222.

Fitterman, D.V., (1978). Electrokinetic and magneticanomalies associated with dilatant regions in alayered earth, J. Geophys. Res., 83, 5923-5928.

Fitterman, D.V., (1979). Theory of Electrokineticmagnetic anomalies in a faulted half space, J.Geophys. Res., 84, 6031-6040.

Fitterman, D.V., (1981). Correction: Theory of elec-trokinetic-magnetic anomalies in a faultedhalf-space, J. Geophys. Res., 86, 9585-9588.

Florio, G., Fedi, M., Cell, F. and Rampolla, A.,(1999). The Campanian Plain and Phlegreanfields: structural setting from potential fielddata, J. Volcanol. Geotherm. Res., 91, 361-379.

Ishido, T. and Mizutani, H., (1981). Experimentaland theoretical basis of electrokinetic phenom-ena in rock-water systems and its applicationto geophysics, J. Geophys. Res., 86, 1763-1775.

Johnston, M.J.S., (1978). Local magnetic field obser-vations and stress changes near a slip discon-tinuity on the San Andreas fault, J. Geomag.Geoelectr., 30, 607-617.

Marzocchi, W., Scandone, R. and Mulargia, F.,(1993). The tectonic setting of Mount Vesuviusand the correlation between its eruptions andthe earthquakes of the Southern Apennines. J.Volcanol. Geotherm. Res., 58, 27-41.

Mizutani, H., Ishido, T., Yokokura, T., and Ohnishi,S., (1976). Electrokinetic phenomena associat-ed with earthquakes, Geophys. Res. Lett., 3,365-368.

Mogi, K., (1958). Relations between the eruptions ofvarious volcanoes and the deformations of theground surfaces around them, Bull. Earthq.Res. Inst., Univ. Tokyo, 36, 99-134.

Murakami, H., (1989). Geomagnetic fields producedby electrokinetic sources, J. Geomagn.Geoelectr., 41, 221-247.

Murakami, H., Mizutani, H., and Nabetani, S.,(1984). Self-potential anomalies associatedwith an active fault, J. Geomag. Geoelectr., 36,351-376.

Murakami, H., Mizutani, H., and Nabetani, S.,(1987). Correction: Self-potential anomaliesassociated with an active fault, J. Geomag.Geoelectr., 36, 351-376.

Nourbehecht, B., (1963). Irreversible thermodynam-ic effects in inhomogeneous media and theirapplications in certain geoelectric problems,PhD thesis, MIT, Cambridge.

Okada, Y., (1992). Internal deformation due to shearand tensile faults in a half-space, Bull. Seism.Soc. Am., 82, 1018-1040.

Oshiman, N., (1980). Local magnetic changes asso-ciated with fault activity, M. Sc. Thesis, TokyoInst. Tech., 178 pp.

Santacroce, R., (1987). Somma-Vesuvius. CNRQuad. Ric. Sci., 114, vol. 8, 251 pp.

Sasai, Y., (1979). The piezomagnetic field associatedwith the Mogi model, Bull. Earthq. Res. Inst.,Univ. Tokyo, 54, 1-29.

Sasai, Y., (1980). Application of the elasticity theoryof dislocations to tectonomagnetic modeling,Bull. Earthq. Res. Inst., Univ. Tokyo, 55, 387-447.

Sasai, Y., (1983). A surface integral representation ofthe tectonomagnetic field based on the linearpiezomagnetic effect, Bull. Earthq. Res. Inst.,Univ. Tokyo, 58, 763-785.

Sasai, Y., (1991a). Piezomagnetic field associatedwith the Mogi model revised: analytic solutionfor finite spherical source, J. Geomag.Geoelectr., 43, 21-64.

Sasai, Y., (1991b). Tectonomagnetic modeling on thebasis of the linear piezomagnetic effect, Bull.Earthq. Res. Inst., Univ. Tokyo, 66, 585-722.

Scandone, R., Bellucci, F., Lirer, L. and Rolandi, G.,(1991). The structure of the Campanian Plainand the activity of the Neapolitan volcanoes, J.Volcanol. Geotherm. Res., 48, 1-31.

Stacey, F.D., (1964). The seismomagnetic effect,Pageoph, 58, 5-22.

Stacey, F.D., Barr, K. G. and Robson, G. R., (1965).The volcanomagnetic effect, Pageoph, 62, 96-104.

Talwani, M., (1965). Computation with the help of adigital computer of magnetic anomaliescaused by bodies of arbitrary shape, Geophys.,30, 797-817.

Utsugi, M., Nishida, Y. and Sasai, Y., (2000).Piezomagnetic potentials due to an inclinedrectangular fault in a semi-infinite medium,Geophys. J. Int., 140, 479-492.

96


Project and Manufacturing of anAutolevelling Vectorial Magnetometer

for Volcanic Areas Monitoring

Paolo Palangio, Claudia Rossi, Achille Zirizzotti,Antonio Meloni and Lili Cafarella

Istituto Nazionale di Geofisica e Vulcanologia,Roma, Italy

AbstractIn the frame of EPOT project (technolog-

ical innovation and automation in the integratedapplications of Electromagnetic and POTentialfield methods in active volcanic areas) an autolevelling magnetometer for geomagnetic fieldmonitoring in volcanic areas, was proposed. Inthis paper a brief description of this magne-tometer and some preliminary tests aredescribed. In particular some characteristics ofthe non-diagonal elements of the field transformmatrix A between the observatory system andthe magnetometer placed in a far location arediscussed with the relative implication whenone of the two magnetometers would be locatedin a volcanic area.

Key words autolevelling magnetometer – mag-netic monitoring - thermal drift

1. Introduction

Magnetic monitoring of volcanoes ismade generally by means of proton precessionmagnetometers for total field measuring.However these observations, although very use-ful and effective [Stacey et al., 1965; Johnstonand Stacey, 1969a; Johnston and Stacey, 1969b;Johnston and Muller, 1981; Johnston andMuller, 1987; Zlotnicki et al., 1993; Zlotnickiand Bof, 1996; Avdeev et al., 1997], provideonly partial information because changes oflocal magnetic inclination and declination couldcause null changes of the total field. Moreoverthe scalar measure of the local field does notfurnish information on changes of the X, Y andZ components. On the other side the employ-ment of vector magnetometers in the uninter-rupted monitoring of the geomagnetic field,presents different problems in relation to thephysical conditions of the volcanic areas: fluc-tuations of the apparent vertical, torsionalmovements, strong distortion of the geomagnet-ic field lines, intense local magnetic field gradi-ents, are in fact only some of the most importantremarkable characteristics of these areas

[Rikitake and Yokoyama, 1955; Davis et al.,1979; Muller and Johnston, 1981; Meloni et al,1998; Sasai et al, 2001; Sasai et al. 2002]. Inparticular, the fluctuations of the apparent verti-cal can cause effects on the X, Y and Z compo-nents; therefore the reference system materi-alised by the sensor axes, should be inertiallycoupled to an absolute reference frame. The dis-tortion of the local field lines is reflected on thesensor orientation while the field gradients arereflected on the precision of the measurementsince the field is integrated over the space occu-pied by the sensor.

In order to try to solve these problems wepropose here the theory and realization of ourautolevelling vector magnetometer that canproperly operate in volcanic areas. The newdesigning criteria have been oriented towards ahigh long term stability and a low thermal drift.This instrument can be employed for continuousmeasurements of the geomagnetic field inremote stations, where regular carrying out ofabsolute measurements cannot be guaranteed.

2. The magnetometer

A prototype of the autolevelling magne-tometer here proposed was realized at the geo-magnetic observatory of L’Aquila, Italy. Themagnetometer consists of a flux gate sensor, itsdriving electronic circuits (Fig. 1) and dataacquisition system. The magnetometer allowsfluctuation adjustments of the bearing surfacewith an indeterminateness of less than 4” and adynamic extension of ±5°. The geomagneticfluxgate sensor was designed in order to strictlyfit the proposed technical requirements.

The sensor hanging system was madeusing a compound gimbals with amagnetic ball-bearing made with copper and beryllium alloy(Fig. 2). The non-orthogonality of the hangingplanes (materialized by the suspension) is lessthan 0.1°.

Since the best geometric shape for a flux-gate sensor is the toroidal one, the sensor wasconstituted of two torus each with two copperwindings. Each nucleus measures two geomag-netic field components: the first sensor meas-ures horizontal elements X and Y while the sec-ond one measures Y and Z components. In thisway two different measurements of Y compo-nent are obtained. This opportunity is used tominimize the noise using appropriate software.

In order to choose the best material forthe sensor realization, measurements of back-ground noise in crystalline and amorphousmaterials have been implemented in different


97

environmental conditions. With respect to crys-talline materials, amorphous materials werefound to satisfy the following peculiar charac-teristics [Igoshin and Sholpo, 1979]:

1. 5-10 times lower magnetostriction coeffi-cient

2. lower Barkhausen noise3. lower general noise (1/f)

The analysis of the collected data in factshows best results by materials with low level ofinternal structure of crystallization. In particularthe VITROVAC 6025 showed the best perform-

98


Figure 1. Synoptic scheme of the tri-axial two core magnetometer sensor.

ance.The two torus size and the choice of the

carrying structure, are extremely critical factors.Each torus was realized using a 27 mm diameteraluminum hold on which 10 layers of amor-phous material 25 µm wide have been wrapped.

The toroidal sensor linearity dependsessentially on the surrounding magnetic field.Therefore in order to minimize the non-linearityerror the torus must be constantly immersed in anull field. To realize this condition the nucleushas been surrounded with proper size coils (on aquartz support) in order to create a magneticfield always opposite to the measured one. Themeasurements of the electric currents in the

compensation coils can give preliminary valuesfor the X, Y and Z DC base line current with anerror less the 10 nT. In order to check the stabil-ity of the vector magnetometer, these values canbe used to compare the estimated total intensityof the field (from X, Y and Z) with the intensitymeasured independently by a proton precessionmagnetometer. The principal instrumental char-acteristics are summarized in table I.

3. L’Aquila preliminary test

Magnetic field measurements were con-ducted for a long period to determine the geo-


99

Figure 2. Project of the gimbals of the sensor. One of the two biassial parts of the sensor is visible inthe lower part of the figure.

Table I. Characteristics of the autolevelling vectorial magnetometer.

magnetic field transform matrix A from the autolevelling magnetometer station to the referencesystem of the observatory magnetometer. Theobservatory magnetometer has the same charac-teristics of the suspended one. The magnetome-ters were placed 40 km far apart.The experiment aim was the determination ofthe nine elements of the geomagnetic fieldtransform matrix A.The elements of this matrix take into accountthe reciprocal orientation of the two sensors, thenon-orthogonality of the axes and the two sen-sor transfer function differences.

In figure 3 the geomagnetic field compo-nents as recorded at the different sites are report-ed. In figure 4 and 5 the non diagonal elementsof A when the magnetometers are in the samesite and in two different sites are shown respec-tively. In the ideal case in which the sensors areperfectly aligned, the transfer functions are thesame, A is an unit matrix. In a more realistic sit-uation, the non diagonal elements of A are dif-ferent from 0 and the diagonal elements are dif-ferent from 1.

Once the installation of the magnetome-ters is realized, 120 samples are sufficient inorder to define the matrix elements Aij with anerror less than the experiment indeterminate-ness.

The magnetic field H of the suspendedmagnetometer can be written in the fixed mag-

netometer coordinate system thanks to A:

Hx=A11Hrx+A12Hry+A13HrzHy=A21Hrx+A22Hry+A23HrzHz=A31Hrx+A32Hry+A33HrzWhere X1...Xn, Y1...Yn e Z1...Zn are the sus-pended magnetometer measurements andXr1...Xrn, Y1r...Yrn e Zr1... Zrn are the observa-tory magnetometer measurements, n=120 andA11, A22 e A33 are the diagonal elements of A

that in this case are constant. Aij depend on theorientation of the reference frame only in thehypothesis that the geomagnetic field variations

100


Figure 3. Geomagnetic field component X, Y and Z as recorded in two different sites placed 40 km farapart. In the first site the new autolevelling magnetometer (a in the figure) while in the second site anobservatory magnetometer were installed (o in the figure).

at the two sites are the same. This hypothesisunfortunately is not true if we choose two sitesfar apart also few kilometers. Necessarily wecan find a local geomagnetic field anomalousbehaviour using these non diagonal elementsonly fixing some parameters in the preliminaryoperations considering that, thanks the magne-tometer characteristics, they will not changeduring the measurements.

In figure 4 and 5 the values of the non

diagonal elements are reported: as we can see,they are complex functions depending essential-ly on the non homogeneity of the geomagneticfield and on inductive phenomena (figure 4: themagnetometers are in the same site, figure 5 themagnetometers are 40 km far apart).

These considerations suggest that therequired procedures to evaluate the backgroundnoise elements are very laborious also in thesimple case in which soil deformations are not


101

Figure 4. Plot of non-diagonal elements of A matrix when the magnetometers are placed in the samesite.

Figure 5. Plot of non-diagonal elements of A matrix when the two magnetometers are placed in twodifferent sites 40 km far apart.

present.

4. Conclusions

The magnetometer described in this paperwas proposed in order to compensate the move-ments of the ground in volcanic areas. The sen-sor was suspended using a compound gimbalswhile the problem concerning the azimuthalmovements of the sensor frame was compensat-ed monitoring the sensor orientation using aremote reference frame (installed far from thevolcanic area). The proposed method is basedon the determination of the nine geomagneticfield transform matrix elements every 120 min-utes. The plots of these parameters can indicatepossible local anomalies linked to the geomag-netic filed variations and to ground movementsat the reference system. Ground movements(earthquake) at the volcanic station cannot dis-turb the measured geomagnetic components dueto the auto levelling characteristics of the mag-netometer.

The characteristics of the anomalies can bedefined considering various contributions of thebackground noise using A matrix. The non-diagonal elements of the matrix are complexfunctions of the anomaly characteristics. Theanalysis of the factors of a geomagnetic anom-alous behaviour can give important informationin order to choose a procedure to investigate sig-nals and consequently isolate the anomalies.

Acknowledgements

This research was partially supported by theGNV through the Epot project.

References

Avdeev, D. B., Kuvshinov, A. V. and Pankratov, O.V, (1997). Tectonic process monitoring byvariations of the geomagnetic field absoluteintensity, Annali di Geofisica, 40, 2, 281.

Davis, P. M., Stacey, F. D., Zablocki, C. J. and Olson,J. V., (1979). Improved Signal Discriminationin Tectonomagnetism: discovery of aVolcanomagnetic effect at Kilauea, Hawaii.Physics of the Earth and Planetary Interiors,19, 331.

Igoshin, L. A. and Sholpo, L. E., (1979). Effects ofPressure on the Magnetic state of the Rocks.Izvestiya, Earth Physics, 15, 9.

Johnston, M. J. S. and Stacey, F. D., (1969).Transient Magnetic Anomalies accompanyingVolcanic Eruptions in New Zealand, Nature,224, 1289.

Johnston, M. J. S. and Stacey, F. D., (1969). Volcano-

magnetic effect observed on Mt. Ruapehu,New Zealand. Journal of GeophysicalResearch, 75, 6541.

Johnston M. J. S. and Muller R. J., (1981). Volcano-magnetic observations during eruptions May-August 1980. U.S. Geologhycal Survey, 1250,183.

Johnston, M. J. S. and Muller, R. J., (1987).Seismomagnetic Observation During the 8July 1986 Magnitude 5.9 North Palm SpringsEarthquake, Science, 237, 1201.

Meloni, A., Mele, G. and Palangio, P., (1998).Tectonomagnetic field observations in centralItaly 1989–1995, Physics of the Earth andPlanetary Interiors, 105, 145.

Muller, R. J. and Johnston, M. J. S., (1981).Precision of magnetic measurements in a tec-tonically active region, Trans. Am. Geophys.Un., 62, 1054.

Rikitake, T. and Yokoyama, I., (1955). VolcanicActivity and Changes in Geomagnetism.Journal of Geophysical Research, 60, 2.

Sasai, Y., Zlotnicki, J., Nishida, Y., Uyeshima, M.,Yvetot, P., Tanaka, Y., Watanabe, H. andTakahashi, Y., (2001). Evaluation of electricand magnetic field monitoring of Miyake-jimavolcano, Central Japan, Annali di Geofisica,44, 239.

Sasai, Y., Uyeshima, M., Zlotnicki, J., Utada, H.,Kagijama, T., Hashimoto, T. and Takahashi,Y., (2002). Magnetic and electric field obser-vations during the 2000 activity of Miyake-jima volcano, Central Japan, Earth andPlanetary Science Letters, 769.

Stacey, F.D., Barr, K.G. and Robson, G.R., (1965).The Volcano-magnetic Effect. Pure andApllied Geophysics,62, 96

Zlotnicki, J., Le Mouel, J. L., Delmond, J. C.,Pambrun, C. and Delorme, H., (1993).Magnetic variations on Piton de la Fournaisevolcano. Volcanomagnetic signals associatedwith the November 6 and 30 eruptions.Journal of Volcanology and GeothermalResearch, 56, 281.

Zlotnicki, J. and Bof, M., (1996). Volcanomagneticsignals associated with the quasi-continuousactivity of the andesitic Merapi volcano(Indonesia): 1990-1995. Physics of the Earthand Planetary Interiors, 105, 119.

102


Technoplogical Improvements in GravityMonitoring of Active Volcanoes

Gennaro Budetta, Daniele Carbone,Filippo Greco

Istituto Nazionale di Geofisica e Vulcanologia –Sezione di Catania

Piazza Roma 2, 95123 - Catania, Italy

AbstractThe conditions at a site close to an active

crater are far from the clean, ideal laboratoryand so it is quite difficult to attain the requiredprecision in the continuous gravity data.Because of this, continuous gravity observationat active volcanoes have not developed asquickly as other geophysical techniques.However, technological improvements in recentyears have allowed most of these difficulties tobe overcome. Since 1998, to couple the networkfor discrete measurements and extend the rangeof periods of measurable anomalies down to afew minutes, three continuous gravity stations atdistances from the active craters rangingbetween 1 and 10 Km have been installed atMount Etna. The stations, equipped withLaCoste and Romberg spring gravimeters,acquire, at 1 datum/min sampling rate, gravityand other parameters which are used to reducethe gravity signal in order to assess the volcano-related signal. To improve the possibilities ofcontinuous gravity observation at active volca-noes and to achieve a better signal/noise ratiowe have developed (i) a special station setupaimed to reduce the influence of external pertur-bations on the gravity sensor; (ii) a softwareunder the LabVIEW® environment to quicklyanalyse long gravity data-sequences and (iii)algorithms aimed to model how the meter out-put depends on the interfering meteorologicalsignals.

Key words microgravity - volcano monitoring -continuous recording - data reduction - Mt. Etna

Introduction

During the past few years, microgravitystudies at active volcanoes have becomeincreasingly important and have yield valuableresults. Numerous studies have directly associ-ated the systematic variations of the gravityfield to volcanic processes [Jachens and Eaton1980; Eggers 1983; Rymer and Brown 1987;Sanderson 1982; Rymer et al. 1993; 1995;

Budetta and Carbone, 1998; Budetta et al. 1999;Carbone et al. 2003a].

Temporal gravity changes at volcanicareas are usually detected by discrete (repeated)measurements. Discrete gravity measurementshave been carried out at Mt Etna since 1986.The Etna gravity network (Fig. 1) for discretemeasurements is now composed of about 70 sta-tions 0.5 to 3 km apart, covers an area of about400 km2 and consists of four integrated subar-rays [Budetta and Carbone, 1998; Budetta et al.1999; Carbone et al., 2003a]. The quality andspace resolution of gravity data acquired alongthe Etna network through discrete measure-ments is now more than suitable for assessingmass redistributions occurring over a widerange of depths along Etna’s plumbing system(roughly between 8 km b.s.l and a few hundredmeters below the surface). The limit of this tech-nique is the time interval at which the networksare reoccupied, ranging typically from severalweeks to one year, which allows only long-peri-od variations, related to long term magmaticprocesses, to be recorded and studied.Shortcomings such as snow coverage on thesummit zone of high volcanoes often makegravity changes not identifiable on a timescaleof less than 6 months during the winter time. Ifone also considers the need to reduce the expo-sure of personnel in active areas, the importanceof developing effective continuous gravity mon-itoring appears clear.

Continuous gravity observations can fur-nish excellent temporal resolution, with meas-urements collected every second if desired, butthe spatial resolution is limited by the number ofinstruments available. Given the high cost ofgravimeters, it is necessary to place the instru-ments in a position where there is the greatestchance of detecting meaningful gravity changes.Often this is close to an active crater.

Continuous gravity observations aimed tomonitor active volcanoes have been scarcelyperformed in the past [Davis, 1981; De Meyer etal. 1995; Berrino et al. 1997] because of thelogistic difficulties of running them in non-lab-oratory conditions. However, technologicalimprovements in recent years have allowedsome of the difficult linked to the inadequacy ofthe site to be overcome.

The combined use of discrete and contin-uous gravity measurements is an unique toolboth for studying the internal dynamic of a vol-cano and for surveillance purposes [Carbone,2001; Carbone et al. 2003b]. Discrete measure-ments allow both the actual magnitude of thesubsurface mass change and the position andspatial characteristics of the source to be


103

the most expensive item). Some sort of buildingis also essential, but it can be very basic provid-ed that it has a firm basement floor and providesprotection from the elements. We have devel-oped a setup for continuous gravity measure-ments at active volcanoes which consists of 3components [Budetta et al. 2002; Carbone et al.2003b]: the power system, the acquisition sys-tem and the transmission system (Fig. 2).

The power system comprises equipmentto generate, store and feed electricity to theinstrumentation. It employs solar panels con-nected to trickle-charged batteries. The powerrequirement of the whole setup is approximately12 W assuming external temperatures around thefreezing mark; four 115 Ah batteries can thusmaintain the system for at least 10 days withoutadditional power input. To provide a constantpower supply to the feedback of continuouslyrecording L&R meters (must be within a fewhundredth of a Volt not to affect the quality ofdata) a dc-dc converter coupled with a low-dropout tension stabilizer is used. The acquisi-tion system comprises the gravity meter itself,equipped with any feedback system [Torge,1989; VanRuymbeke, 1989] and outputting ana-logue signals representing the feedback forceand the long and cross levels, and sensors for theatmospheric temperature, pressure and humidity.

For a gravity meter that is to be left operatingwithout intervention for extended periods oftime, instrumental drift [Torge, 1989] maybecome important (if the instrument driftsbeyond the range of operation of the feedbacksystem). The meters installed at Etna’s continu-ous stations are thus equipped with remote con-trolled stepper motors to reset them. The wholeacquisition system is placed inside a thermallyinsulating polystyrene container. Data areacquired every second by CR10X dataloggers byCompbell Scientific. The average over 60 meas-urements is than calculated and stored in thesolid-state memory of the data logger (at 1datum/min). Data, after being temporally stored,are dumped automatically every 24 hours by thetransmission system which employs a cellularphone. Using a suitable software on a remotecomputer is also possible a) to remotely activatethe stepper motor which turns the meter dialallowing the meter to be reset and b) to monitorin real time all the parameters recorded.

3. Improving the signal-to-noise ratio of con-tinuous gravity sequences

Gravity changes on active volcanoes arecaused by the redistribution of subsurface mass-


105

Figure 2. Block diagram showing the three component setup (power supply system, acquisition sys-tem and transmission system) developed for continuous gravity stations at Mt. Etna.

es and by changes in surface elevation as theedifice inflates and deflates. To evaluate thecontribution of subsurface mass redistribution,therefore, it is necessary also to monitor the ele-vations of the measuring stations. The elevationof each continuous gravity station is not system-atically monitored. Nevertheless, discreteground-deformation surveys routinely per-formed on Etna provide enough data to evaluateEtna’s vertical deformation to a detail suitablefor our purposes. Local height variations onEtna are usually too small to significantly affectsurface gravity measurements [Budetta andCarbone, 1998; Budetta et al. 1999; Carbone etal. 2003a]. Accordingly, where adequate eleva-tion data are not available, large gravity changescan be assumed to be the result only of subsur-face variations in mass.

Continuous gravity sequences acquiredon volcanoes can be split into two main compo-nents: i) anomalies linked to the activity of thevolcano itself (useful signal) and ii) signal dueto tides, instrumental and meteorological effects(assumed as noise).

The improvement of the signal-to-noiseratio is fundamental to recognize the anomaliesdue to volcanic activity within a gravitysequence. To achieve this goal the three mainpath described below have been followed.

3.1. Reducing the influence of external pertur-bations

To assess reliable gravity sequences, it is

vital to measure all the perturbations which canaffect the gravity signal (tilt, temperature, pres-sure, humidity, etc.) at each station and to suit-ably remove their effect from the gravity signal.Ours and other Author’s experience has shownthat gravimeters are affected mostly by temper-ature changes which can cause strong apparentgravity anomalies. To reduce the effect ofatmospheric temperature changes on the gravitysignal, we place the whole acquisition systeminside a two level thermally insulating poly-styrene container. The gravity meter togetherwith a temperature sensor is kept on the lowerlevel and the data logger on the upper level in awatertight PVC container (IP65 standard). Bothcompartments are dosed with silica gel. Thetemperature inside the low level of the box ismaintained at 15-20°C above ambient; this strat-egy also reduces the power consumption ofgravity meters (whose sensor usually works atabout 50°C). A new system for actively ther-mosetting the environment around the meter isalso under development.

3.2. Designing software to quickly analyse longgravity data-sequences

We have designed an advanced softwarepackage which allows the large data sets comingfrom the remote stations to be analyzed quicklyand with a high level of automation. The soft-ware allows a quick visual pre-analysis which isvery important for addressing further analysissteps (i.e. strategies for removing the effect of

106


Figure 3. Interface of the program developed under LabVIEW® for real-time (pre-) analysis and pres-entation of data coming from each continuously recording gravity station. Rectangular buttons are con-trols, rectangular windows with arrows are selectors, other windows are indicators.

external perturbations). Since this software isquite easy to implement, it allows changes in thecontinuously recording array to be accommo-dated on one hand, and can be used to handledata from other similar arrays on the other.

The above software package has beendesigned under LabVIEW® (Laboratory VirtualInstrument Engineering Workbench), a softwarewhich features a graphical programming envi-ronment and all the tools needed for data analy-sis and presentation.

Great care was taken in designing the pro-gram interface to make it usable even by theinexperienced operator and to allow a quasi-real-time visualization of the reduced sequenceswhich is vital for volcano monitoring purposes.LabVIEW® features a large library of analysistools (spectra, Furier Transform, filters, curvefit, probability and statistic, etc.) through whicheven complex analyses on large data sequencescan be performed in near real time.

The program features controls to performthe following operations:

• choose a temporal window within which allsubsequent operations will be performed;• correct the gravity data for the earth tide;

• correct the data for the instrumental drift(modelled as a linear or polynomial curve);• filter unwanted frequencies from the datasequences;• performs time-domain to frequency-domain transformations (spectra).

Figure 3 shows the interface of this pro-gram (data refer to PDN station). The programinterface consist of four charts. The top one dis-plays gravity whereas the parameter to be dis-played in the other ones can be set by the oper-ator via menu rings on the right side of eachchart (the default from top to bottom is: rawgravity, theoretical tide, X level, Y level). Alsothere is a rectangular frame on the side of eachchart where the list of all the operations per-formed on the data presented in the chart arereported.

3.3. Modelling how the meter output depends onthe interfering meteorological signals

Meteorological perturbations (tempera-ture, pressure, humidity) affect continuous grav-ity sequences and give rise to a pseudo-signalwhich is often stronger than the useful one.


107

Figure 4. Data set from three gravimeters which worked continuously for about 50 days at a site faraway from active zones. The figure shows (a) the reduced gravity sequences, after removal of the bestlinear fit and the theoretical Earth Tide and (b) the reduced gravity sequences, after removal of the bestlinear fit, the theoretical Earth Tide and the effect of atmospheric temperature modelled through aNeuro-Fuzzy algorithm. Final residuals are within a few µGal peak-to-peak.

To remove the effect of these perturba-tions is not easy given that the transfer functionsare frequency-dependent and are different foreach gravimeter employed. We have tested var-ious algorithms to model the effect of meteoro-logical perturbations on the gravity signal.Using a one-year-lasting data-set from SLN sta-tion, Andò and Carbone (2001) showed that a -linear (Neuro-Fuzzy) algorithm can be used tomodel satisfactorily how the meter outputdepends on atmospheric temperature and pres-sure.

The same algorithm was also tested overa data set from three gravimeters which workedcontinuously for about 50 days at a site far awayfrom active zones. After accomplishing thereduction of the gravity series, residuals werewithin a few µGal peak-to-peak, thus confirm-ing the capabilities of the Neuro-Fuzzy algo-rithm (Fig. 4a, b).


At Mt Etna we have developed a new sys-tem for continuous gravity monitoring. Throughthe experiments accomplished since 1998 manysteps forward have been made towards the reg-ular acquisition of high-quality data. We havedesigned both a suitable station setup and algo-rithms to reduce the signal for the effect of per-turbations.

Our current target is to consolidate ourexperience (in particular as for the algorithmsfor continuous data reduction) using the longersequences now available. Once the gravity sig-nal from continuously recording stations is suit-ably reduced for the effect of external perturba-tions (which proved to be stronger by one orderof magnitude than the volcanic effect) eventswith amplitude and/or characteristic anomalouswith respect to the “normal” signal will be evi-denced within different frequency bands.Possible time correlations between such anom-alous items and the volcanic activity will be alsotentatively evidenced to define gravity forerun-ners of paroxysmal eruptive episodes.

We also expect the combined use of dis-crete and continuous gravity measurements toprovide, through the detection of phenomenawith a wide range of evolution rates (periodsranging from minutes to years), both substantialimprovements in the knowledge of the dynam-ics of the shallow plumbing system of the vol-cano and the identification of any possible grav-ity transient before and during volcanic erup-tions.

Acknowledgements

This research was supported by the Epot projectof the GNV.

References

Andò, B. and Carbone, D., (2001). A Methodologyfor Reducing the Signal from a ContinuouslyRecording Gravity Meter for the Effect ofMeteorological Parameters. IEEETransactions on Instrumentation andMeasurement, 50 (5), 1248-1254.

Berrino, G., Corrado, G., Magliuolo, R. andRiccardi, U., (1997). Continuous record of thegravity changes at Mt. Vesuvius. Annali diGeofisica, Vol. XL. N. 5, 1019-1028.

Budetta, G. and Carbone, D., (1998). Temporal vari-ations in gravity at Mt Etna (Italy) associatedwith the 1989 and 1991. Bull. Volcanol., 59,311-326.

Budetta, G., Carbone, D. and Greco, F., (1999).Subsurface mass redistribution at Mount Etna(Italy) during the 1995-96 explosive activitydetected by microgravity studies. Geophy. J.Int., 138, 77-88.

Budetta G., Carbone D., Greco F. (2002).Installazione ad alta quota di una stazionegravimetrica in telemetria: applicazioniall’Etna. Quaderni di Geofisica, n. 23 – 8 pp.

Carbone, D., (2001). Gravity monitoring of MountEtna (Italy) through discrete and continuousmeasurements. PhD Thesis, The OpenUniversity, Milton Keynes, UK.

Carbone, D., Budetta, G. and Greco, F., (2003a).Possible mechanisms of magma redistributionunder Mt. Etna during the 1994-1999 perioddetected through microgravity measurements.Geophys. J. Int., 152, 1-14.

Carbone D., Budetta G., Greco F. and Rymer, H.,(2003b). Combined discrete and continuousgravity observations at Mt. Etna. J. Volcanol.Geotherm. Res., 2581, 1-13.

d’Oreye, N., Ducarme, B., Hendicks, M., Laurent,R., Somerhausen, A. and Van Ruymbeke, M.,(1994). Tidal gravity observations at MountEtna volcano. In: Volcanic deformation andtidal gravity effects at Mt. Etna, Sicily, FinalReport. Project no. ERB40002PL900491, pp60-80, EEC SCIENCE.

Davis, P. M., (1981). Gravity and tilt earth tidesmeasured on an active volcano, Mt Etna,Sicily. J. Volcanol. Geotherm. Res., 11, 213-223.

De Meyer F., Ducarme B. and El Wahabi A., (1995).Continuous gravity observations at MountEtna (Sicily). IUGG XXI General Assembly,Boulder, Colorado, July 2-14.

Eggers, A. A., 1983. Temporal gravity and elevationchanges at Pacaya volcano, Guatemala, J.Volcanol. Geotherm. Res., 19, 223-237.

El Wahabi, A., Ducarme, B., Van Ruymbeke, M.,d’Oreyè, N. and Somerhausen, A., (1997).Continuous gravity observations at MountEtna (Sicily) and Correlations between tem-perature and gravimetric records. Cahiers duCentre Européen de Géodynamique et de

108


Séismologie 14, 105-119.Jachens, R. C. and Eaton, G. P., (1980). Geophysical

observations of Kilauea volcano, Hawaii, 1.Temporal gravity variations related to the 29November, 1975, M = 7.2 earthquake andassociated summit collapse. J. Volcanol.Geotherm. Res., 7, 225-240.

Rymer, H. and Brown, G. C., (1987). Causes ofMicrogravity change at Poás volcano, CostaRica: an active but non-erupting system.Bull. Volcanol., 49, 389-398.

Rymer, H., Murray, J.B., Brown, G.C., Ferrucci, F.and McGuire, J., (1993). Mechanisms ofmagma eruption and emplacement at Mt Etnabetween 1989 and 1992. Nature 361, 439-441.

Rymer, H., Cassidy, J., Locke, C.A. and Murray, J.B.,(1995). Magma movements in Etna volcanoassociated with the major 1991-1993 lavaeruption: evidence from gravity and deforma-tion. Bull. Volcanol., 57, 451 461.

Sanderson, T.J.O., (1982). Direct gravimetric detec-tion of magma movements at Mount Etna.Nature, 297, 487-490.

Torge, W., (1989). Gravimetry. Ed. Walter deGruyter., Berlin-New York.

VanRuymbeke, M., (1989). A new Feedback Systemfor Instruments Equipped with a CapacitiveTransducer. In Proceedings of 11th

International Symposium on Earth Tides, pp51-60, Helsinki, 1989.


109

Fabrication of IPMC andCharacterization of its SensorialProperties: Preliminary Results

Claudia Bonomo1, Ciro Del Negro2, Luigi Fortuna1

and Salvatore Graziani1

1Dipartimento di Ingegneria Elettrica, Elettronica e deiSistemi, Università di Catania, Italy

2Istituto Nazionale di Geologia e Vulcanologia, Sezionedi Catania, Italy

AbstractIonic Polymer Metal Composites

(IPMCs) are innovative materials obtained bydeposition of a metal on a ionic polymer mem-brane. IPMCs bend, when an electric field isapplied along their thickness, and vice versagenerate a voltage when mechanicallydeformed. Hence, it makes sense to investigatethe opportunity to use IPMCs to build eitheractuators or sensors. A full comprehension ofthe behavior of IPMCs sensing capability and acorresponding metrological characterizationcould be useful for their application to buildsensing elements in the geophysical field, e.g. torecord earthquakes and study their nature, espe-cially because these materials are able to surveyalso very small displacement, at very low fre-quencies. To this aim a laboratory was equipped.Applying some variations to the standard fabri-cation procedure, many samples were fabricatedand tested in order to improve the performanceof the material. Moreover, some results of theanalysis of sensing properties of an IPMC stripare presented. Experimental data suggest thatthe output voltage is roughly linear in deforma-

tion. Moreover, a nonlinear behavior seems tooccur in particular working conditions. Toauthors’ knowledge such a behavior neverbefore has been reported in literature.

Key words ionic polymer metal composites -actuators - sensors

1. Introduction

Ionic Polymer Metal Composites(IPMCs) are innovative materials obtained bydeposition of a metal on a ionic polymer mem-brane [Arena et al., 2002]. Some details on theirstructure are necessary in order to understandtheir sensing properties.

Ionic polymers have inner ionizablegroups. These groups dissociate in a fixed partand in a movable one in a variety of solventmedia. Usually, the fixed groups have negativecharge while cations can freely move. Bymechanically bending the material it is possibleto change the distribution of the charges withrespect to the membrane neutral axis (see Fig.1): the applied stress will contract one side ofthe membrane while will spread the other, themobile ions will move consequently toward theregion characterized by a lower charge densityparasitically carrying the solvent molecules (i.e.deionized water).

A deficit of negative charges and anexcess of the positive ones will therefore resultin the expanded side. In the contracted side theopposite will occur. This phenomenon producesa voltage gradient collected at the metal elec-trodes. It is intuitive as this property results in asensing capability [Shahinpoor et al., 1998].

In the following some suggestions to


111Figure 1. Effect of stress applied to the IPMC strip on charge distribution.

improve the quality of the electrodes and, as aconsequence, the performances of the materialare given. Moreover, a system for the character-ization of the sensing properties of an IPMCstrip is described. It allows to investigate thedependence of the voltage generated within thestrip on the imposed deformation.

2. Variations to the standard fabrication pro-cedure

One way to fabricate IPMCs refers to thestandard procedure [Keisuke Oguro, 2003] todepose the metal layers on the polymer surface.Many matters are with this procedure. First ofall the metal particles distribution on the poly-mer surface does not result uniform. This isbecause of the sandblasting using emery paperand the formation of metal clusters. These phe-nomena cause an increase of the surface resist-ance that means a bad quality of the electrodes.

To reduce the first cause, the sandblasting

was obtained by mechanical pressure of theemery paper on the polymer, without scratchingthe surface; in order to transfer the uniformglass chips distribution. The results of theapplied method are shown in Fig. 2.

As regards the second problem, an anti-clotting additive was added to the solution dur-ing the plating steps. Also in this case the resultswere good and they are shown in Fig.3.

3. Experimental setup

A system for the characterization of thesensing properties of an IPMC strip has beenbuilt and it is here described. It allows to inves-tigate the dependence of the voltage generatedwithin the strip on the imposed deformation.

The experimental analysis was performedon a strip built by using the ionic polymerFlemionTM (by Asahi Glass) with gold deposedon both sides [Bar-Cohen et al., 2002]. The sam-ple was 38 mm long by 6 mm large; its thick-

112


Figure 2. Sandblasting effects: microscopic images (20x) of the IPMC surface. To the left a samplefabricated by the standard procedure; to the right a sample where the sandblasting was obtained bymechanical pressure of the emery paper on the polymer, without scratching the surface. The reader cannotice the difference in the uniformity of the metal distribution.

Figure 3. Anti-clotting additive effects: microscopic images (100x) of the IPMC surface. To the left asample fabricated by the standard procedure; to the right a sample obtained using an anti-clotting addi-tive.

ness was about 200 µm.Before each measuring survey, the strip

was opportunely hydrated by immersion indeionized water. In fact a dependence of thesensing properties on the solvent contents wasnoticed and will be described in the following.The hydrated sample presented a weak curva-ture probably caused by a non uniform initialdistribution of the ions.

The experimental setup is composed of asystem to impose a displacement to the mem-brane tip and a circuit to amplify resulting out-put voltage. The schematic of the experimentalsetup is shown in Fig. 4.

The strip was fixed from one end in a can-tilever configuration by a clip with cupper con-tacts, wired to the electronic circuit. The otherend was pinned to the wiper of a linear poten-tiometer. The wiper was moved by a rod con-nected to a DC motor working at different fre-quencies, as shown in Fig. 5.

The strip was inserted at all times in sucha way that its natural curvature was always inthe positive direction of the x’ axis (Fig. 6).

While the motor turns, it moves the rod and therotational movement is converted in a translato-ry one by the wiper of the potentiometer andconsequently the membrane is bent on bothdirection.

This causes both a production of a voltagesignal VIPMC across the membrane thicknessand a variation of the voltage V1 across thepotentiometer. The membrane output signal wasopportunely amplified. The gain was fixed to270, in order to raise the voltage magnitudefrom less than 1 mV to about 300 mV. Then theamplifier output was acquired by the dataacquisition board AT-MIO 16E-10 Series(National Instruments) from a PersonalComputer. The potentiometer was used both tomove the strip and to transduce its position intoa voltage signal, as shown in Fig. 6. It must benoticed that, based on the chosen referencedirections, a positive strip displacement corre-sponds to a negative voltage across it.

A number of data acquisition sessionswere performed, tuning the DC voltage appliedto the motor and hence changing the frequency


113

Figure 4. Schematic of the experimental setup used to characterize the sensing properties of an IPMCstrip.

Figure 5. Photo of the mechanical system usedto force the displacement on the IPMC strip andof the amplification circuit for the sensor out-put.

Figure 6. Electric circuit to convert the IPMCdisplacement into a voltage signal to be relatedto the voltage generated across the strip. Basedon the chosen reference directions, a positivestrip displacement corresponds to a negativevoltage across it.

of the IPMC strip excitation signal.Actually, the excitation point on the strip

varies while the rod moves the cursor of thepotentiometer. However it is possible to neglectthis phenomenon being the distance δ betweenthe two farthest excitation points, that is a meas-ure of this variation, much smaller than the dis-tance between the fixed end and the excited one.The wiper displacement, referred to the centralposition, was +1.2 cm.

4. Data Analysis

One thousand samples per second wereacquired for each frequency and each acquisi-tion lasted ten seconds, i.e. ten thousand sam-ples for each acquisition sessions were collect-ed. The range of the tested frequencies spannedfrom 1.0 Hz to 10.0 Hz, with steps of 0.5 Hz.These values were fixed because of the inertialconstraints imposed by the DC motor. Recordeddata were analyzed by using LabVIEW soft-ware.

The voltage signal V1, picked up by thewiper of the potentiometer, is a wave oscillatingapproximately in the range 2.0 ÷ 6.0 V. Thissignal was translated into a symmetric voltageV2 and then attenuated to the range –1.2 ÷ 1.2 Vin order to give the position of the membrane tipx’ directly in centimeters.

A second manipulation block was devel-oped to estimate the displacement of a fixedpoint of the strip. Referring to Fig. 7, it corre-sponds to the estimation of the displacement xbased on x’. Then

x =

5. Results

Some typical examples of collected data sets aredescribed in the following. In particular theinfluence of the input signal frequency is shownin Fig. 8. Both the time plots of the input x andof the output VIPMC signals and the correspon-ding inputoutput plot are shown. In Fig 8a theinput signal frequency is 3.69 Hz and in Fig. 8bit is 5.6 Hz.

It can be noticed that the potentiometeroutput shows a threshold phenomenon at itsmaximum value. This effect is due to themechanical resistance met from the rod to invertthe slider’s motion direction and it is more evi-dent at the lower frequencies. The presence of anon-linearity has to be pointed out on the sensoroutput signal each time the wiper crosses the

zero position superimposed to a ringing signal.Also, the non-linearity effect looks more evidentat lower frequencies. The phenomenon could beattributed to the initial deformation of the strip.

The analysis of acquired data suggeststhat the input-output peak-to-peak amplituderatio is constant in the considered range of fre-quencies.

Also, it is possible to observe the pres-ence of a time delay between the imposed dis-placement and the voltage response of themembrane. The time delay td between the stim-ulus and the sensor response is frequencydependent as it can be noticed in the data report-ed in Fig. 8. It seems to decrease as the excita-tion frequency increase. Indeed as regards thecase (a) td is 220 ms, and in the case (b) td is 160

114


(1)

Figure 7. Dependence of the displacement x ofa fixed point of the strip on the displacement x’forced by the potentiometer wiper position.

Figure 8. Time plots of the input x and of theoutput VIPMC signals and the correspondinginput-output plot: (a) at 3.69 Hz and (b) at 5.6Hz.

ms.The influence of the hydration level on

the strip behavior was also addressed. For thesake of comparison the same set of input signalfrequencies was considered also in the case ofthis analysis.

In Fig. 9 the time plots of the input x andof the output VIPMC signals and the relativeinput-output plot when the strip is partiallydehydrated and the input frequency is 5.6 Hz areshown (see Fig. 8b).

6. Conclusions

In this paper some preliminary resultsabout the sensing properties of an IPMC striphave been presented. A system to gather therequired data has been built.

The dependence of a strip of IPMC onboth the input signal frequency and on thehydration level of the strip has been addressed.

Further work to extend the frequencyrange of the acquired data in order to bettercharacterize the sensor is in progress.

A full comprehension of the behavior ofIPMCs sensing capability and a correspondingmetrological characterization could be usefulfor their application to build sensing elements inthe geophysical field, e.g. to record earthquakesand study their nature, especially because thesematerials are able to survey also very small dis-placement, at very low frequencies.

Acknowledgements

The work was developed in the frame of theTecnoLab, the laboratory for the technologicaladvance in geophysics organized by DIEES-UNICT and INGV-CT. This research was sup-ported in part by the Epot project of the GNV.

References

Arena, P., Bonomo, C., Fortuna, L. and Frasca, M.(2002). “Electro-Active Polymers as CNNactuator for locomotion control”,Proceedings of ISCAS 2002, Phoenix, May26-29.

Yoseph Bar-Cohen1, Xiaoqi Bao, Stewart Sherrit andShyh-Shiuh Lih (2002). “Characterization ofthe Electromechanical Properties ofIonomeric Polymer-Metal Composite(IPMC)”, Proceedings of the SPIE SmartStructures and Materials Symposium, EAPADConference, San Diego, CA, March 18-21,2002

Keisuke Oguro: “Preparation Procedure of IonicPolymer Metal Composite membrane”, webpage http://ndea.jpl.nasa.gov/nasa-nde/lom-mas/eap/IPMC_PrepProcedure.htm;

M. Shahinpoor, Y. Bar-Cohen, T. Xue, J. O. Simpson,and J. Smith (1998). “Ionic Polymer-MetalComposites (IPMC) as Biomimetic Sensorsand Actuators”, Proceedings of SPIE’s 5thAnnual International Symposium on SmartStructures and Materials, San Diego, CA,March 1-5, 1998.


115

Figure 9. Time plots of the input x and of theoutput VIPMC signals and the relative input-out-put plot when the strip is partially dehydratedand the input frequency is 5.6 Hz are shown(see Fig. 8b).

Beta Version of MADAP: AModularArchitecture for MAgnetic DAtaProcessing Acquired by Volcanic

Monitoring Networks

Gilda Currenti1,2, Ciro Del Negro1, Luigi Fortuna2,Salvatore Graziani2, Rosalba Napoli1,

Alessandro Rizzo3 and Annamaria Vicari1,2


2Università di Catania – Dipartimento di IngegneriaElettrica Elettronica e dei Sistemi, Italy

3Politecnico di Bari – Dipartimento di Elettrotecnica edElettronica, Italy

AbstractThe preliminary version of a modular softwarearchitecture is presented. It is devoted to theautomated elaboration of magnetic data record-ed at volcanic sites. To improve the effective-ness of volcano monitoring, it is essential thatdata gathered over a volcanic area are processedquickly and effectively. To pursue this goal, ourLaboratory of Geomagnetism has been develop-ing an automated system of data acquisition andreduction for magnetic data, called MADAP (byMAgnetic DAta Processing). The softwareapplication, designed under Visual C++, con-sists of three modules. The first, calledMagTalk, is a package of procedures for theacquisition and transmission of signals fromcontinuously recording sensors to a centralobservatory. The second, called MagTool, con-tains a set of analysis routines able to reduce theincoming data, produce interpretable parametersand store the data in permanent files. The third,called MagWarn, is a methodology devoted tocomparing the calculated parameters with pre-scribed limits; a warning signal is displayed ifthe limits are exceeded.

Keywords volcano monitoring - data-handlingsystem - volcanomagnetic signals - Mt. Etna

1. Introduction

In the recent past the magnetic methodhas proved its ability to detect small changes ofthe magnetic field linked to volcanic activity[e.g.: Zlotnicki and Bof, 1998; Del Negro andCurrenti, 2003]. This technique is now relevantto give valuable and specific information on thestate of a volcano. Till now the expertise in thisdomain is not integrated in an automated system

in which the data are continuously analyzed andevaluated. A brief examination of the devicesinstalled throughout the world for the magneticmonitoring of active volcanoes generally showsa low degree of automation. State of the art involcano monitoring as practiced today lagsbehind the available technology. This delayimplies that data cannot be evaluated in real-time or near real-time, with obvious conse-quences in crisis periods. Information gatheredby a wide variety of sensors, which are distrib-uted over a vast area, must be transmitted on-line to an observatory with specialized staff,where conditions for receiving and evaluatingthe data have to be tuned to maximum efficien-cy and reliability. It is therefore fundamental tominimize the workload as much as possible bymeans of technological innovation to resolve themain burden of standard reduction process ofdata and give the operators already elaboratedinformation as far as the software available willallow.

Our Laboratory of Geomagnetism(MagLab) has been developing methods, hard-ware and know-how for the automated acquisi-tion and management of data simultaneouslyacquired at a variety of remote magnetic sta-tions. We aim to provide a basis for real-timeresponse during eruptive events, therefore, thereis the wish to realize an automated system thatstarting from a reconstruction of the physicalbehavior of the volcano, provides a model andwhich, when on-line data are available, allowsto observe and foresee the propagation/evolu-tion of phenomena. The structure of classicalcomputations proves to be inadequate to resolveproblems of this kind, which require informa-tion from a certain number of cases to be gener-alized. As a consequence, the necessity to resortto innovative computational paradigms, whichoperating in integrated mode may efficientlyconfront such problems, has arisen. In particu-lar, we refer to those techniques, known as softcomputing, which allows problems requiringthe intervention of human experts to be solved.These techniques are able to give an estimate ofthe uncertainty with which a model of a dynam-ic system is obtained (the volcano), having in-out value couples available.

Automation in volcano monitoring can bedivided into three steps: (i) signal transmission,(ii) signal evaluation, and (iii) notifying of awarning signal. With this aim we have beendeveloping a graphic user interface based appli-cation, called MADAP (MAgnetic DAtaProcessing), which is able to rapidly manage awide variety of data coming from remote sta-tions of monitoring networks and to execute


117

quickly different analysis techniques. The soft-ware, designed under Visual C++, consists ofthree modules, one for each step, characterizedby high automation level and development flex-ibility (Fig. 1). The first two modules have beencompletely implemented. The former, calledMagTalk (Communication module), is a pack-age of procedures for the acquisition and trans-mission of signals from continuously recordingsensors to a central observatory. The latter,called MagTool (Analysis module), contains aset of analysis routines for reduction and evalu-ation of the incoming data to produce inter-pretable parameters and store the data in perma-nent files. Currently, we are developing the thirdmodule, called MagWarn (Warning module),which aims to develop the best possible method-ology to compare the calculated parameters withprescribed limits and subsequent activate awarning signal if the limits are exceeded. Theautomation process also requires the results ofthe analyses to be integrated to provide an esti-mate on the state of volcano. We will brieflysummarize the preliminary achievements relat-ed to the planning of MADAP, and its applica-tion on Etna. This report describes work that isstill in progress, but sufficiently mature to war-rant attention.

2. The Communication Module

The architecture of MADAP system hasbeen developed taking into account the specificrequirements by the magnetic network installedon Mt. Etna. During the last two decades, the

MagLab has been intensively monitoring themagnetic field on Mt. Etna. We have observedsignificant correlations between volcanic activi-ty and changes in the local magnetic field, up toa few tens of nanoteslas [e.g.: Del Negro et al.,1997; Del Negro and Ferrucci, 1998]. Detectionof clear magnetic signals associated with therenewal of the volcanic activity has led to anincrease in the magnetic monitoring of Mt. Etna.Since the end of 1998 a permanent magneticarray equipped with Overhauser effect magne-tometers has been set up [Del Negro et al.,2002]. All remote stations are equipped withOverhauser effect magnetometers (0.01 nT sen-sitivity) and synchronously sample the Earth’smagnetic field every 10 seconds.

MADAP uses data from the array of con-tinuously recording remote stations (RS) spreadover the volcanic area and linked by mobilephone to the control center (CC) at the localobservatory (e.g. at the INGV-CT). The controlcenter is a computer-based magnetic data acqui-sition system situated in a local observatorywhere mains electricity and telephone servicesare available. At this location a computerreceives the data and performs data sorting andreduction as well as limited evaluation to detectabnormal behavior or breakdown of remote sen-sors. A communication module, called MagTalkand linking CC to RS, has been developed witha client/server structure (Fig. 2). At predeter-mined intervals (e.g. once a day) the client (CC)connects to the server (RS) to download the lat-est data. Data coming from each station are col-lected in the host-computer at the observatorywhere they are preliminarily examined to iden-

118


Figure 1. MagWarn system expressed through a block-diagram representation.

tify and correct possible errors. In particularfour main functions are applied:

• check for possible time gaps within datasequence or repetition of the same sample;• verify the standard of the format of datatransmission, the possible incoherence in theexamined string is immediately indicated tothe operator who can decide to eliminate orcorrect the string;• select data measured by the magnetometeron the grounds of the quality index associat-ed with each datum. This application deletesdata that do not fall within the quality rangepreviously defined by the operator;• store data in the local database from whichthey can be easily retrieved at any moment tobe processed.

In order to ensure problem-free runningthe computer system is furthermore pro-grammed to provide a daily report to check if alldata have come through normally. The comput-er system is also programmed to calculate auto-matically and display in real-time simple differ-ences and spectral content of incoming signals,providing a quantitative measure of magneticactivity. These data can be the basis for rudi-mentary alarm systems, notifying observatorystaff that something has happened and requiresfurther evaluation. An operator can then investi-gate the problem and decide which action isneeded, such as changing the transmission fre-quency, if greater information is required, or ifsome equipment failure needs correcting.Web Site

The local control center has also beendevised to upload data to a distant user immedi-ately after acquisition and re-formatting. Dataprocessed at the “distant desk” can be down-loaded a few hours later and used by the per-sonnel in charge of the volcano forecast. Theon-line availability of crude or pre-processeddata to authorized users connected to a wide-area network, fosters the possibility of monitor-ing active volcanoes without concentrating allhuman resources in a single observatory.Provided that the field maintenance and supportare available at the volcano observatory chosen,such a scheme would allow special instrumentsto be run even without any expertise in process-ing and interpretation of specific data.

Some new pages have been added to theINGV-CTWeb site under the item Laboratory ofGeomagnetism to share the measurementsthroughout the world. At the addresshttp://maglab.ct.ingv.it it is possible to examinegeomagnetic observations carried out at Mt.Etna. In the Web site the 10-minute average ofthe magnetic field total intensity and the relatedstandard deviation for each station are plotted(Fig. 3). In particular, any external users havinga password are able to download directly dataacquired at the stations of the magnetic networkof Mt. Etna.

3. The Analysis Module

To handle rapidly the huge amount of datacoming from a continuously recording monitor-


119

Figure 2. Output screen of the communication module.

ing network (e.g.: 8640 measurements per dayfrom each station, using a 10 s sample rate) andto apply faster different analysis techniques wehave developed a second module, calledMagTool, which allows a high skill level to beachieved by the operator. Our application isbuilt to be user friendly and specifically to min-imize time taken in data reduction processes andimprove the ability to recognize magneticevents due to geophysical sources. MagToolincludes a powerful, comprehensive package ofanalysis routines for processing acquired data.This package is rich in statistics, regressions,linear algebra, time and frequency domain algo-rithms, windowing routines, and digital filters(Fig. 4). Described below are some dedicatedroutines available in the package.

Simple differences

The observation of a volcanomagneticevent (a few nT or less) attributable to thedynamics of a volcano is strongly tied to theability to cancel out the normal variation in theEarth’s main and transient fields. To date, themost used and reliable method is the classicaldifferential technique, based on simultaneoussimple differences among the magnetic fieldamplitudes recorded at several points on a vol-cano. This method was implemented with theoption to verify the synchronization betweensignals recorded at different stations. To do thisa cross-correlation function has been included,since if two signals are perfectly synchronizedthey are also cross-correlated with each other.Thus, when two signals are not synchronized,

the cross-correlation function computes thedelay/advance of the signals and re-synchro-nizes them on the grounds of these results. Wealso included Steppe’s [1979] method to finddifferences between a given station and aweighted linear combination of the remainingstations in a total field array, where the weightsare determined by linear regression.

Empirical transfer functions

Recently a vector magnetometer for con-tinuous monitoring of the inclination and decli-nation of the Earth’s magnetic field has beentested in the reference station of Mt. Etna mag-netic network. We implemented a more detaileddata analysis by employing the method devel-oped by Poehls and Jackson [1978], whichrelates the vector field at the reference site to thetotal field at the observation sites by transferfunctions to filter out residual variations causedby transitory fields. The use of complex, fre-quency-dependent transfer functions to relatethe vector field at a reference site to the totalmagnetic field effectively filters out residualvariations caused by atmospheric disturbances,their associated ground currents, and local vari-ations in magnetic susceptibility. This method isespecially effective in reducing the residualsassociated with diurnal variations, thus allowingtectonomagnetic events even shorter than a fewdays duration to be detected.

Correlation analysis

In order to distinguish between transients120


Figure 3. The web site at the address http://maglab.ct.ingv.it.

of volcanomagnetic origin and transients gener-ated by strong variations in the external transi-tory magnetic field, we implemented themethod devised by Del Negro and Ferrucci[2000]. This method was inspired by the obser-vation that at two stations spaced a few kilome-ters apart the transients in one signal were pro-portional in magnitude to those in another sig-nal. This led to the hypothesis that the contribu-tion to the signal generated by the transitorymagnetic field may be broken down into twoparts: one of external origin, which is identicalfor both stations given their geographical prox-imity, and another of internal origin, proportion-al to the former, but dependent on the site.Following on from this simple description of themagnetic field, an accurate analysis, whichtakes into account the correlation between themeasurements at two stations, was developed.

Spectral analysis

Another method for the detection of thevolcanomagnetic transients is that of analyzingthe spectral amplitude changes in signals gath-ered at continuously recording stations [DelNegro et al., 1997]. The spectral analysis is per-formed on mobile windows, and the windowmaximum peak of the spectral amplitude isassociated with each time window. An ampli-tude increase in the power spectrum, caused bya significant change in the local magnetic field,is expected to occur in the presence of volcanicactivity. This method is suitable to detect noise-corrupted signals, especially when the signal-to-noise ratio (SNR) is very low. In such cases the

time window averages are affected by large sta-tistical error, and the simple difference methodfor the detection of the volcanomagnetic tran-sients quickly becomes ineffective.

Joint Time Frequency Analysis

Conventional analysis can describe agiven signal as a function of time, showing thesignal amplitude changes over time, or alterna-tively as a function of frequency, defining itsfrequency content but without clearly indicatinghow those frequencies evolve with time. Giventhe intrinsically time-varying nature of magnet-ic signals, a module for the Joint Time-Frequency Analysis (JTFA), a signal processingtechnique in which signals are analyzed in boththe time and the frequency domain simultane-ously, has been implemented (Fig. 5). Moreover,the JFTA module uses a rather sophisticatedtime-dependent spectrum analysis that allowsthe instantaneous spectrum of a signal to beextimated. Time changes of the spectrum pro-vide a more complete representation of the sig-nal and consequently a better understanding ofits nature.

Predictive filtering

Currently, we are concerned with reduc-tion of changes in the difference fields due tocontrasting responses at magnetometer sites,using methods of predictive filtering, with thefilters giving the relative responses betweensites. Davis et al. [1981] developed the first type


121

Figure 4. Output screen of the analysis module.

of approach based on Wiener’s classic filterstheory. The predictive analysis allows sometime-intervals where important statistical varia-tions of the signal are present to be identified.These intervals are also called non-stationaryzones. Considering that this phenomenology istime-variant, a non-stationary approach is moresuitable to describe the physical effects tied tovolcanic processes. For this reason we have alsobeen implementing an adaptive type approach.In the non-stationary analysis all the variablesare time varying. Therefore the weight vector ofprediction as well as the cost function (meansquares error) will also depend on time. Thetechnique of analysis is based on a set of adap-tive mutual predictors, trained on a sliding time-window, which describe the changing statisticalcharacteristics of the observed time series. Inpractice, each sample within a sliding window isweighted through a time-varying vector in orderto obtain a minimization of the cost function.This procedure allows the time intervals wherethe predicted time series is different from theoriginal sequence to be identified. These inter-vals are likely to be affected by volcanomagnet-ic effects.

Diffusion of atmospheric temperature changeinto the ground

From recent observations an annual com-ponent clearly appears in the reduced signals.The amplitude of these annual changes is about4 nT at all sites. These periodic fluctuations arepresent even when there was no volcanic activi-ty and they well correlate with seasonal temper-

ature variations (the correlation coefficient is0.88). Recent and more accurate studies claimthat annual variations in the geomagnetic totalintensity could be caused by seasonal changes inthe heterogeneous magnetization of near-sur-face rocks due to a diffusion of atmospherictemperature change into the ground. Using themethod proposed by Utada et al. [2000], the fea-tures of annual variations (∆FT) can be quantita-tively estimated by a simple one-coefficient fil-ter as:

where ∆T is time variation in the ground tem-perature, h0 is the amplitude ratio of annualchanges estimated by a least squares method,and t0 is the time lag calculated from the phasedifferences between total intensity and tempera-ture. Although the simple linear filtering iseffective a residual annual component remains.It is supposed to be due to non-linear effect ofthe temperature. To model this effect, we pro-pose a non-linear filter based on a fuzzy logicalgorithm. The effectiveness of this filteringtechnique can be tested through the statisticalmeasures of residual component.

4. The Warning Module

In order to integrate the results of theanalyses with modelling, and provide an esti-mate of the level of volcanomagnetic activity,we have implemented a third module, calledMagWarn. It is a complex environment still

122


Figure 5. Interface of the joint time-frequency analysis routine.

under realization. To be run on-line it was builtwith “blocks”. This way, the system just needsto load each block onto memory once. Theworking process was hard to design, but onceimplemented, it allowed complicated scenery tobe built quickly. MagWarn is divided in fivemain blocks:

• Data homogenization on a common timebase (DAHO block),• Relating information from different sources(RIDS block),• Automatic signal recognition and classifi-cation (ASIRE block),• Real time modelling (RTM block),• Evaluation of the volcanomagnetic activity(EVA block).

In the following the most important func-tion performed by each block are described.Each block processes the output from the previ-ous ones and outputs data to the followingblocks.

DAHO block

The first block, called DAHO, handles thelarge amount of heterogeneous data acquired involcanic areas. Visualizing these data on a com-mon time base is critical to interpreting themcorrectly and reacting suitably to possible geo-physical changes (Fig. 6). DAHO gathers andclassifies the available information in homoge-neous domains readable by the automated sys-tem. Three specific databases are continuouslyupgraded in the same software environment.The first corresponds to the eruptive history of

the volcano (past activity, dynamism, etc.). Thesecond concerns the disturbances (ground tem-perature, solar wind velocity, K index, etc.) thataffect the magnetic field measurements. Thethird is devoted to the magnetic time seriesobtained by the real-time monitoring networkon the field. These databases homogenize thedata format and classify all the different param-eters, which will be the input data for bothASIRE and RTM blocks.

RIDS block

The second block, called RIDS, assem-bles and properly organizes all the dispersedinformation that contains a location reference,placing that information at some point on thevolcano. The whole information is collected in aglobal GIS (Geographic Information System),which ensures the compatibility among all dataand the flexibility and easy running to users[Carrara and Guzzetti, 1995]. A GIS is a com-puter system capable of capturing, storing, ana-lyzing, and displaying geographically refer-enced information (data are identified accordingto a location). The power of a GIS comes fromthe ability to relate different information in aspatial context and to reach a conclusion aboutthis relationship. RIDS is constituted of threeparticular GIS (Fig. 7). The first is mainly filledby the knowledge of the volcanic activity: thelava flows distribution, the thickness of ejecta,regional geodynamics, and the time and spatialevolution of fractures. The second collects dif-ferent types of geophysical reconstruction of the


123Figure 6. Output screen of the DAHO block.

volcano. Some of them integrate information ofthe volcano structure: location of magma com-plex, tectonic discontinuities, ground waterflows and resistivity structure or earthquakesfoci. The third pulls together the results of theforward modelling obtained by RTM block.These models are based on laboratory experi-ments and constrained by the anomalies evi-denced by theASIRE block. Human experts willvalidate all this information, before combiningthem in the global GIS [Emmi and Horton,1995].

ASIRE block

The third block, called ASIRE, is devotedto the automatic signal recognition and classifi-cation by cross correlation analysis. The block isa fuzzy logic based technique [Sugeno, 1985],which aims to recognize intervals of anomalousbehavior of the recorded and homogenized geo-physical parameters under investigation. A criti-cal point is the identification of the most reliablecriteria that permit discriminating the occur-rence of a volcanomagnetic event. In particular,these criteria could not be viewed as a simplethreshold system that rigidly classifies the activ-ity level. Generally, geophysical processes arenot sufficiently well known to be quantitativelydescribed and human knowledge and experienceinevitably play a crucial role in making deci-sions about the state of volcano. A key point instudying geophysical signals is related to thedifficulties to deal with the natural uncertaintyof the available data, resulting from the impre-

cise knowledge of the underlying phenomena.Moreover, the needed information is not com-pletely available and/or too complex to be stud-ied with the most traditional algorithms. Whileconventional computing requires a deep under-standing of a system, exact equations and pre-cise numeric values, soft computing is tolerantof imprecision, uncertainty and partial truth[Zadeh, 1965]. Soft computing mimics thehuman ability to find precise solutions in anenvironment of uncertainty and imprecision.One of the principal constituents of soft com-puting is fuzzy logic that, in this perspective,provides a remarkably simple way to draw exactdecision from inaccurate information. Sincefuzzy logic can handle approximate informationin a systematic way, it is an appropriate tool formodelling complex systems when accurate mathequations, governing the process, are notknown. Fuzzy logic is able to describe complexsystems by mapping human knowledge andexperience in simple rules. The linguistic infor-mation is represented by mathematical functionswhich map the linguistic expression into exactnumeric ranges. Fuzzy rules are very easy tolearn and use (Fig. 8). It typically takes only afew rules to describe systems that may requireseveral lines of conventional software. As aresult, fuzzy logic could improve significantlythe ability to recognize the “events” among thesignals.

RTM block

The fourth block, called RTM, calculates

124


Figure 7. Volcanological and geophysical information stored in a global GIS by RIDS block.

models in real time and integrates the results ina global GIS. It is worth stressing that real-timemodelling is now possible thanks to recentimprovements in hardware and software per-formance. Fine adjustments to models can beperformed continuously on the grounds of (i)analysis of the latest data, and (ii) new con-straints available (Fig. 9). For example the mag-netic stations on Mt. Etna are located along a S-N profile crossing the volcano summit. This lay-out, symmetrical with respect to the centralcraters, allows continuous prospecting of thevolcanomagnetic field along this section of Mt.Etna. The alignment of such continuous stationswill deliver – in real time and for a given timewindow – a 2 or 2 D forward modelling of themagnetization versus depth [Del Negro and

Currenti, 2003].After individual evaluation of the compat-

ibility between the observed anomalies detectedby ASIRE and the independent forward model-ling, all the results will be integrated in the glob-al GIS upgraded by RIDS, in which all 3Dreconstructions, forward modelling and vol-canic activity will be cross-correlated. In thisblock the time duration of the magnetic anom-alies, their number and the location on the vol-cano will be taken into account in order to rec-ognize the typology of sources. The degree ofcompatibility with the possible anomaliessources deduced from the different modellingwill graduate levels of volcanomagnetic activi-ty. A high coherence level between detectedanomalies and the integrated forward modelling


125

Figure 8. Fuzzy rules contained in ASIRE block.

Figure 9. Piezomagnetic field due to a rectangular fault with strike-slip calculated by RTM block.

will lead to evaluate the state of activity.

EVA block

The fifth block, called EVA, starting froma reconstruction of the physical behavior of thevolcano, provides a model and, when on-linedata are available, allows to describe its timeevolution. Modelling involves an analysis oferuptive history and monitoring results in orderto find patterns that can be applied to futureactivity. This allows us to build a model formaking foresees that focus our efforts on themost probable activity of the volcano.Therefore, two different typologies of informa-tion interfere in this block:First, the information given by the lower blocksthat will detect anomalous and correlatedchanges, the sources of which will be in agree-ment with the characterization of the volcano,Second, the knowledge base deduced from thepast activity of the volcano.At this stage, EVA prepares a report of findingsfrom all available information (Fig. 10):

• The stations which indicate a reliableanomaly.• The level of reliability of the anomalies.• The duration of their changes.• The amplitude and their distribution.• The correlations between the differentparameters.• The possible locations of the sources of theanomalies.• The similar changes that have occurred inthe past.

EVA’s reports are based on a fuzzy deci-sion making method [Zimmermann, 1996] witheffective visualization of all processed data andintermediate results. Such information is contin-uously re-evaluated by the lower levels(blocks). The reports will have to be secured byman-made expertise. Different cases couldappear which cannot be considered with thesame level of activity. Even if MagWarn is ableto make recommendations, the final decision ofthe level of volcanomagnetic activity will beensured by experts who will take into accountthe past activity knowledge base.

5. Conclusions

The computer-based system MADAP wasdesigned and implemented at the MagLab formagnetic monitoring of Etna volcano. The sys-tem is intended to solve the problem of moni-toring the volcano at large distances from thelocal observatory, with the requirement of pro-viding an estimate of the level of geomagneticactivity. When studying a system as complex asa volcano, to be able to simplify it without los-ing relevant information is vital. MADAP is amodular structure using physical buildingblocks that allow the global problem to be splitinto smaller and easier sub-problems, eachsolved within a single module. The multi-reso-lution approach allows data with diverse charac-teristics to be elaborated effectively. A variety ofblocks with different procedures, depending onthe nature of available data, were implemented.

126


Figure 10. Reports of findings made by EVA block.

In particular, both traditional elaboration proce-dures and innovative ones were used. The inter-action among the various blocks was organizedin a complex computing structure that uses anintegrated approach based on the techniquesknown as soft computing to extract, as efficient-ly as possible, information from the availabledata [Jang, Sun, and Mizutani, 1997]. The flex-ibility of the proposed structure allows bothchanges to the current modules and implemen-tation of new modules to be easily performed.This architecture will avoid dispersion in humanresources and will drastically decrease the timeresponse to evaluate the volcanomagnetic activ-ity as well as to notify a warning signal.

We aim to develop the best possiblemethodology to understand, monitor and fore-see the volcanic activity by focusing researcheson magnetic monitoring. Such methodologymust allow the available information to be han-dled quickly and effectively. To act “quickly”,automated systems able to correlate incominginformation with a set of predefined policies anddecision strategies are necessary, so that aresponse can be given when needed. Acting“effectively” means that operators must be ableto evaluate the success of their policies andstrategies and continually refine them toimprove the performance. And, the concept that“methodologies” must accomplish this indicatesthat actions must be consistent across all opera-tions and not be restricted to individual employ-ees, systems, locations, or communication chan-nels. The methodology we have been buildingup is founded on a fuzzy-logic based architec-ture. The approach pursues a main target: tobuild up an architecture in which new inputs canbe continuously integrated. Such a system auto-matically delivers levels of geomagnetic activi-ty. Higher levels will be controlled by both theautomated system itself and by human experts,before a warning signal is delivered.

Finally, MADAP is an example of the rap-idly growing technologies involved in managinggeophysical data. It is centered on three majorthemes, including World Wide Web (WWW)database access systems and methodologies;development of Graphical User Interface (GUI)based data processing applications; and recov-ery of pre-digital analog data records (i.e. theeruptive history of the volcano). As databasesgrow in size and complexity, new capabilitiesare needed to access the data rapidly and effi-ciently. New software for faster processing andanalyzing magnetic data recorded by monitoringnetworks was produced. GIS technologies ableto analyze results from forward modelling andto manage geological and geophysical data were

also included.

Acknowledgments

We are indebted to all personal ofGeomagnetism Laboratory of INGV-CT whoensure the regular working of the permanentmagnetic network on Etna volcano. TheMagWarn system was developed in the frame ofthe TecnoLab, the laboratory for the technologi-cal advance in geophysics organized by DIEES-UNICT and INGV-CT. This research was sup-ported by project EPOT of the GruppoNazionale per la Vulcanologia of the INGV.

References

Carrara, A., and Guzzetti, F., Editors (1995).Geographical Information Systems inAssessing Natural Hazards. KluwerAcademic Publishers.

Davis, P. M., Jackson, D. D., Searls, C. A. andMcPhernon, R. L. (1981). Detection oftectonomagnetic events using multichannelpredictive filtering. J. Geophys. Res., 86,1731-1737.

Del Negro, C. and Currenti, G. (2003).Volcanomagnetic signals associated with the2001 flank eruption of Mt. Etna (Italy).Geophys. Res. Letters., 30 (7), 1357.

Del Negro, C., and Ferrucci, F. (1998).Magnetic his-tory of a dyke on Mt. Etna. GeophysicalJournal International, 133, 451-458.

Del Negro, C., and Ferrucci, F. (2000).Volcanomagnetic effects at Vulcano Island(Aeolian archipelago, Italy). GeophysicalJournal International, 140, 83-94.

Del Negro, C., Ferrucci, F., and Napoli R. (1997).Retrieval of large volcanomagnetic effectsobserved during the 1981 eruption of Mt.Etna. Annali di Geofisica, Vol. XL, 2, 547-562.

Del Negro, C., Napoli, R., and Sicali, A. (2002).Automated system for magnetic monitoring ofactive volcanoes. Bull. Volcanol., 64, 94-99.

Emmi, P.C., and Horton, C.A. (1995). AMonte Carlosimulation of error in a GIS-based assessmentof seismic risk. Int. J. of GIS, 9, No. 4. pp.447-461.

Jang, J.-S. R., Sun, C.-T., and Mizutani, E. (1997).Neuro-Fuzzy and Soft Computing. PrenticeHall.

Poehls, K., A., and Jackson D. D. (1978).Tectonomagnetic event detection using empir-ical transfer functions. J. Geophys. Res., 83,B10, 4933-4940.

Steppe, J. A. (1979). Reducing noise in tectonomag-netic experiments by linear regression. J.Geophys. Res., 84, B6, 3063-3067.

Sugeno, M. (1985). Industrial Application of FuzzyControl. Elsevier Science Publishers Co.

Utada, H. M. Neki, and Kagiyama, T. (2000). A studyof annual variations in geomagnetic totalintensity with special attention to detecting


127

volcanomagnetic signals. Earth Planets Space,52, 91-103.

Zadeh, L. A. (1965). Fuzzy Sets. Information andControl, vol. 8, pp. 338-353.

Zimmermann, H. J. (1996). Fuzzy Set Theory and ItsApplications. 3rd ed., Kluwer AcademicPublishers, Boston, MA.

Zlotnicki J., and Bof, M. (1998). Volcanomagneticsignals associated with the quasi-continuousactivity of the andesitic Merapi volcano,Inodonesia: 1990-1995. Physics of the Earthand Planetary Interiors, 105, 119-130.

128


Date post:	11-Aug-2019
Category:	Documents
Upload:	lamdat
View:	213 times
Download:	0 times

PRELIMINARYRESULTSFROMTHEEPOT...

Documents