Interpretation of tensor gravity data using an adaptive tilt angle method

Geophysical Prospecting, 2013, 61, 1065–1076 doi: 10.1111/1365-2478.12039

Interpretation of tensor gravity data using an adaptive tilt angle method

Ahmed Salem1,2,3∗, Sheona Masterton1, Simon Campbell1, J. Derek Fairhead1,2,Jade Dickinson4 and Colm Murphy4

1GETECH, Kitson House, Elmete Hall, Elmete Lane, Leeds, LS8 2LJ, UK, 2School of Earth and Environment, University of Leeds, Leeds,LS2 9JT, UK, 3Nuclear Materials Authority, Cairo, Egypt, and 4Bell Geospace Ltd., Aberdeen, UK

Received October 2011, revision accepted December 2012

ABSTRACTFull Tensor Gravity Gradiometry (FTG) data are routinely used in exploration pro-grammes to evaluate and explore geological complexities hosting hydrocarbon andmineral resources. FTG data are typically used to map a host structure and locate tar-get responses of interest using a myriad of imaging techniques. Identified anomalies ofinterest are then examined using 2D and 3D forward and inverse modelling methodsfor depth estimation. However, such methods tend to be time consuming and relianton an independent constraint for clarification. This paper presents a semi-automaticmethod to interpret FTG data using an adaptive tilt angle approach. The presentmethod uses only the three vertical tensor components of the FTG data (Tzx, Tzy and

Tzz) with a scale value that is related to the nature of the source (point anomaly orlinear anomaly). With this adaptation, it is possible to estimate the location and depthof simple buried gravity sources such as point masses, line masses and vertical andhorizontal thin sheets, provided that these sources exist in isolation and that the FTGdata have been sufficiently filtered to minimize the influence of noise. Computationtimes are fast, producing plausible results of single solution depth estimates that relatedirectly to anomalies. For thick sheets, the method can resolve the thickness of theselayers assuming the depth to the top is known from drilling or other independentgeophysical data. We demonstrate the practical utility of the method using examplesof FTG data acquired over the Vinton Salt Dome, Louisiana, USA and basalt flows inthe Faeroe-Shetland Basin, UK. A major benefit of the method is the ability to quicklyconstruct depth maps. Such results are used to produce best estimate initial depthto source maps that can act as initial models for any detailed quantitative modellingexercises using 2D/3D forward/inverse modelling techniques.

Key words: Gravity, Tensor, Tilt, Depth

INTRODUCTION

Full Tensor Gravity Gradiometry (FTG) has proven to be aneffective tool in both oil and gas and mineral exploration. Itmeasures the derivative of all the three gravity componentsin all three directions and provides a rich source of informa-

∗E-mail: [email protected]

tion for defining edges of geological structures at both localand regional scales (Dickinson, Murphy and Robinson 2010).Several developments in imaging techniques have been pre-sented (Murphy and Brewster 2007; Dickinson et al. 2009)and enable greater insight into a subsurface structure throughthe utilization of full tensor components. A number of pub-lications for estimating depth to source from FTG data havepreviously been presented. Zhang et al. (2000) and Mikhailovet al. (2007) used the deconvolution approach to transform

C© 2013 European Association of Geoscientists & Engineers 1065

1066 A. Salem et al.

FTG data to determine both the location and depth of buriedgravity bodies. However, these methods require the verticalcomponent of the potential gravity (Tz) to be derived fromthe FTG data or to be measured independently. Beiki (2010)used an analytic signal approach applied to FTG data to esti-mate the source location parameters of simple gravity bodies.The disadvantage of the analytic signal approach is that it ismore sensitive to noise than conventional approaches. Otherpublications have dealt with the inversion of FTG data to amodel representing the subsurface (e.g., Li. 2001). However,inversion is not a simple task and generally requires goodprediction of an initial model to obtain good results wheninverting for depth.

In this paper, we present a semi-automatic interpretationmethod to estimate the depth to source using an adaptive tiltangle approach similar to the magnetic tilt-depth method pre-sented by Salem et al. (2007, 2010). In the present methodwe adapt the tilt angle method with a scale value that is re-lated to the nature of the source (point anomaly or linearanomaly) and use three components of the FTG data (Tzx, Tzy

and Tzz). With this adaptation, it is possible to estimate the lo-cation and depth of buried simple gravity bodies such as pointmasses, line masses and sheets. For complicated models suchas thick layers, the approach can provide the thickness of thelayers if the depth to the top is known from drilling or otherindependent geophysical data. We show the practical utilityof the method using theoretical data over simple bodies andtwo field examples of FTG data over the Vinton Salt Dome inLouisiana, USA and basalt flows in the Faeroe-Shetland Basin,UK.

THE M ETHOD

The tilt angle (Miller and Singh 1994; Verduzco et al. 2004)is defined as:

θ = tan−1

⎡⎣ fz√

f 2x + f 2

y

⎤⎦ , (1)

where fx, fy and fz are the derivatives of the field f in the x, y

and z directions, respectively. Salem et al. (2007) studied thetilt angle for magnetic data over a vertical contact model andpresented a simple relationship to locate the contacts frommagnetic data based on the contours of the tilt angle. Thetilt-depth method was first extended to gravity models byCooper (2010, 2011) who presented a similar approach tolocate spheres and vertical line masses from gravity data. Herewe define a generalization of the tilt angle that can work with

Table 1 Summary of the equations for calculation of the adap-tive tilt angle for source models discussed in this study. Verticaltensor components (Tzh and Tzz) are substituted into equation(3) with the appropriate adaptation factor, a, to give the adap-tive tilt angle θa. Vertical tensor components for a point masssource model have been given by Zhang et al. (2000) and allother source model vertical tensor components were derived fromPhillips et al. (2007). G is the gravitational constant, z0 is thesource depth and h is the horizontal distance from the source,

given by h =√

(x − x0)2 + (y − y0)2 and measured perpendicularto the strike of the model. Other parameters are described in thetext

Source model Tzh Tzz tan θa a

Point mass GMs3z0h

(h2+z20)5/2 GMs

2z20−h2

(h2+z20)5/2

2z20−h2

z0h 3

Horizontal line mass GMl2z0h

(h2+z20)2

GMlz20−h2

(h2+z20)2

z20−h2

2z0h 1

Vertical sheet 2Gρt hh2+z2

02Gρt z0

h2+z20

z0h 1

Horizontal sheet 2Gρt z0h2+z2

0±2Gρt h

h2+z20

± hz0

1

several gravity models using some adaptation of the tilt angleequation. The adaptive tilt angle is defined as:

θa = tan−1

⎡⎣a

fz√f 2x + f 2

y

⎤⎦ , (2)

where a is a value characterizing the source type. Substitu-tion of the vertical tensor components (Tzx, Tzy, Tzz) gives theadaptive tilt angle for tensor gravity data:

θa = tan−1

[a

Tzz

Tzh

], (3)

where Tzh =√

(Tzx)2 + (Tzy

)2. The introduction of the adap-

tation factor a, effectively scales the Tzz component accordingto the geometry of the source (See Table 1). The value ofa is related to the nature of the geometry of simple sources(a = 3 for a point mass and a = 1 for a line of mass) and canbe decided using equation (15) of Pedersen and Rasmussen(1990). This allows direct estimation of a) the depth to simplegravity sources from the tensor gravity data and b) thicknessof the thick sheets if the depth to the top is known.

Depth to simple gravity bodies

Here we present formulations for the horizontal distance (h)and depth (z0) calculation of three idealized simple sourcemodels (a point mass, a horizontal line of mass and thin

C© 2013 European Association of Geoscientists & Engineers, Geophysical Prospecting, 61, 1065–1076

Interpretation of tensor gravity data using an adaptive tilt angle method 1067

sheets), according to the adaptive tilt method. The term (h)

is defined as a distance from the horizontal location of thetarget and is perpendicular to the strike line of the target. Thetensor formulae for each of these models (Table 1) exist andhave been discussed extensively (e.g., Zhang et al. 2000 andothers). For each source model, we first define the verticaltensor components (Tzh, Tzz) and then define the adaptive tiltangle in terms of h and z0.

Equations for the vertical tensor components for a pointmass have been given by Zhang et al. (2000) and compo-nents for horizontal line and sheet sources have been given byPhillips, Hansen and Blakely (2007). These components arethen substituted into equation (3) and assigned an appropri-ate adaptation factor (a) to obtain the adaptive tilt angle (θa)from tensor gravity data. The relevant equations and adapta-tion factors for each source model are summarized in Table 1.Following this process, the horizontal location (h = 0) anddepth (z0) of the source body may then be obtained directlyfrom the adaptive tilt angle values. For a point mass sourcewith mass Ms, a horizontal line with mass per unit length Ml

and a vertical sheet with thickness t and density contrast ρ,the horizontal location of the source (h = 0) corresponds to anadaptive tilt angle of 90◦. In the case of a thin vertical sheet,we assume that its thickness t is negligible; we therefore ap-ply the approximation that the edges of the sheet correspondto the horizontal location of the source (h = 0). In contrast,the horizontal location of the edge of a horizontal sheet withthickness t and density contrast ρ corresponds to an adap-tive tilt angle of 0◦. For both the point mass and the verticalsheet sources, the depth (z0) can be obtained by measuring thedistance between the 45◦ and 90◦ adaptive tilt angle values(h = z0). The depth of the horizontal line source correspondsto the distance between the 0◦ and 90◦ adaptive tilt angle val-ues (h = z0). The depth to the edge of the horizontal sheetsource corresponds to the distance between the 0◦ and 45◦

adaptive tilt angle values (h = z0); this result is similar to ver-tical contacts from magnetic data (Salem et al. 2007). Othertilt angles can be used, providing that the ratio between h

and z0 is consistent with the source model described here. Forexample, in the case of the horizontal sheet, if the adaptivevalue is 1, an adaptive tilt angle of 25◦ may be used, such thath = 0.466 z0. Thus depth estimates of the sheet can be deriveddirectly from the tilt angle map by incrementally generatingtwo circles about points on the zero contours. For a givenpoint the radius of the first circle is increased until it intersectsa chosen contour (e.g., −25◦); the radius of the second circleis then increased until it intersects the other contour (+25◦).The two radii can be averaged and used similar to Salem

et al. (2010). The contours of the tilt angle are filled withcolour to represent depth estimates. This is repeated for suc-cessive segments of the contours until the contour interval iscolour filled.

To verify the adaptive tilt angle expressions shown inTable 1, we calculated synthetic vertical tensor gravity dataover a sphere, a horizontal line mass and vertical and horizon-tal sheets. All models were placed at a depth of 5 km. Adaptivetilt angles were then calculated from the vertical tensor com-ponents in order to recover the model source locations anddepth, following the criteria described above; our results aredisplayed in Figure 1. An advantage of the adaptive tilt anglemethod is that it can not only estimate the depth but it can en-hance the resolution of the tensor gravity anomalies associatedwith a weak density contrast. Figure 2(a) shows the verticaltensor gravity component over two horizontal lines of masssources with different densities. We assume that both of thetwo targets are aligned in parallel and that the horizontal dis-tance h is measured from the horizontal location of the targetand is perpendicular to its strike. The first source is locatedat a horizontal location of 30 km and at a depth of 5 km.The second source is located at the same depth but at a hori-zontal location of 70 km, sufficiently far for their signaturesnot to interfere. However, the first source has mass per unitlength equal to 10 times the mass per unit length of the secondsource. Figure 2(b) shows the adaptive tilt angle of the verticaltensor components of the two sources. The adaptive tilt anglecomprises the ratio of the vertical and horizontal derivativesof the vertical gravity component (Tz) and contains no in-formation concerning the physical properties of the causativebodies. The example shown in Figure 2(a) demonstrates thatthe source locations correspond to an adaptive tilt angle of90◦, irrespective of the physical properties of the sources. Itis noted however, that the adaptive tilt angle function doescontain information concerning the frequency content of theanomaly.

Vertical extent of thick sheets

In some situations, gravity sources cannot be approximatedby simple models. Thick geologic layers are examples of suchbodies that cannot be approximated by the above simple mod-els. Prism models are usually used to simulate the gravity re-sponse of many geologic layers (Blakely 1995). Such a prismmodel is not simple because it is a finite 3D source body andthe contribution of the edges cannot be resolved separately(Zhang et al. 2000). Here, we first test the prism model usingthe adaptive tilt angle approach to understand its limitations



Figure 1 Adaptive tilt angle calculated from vertical tensor gravitydata over simple gravity models; (a) sphere, (b) horizontal line ofmass, (c) vertical sheet and (d) horizontal sheet.

Figure 2 (a) Vertical tensor components over two horizontal lines ofmass sources located at a depth of 5 km and horizontal locations of30 and 70 km, respectively. The two sources are aligned parallel inthe same direction. The first source (x = 30 km) has a mass per unitlength equal to 10 times that of the second source (x = 70 km). (b)The adaptive tilt angle over the two sources.

in application to thick sheets. For this purpose, we calculatedtheoretical vertical components of FTG data for 24 differentprism models with a fixed horizontal dimension (40 km × 40km) and a fixed density contrast of 300 kg/m3. The depth totop (z0) was varied from 2–5 km at 1 km interval, and theprism thickness (t) was varied from 1–6 km at 1 km intervals.The FTG data for these models were calculated at a samplinginterval of 1 km covering an area of 100 × 100 km. In orderto study the optimum adaptive tilt values that successfully re-cover the correct depth to the top of the source prism, gridsof the adaptive tilt angle were calculated from equation (3),using our synthetic FTG data and a variety of experimentaladaptive values from 1–3. These grids were then contouredand depths were calculated based on the distance between thecontours. The recovered depths were averaged and comparedwith the original depth to the top of each model. Figure 3(a)shows the best adaptation factor (a) that gives minimum deptherrors for each prism model, plotted against the ratio of thethickness to the depth top (t/z0). The minimum depth errors



Figure 3 Correlation between optimum adaptive values and the ratioof thickness and depth to the top of the layer for different prismmodels.

were ranged between 0–300 m and the maximum standarddeviation was 84 m. Our results illustrate that the adaptivevalue required to correctly recover the depth to the top of aprism source depends directly upon the ratio of the thicknessto the depth to the top. As a first approximation based on theresults of this analysis, we suggest that these parameters arelinearly proportional to each other and may be representedby:

a = 1 + 0.389t/z0. (4)

The relation indicates the adaptive value should be variabledepending on the ratio of the thickness of the depth to thetop of the gravity sources. In fact, the adaptive value plays thesame role as the structural index in the Euler method (Reidet al. 1990). For sheets, the adaptive value increases with sheetthickness. Sheets with ratio values of (t/z0) greater than 5, willhave adaptive values greater than the value of simple pointmass (a = 3). Consequently, correct recovery of the depth tothe top requires good estimation of the adaptive tilt value.Note that all depth methods that depend on simple modelssuffer from the same difficulty when the assumed model typedeviates from the actual ones.

The question now becomes how can we use the presentapproach to deal with thick layers? Here we suggest two al-ternative ways: 1) following the assumption that the layer is of

approximately constant thickness, a variety of adaptive valuesmay be used to estimate layer source depths. The best adap-tive values can be selected based on geologic constraints suchas drilling information; 2) following the assumption of a vari-able layer thickness, the thickness may be estimated using anyavailable information about the source depth (e.g., based onseismic or magnetic interpretation). To explain how we canestimate the thickness using this latter approach, let us firstapply the method using an adaptive value of the thin sheet(a = 1). The relevant equation for the adaptive tilt angle(Table 1) may then be written as:

θ1 = tan−1

[hZ

], (5)

where Z is the estimate of the depth using an adaptive value of1. To estimate the correct depth z0, we need to use the correctadaptive value a, which will reduce the distance h to h/a suchas:

θa = tan−1

[h/az0

]. (6)

From equations (5) and (6), the relation between the estimateof Z and the correct depth z0 is:

Z = az0. (7)

Utilizing the derived linear relation between the adaptivetilt value and the ratio of the thickness to the depth to the topby substituting equation (4) into equation (7), we have:

t = Z − z0

0.389. (8)

Equation (8) shows that the thickness of a layer can be es-timated using the information of the depth to the top layer(z0) and an estimate of the depth to the top using an adaptivevalue of 1. We demonstrate the utility of the approach us-ing tensor gravity data of the prism model located at a depthto the top of 2 km and a thickness of 2 km. Figure 4(a–c)shows the tensor gravity data of this prism model. We firstapply the method using an adaptive value of 1. Figure 4(d)shows the resulting estimated depth. The minimum estimateddepth is 2.63 km and the maximum depth is 3.08 km with anaverage of 2.855 km. Because the model layer is thick, the esti-mated depth results can be considered as approximate values.We then use our estimated depth (Z) and the known depth(z0 = 2 km) to estimate the layer thickness using equation (8).This yields an average thickness of 2.2 km (Fig. 4e), satisfac-torily close to the actual thickness of the model layer (2 km).Our method is therefore able to successfully recover the layerthickness when the depth to the top of the layer is constrainedby additional geological or geophysical information.



Figure 4 Example of applying the adaptive tilt angle approach a) Tzx for a prism model located at a depth of 2 km and a thickness of 2 km.The density contrast is 300 kg/m3. b) Tzy. c) Tzz. d) Estimate of the depth using an adaptive value of 1. e) Estimates of the prism layer thicknessfrom d).

EFFECTS OF N OI SE A N D S OUR C EINTERFERENCE

Despite the resolving power of any gradient data, it must beacknowledged that they are significantly affected by noise. We

have tested the method by simulations of the results from atheoretical anomaly over a thin horizontal sheet layer locatedat a depth of 2 km with a density contrast of 300 kg/m3

(Figure 5a). We added different random noise with zero mean



Figure 5 Adaptive tilt angle plot for a noisy FTG anomaly over ahorizontal sheet with a density contrast of 300 kg/m3 buried at 2 km.The dashed line shows the adaptive tilt angle of a clean anomaly andthe yellow box indicates the location of estimating the depth usingadaptive tilt values of 45o.

and different standard deviations from 0.4–2 E representing1–5% of the amplitude of Tzz component. We used a valueof 1 to calculate the adaptive tilt angle and found when noisewill affect the resolution of the adaptive tilt angle method evenwith the smallest set of noise with a standard deviation of 0.4E. It is observed that in the presence of noise, it is very difficultto determine the correct horizontal location of the edge of thesheet using the zero value of the adaptive angle. In addition,the estimation of the depth based on the adaptive tilt angle,will have a range of uncertainty due to the presence of noise.Generally, if noise is of a high wavenumber, its effect can bereduced by upward continuing the anomalies or applying alow-pass filter. Here, as an example, we present simulationsof the results from a theoretical anomaly contaminated withrandom noise with zero mean and a standard deviation of 2 E(Figure 5b). As we can see it is very difficult to determinethe correct horizontal location of the edge of the sheet and,as a result, the estimation of the depth would be affected bythe presence of noise. However, by applying an appropriatenoise reduction technique such as a low-pass filter > 2 kmto the FTG data and then calculating the adaptive tilt angle

Figure 6 Adaptive tilt angle after applying low-pass filtering to thenoisy FTG anomaly of the horizontal sheet in Figure 5. The dashedline shows the adaptive tilt angle of a clean anomaly and the yellowbox indicates the location of estimating the depth using the adaptivetilt values of 45o in Figure 5.

(Figure 6), it is possible to improve the estimate of both thehorizontal location and depth.

We also tested the effect of source interference using simu-lations of theoretical FTG data over edges of two interferingsheet sources. The first sheet is located at a depth of 2 kmwith a density contrast of 300 kg/m3, the second sheet is lo-cated at a depth of 4 km with a density contrast of 200 kg/m3

and the two edges are horizontally separated by a distance of10 km. Similar to the example of the two lines of masses, weassume that the two sheets are aligned parallel and that thehorizontal distance is measured from the horizontal locationof the source and is perpendicular to its strike.

Figure 7 shows this model with the calculated adaptive tiltangle (a = 1) over the two sheets. The adaptive tilt angleis correlated with the vertical tensor component (Tzz). Thismeans that for a positive density contrast, the adaptive tilt an-gle above the horizontal sheet will be positive above the sheetand be negative away from the edge of the sheet as we see inFigure 7. For the shallower sheet, both the horizontal loca-tion (θa = 0◦) and depth (the distance between the adaptivetilt angles of 0◦ and 45◦) are estimated correctly. However, theinterference has affected both the horizontal location and thedepth estimates for the deeper sheet. The horizontal locationof its edge has been shifted by 0.5 km relative to its true loca-tion. Consequently, the distance between the 0◦ and ±45◦ tiltangles has also been skewed such that the distance betweenthe 0◦ and +45◦ tilt angles and between the 0◦ and −45◦ tiltangles correspond to depths of 3.1 km and 2.5 km, respec-tively. The average depth is therefore estimated at 2.8 km (i.e.,1.2 km shallower than its true depth). Our method is basedon the assumption that the source exists in isolation. Both theskewness of the 0◦ tilt angle value and the underestimation



Figure 7 Adaptive tilt angle from FTG anomaly data over two closelyspaced sheets aligned parallel in the same direction. The dashed linesshow the zero adaptive tilt angle, which indicate the location of theedges of the sheets. The yellow boxes indicate the locations of esti-mating the depth using adaptive tilt values of 45o.

of the source depth in this example, demonstrate an inherentlimitation in the application of the method for non-isolatedsources: there is a tendency for the depth of deeper structuresto be underestimated when the structure is in the presenceof shallower interfering bodies. The location of the edge ofthe deeper structure will tend to be displaced away from theinterfering structure. Having multiple depth estimates for asingle anomaly, based on the variable contour widths used,does help to illustrate the effects of interference.

F IELD EXAMPLES

Vinton Salt Dome

Airborne FTG data were acquired over the Vinton Salt Dome,Louisiana, USA in 2008 as part of a test program for thenewly acquired BT67 aircraft by Bell Geospace (Dickinsonet al. 2010). The airborne FTG data were flown with N-S flightlines with a spacing of 150 m at an average altitude of 75 m.The data were enhanced by band- pass filtering all componentsbetween 500–2500 m spatial wavelengths. The advantage of

the filtering process is to emphasize the signal associated withthe salt body hosting high-density cap rock (Dickinson et al.2010). Figure 8(a–d) shows the filtered vertical tensor gravitycomponents (Tzx, Tzy, and Tzz) and the computed adaptive tiltangle with a = 1. The components Tzx and Tzy identify the EWand NS edges of the cap rock, respectively. The Tzz componentshows the overall shape and structure of the high-density caprock near the centre of the dome. The zero contours of theadaptive tilt angle (Figure 8d) display both the boundaries ofthe cap rock (labelled A) and enhance salt related structuresat the margins of the salt dome (labelled B). Figure 8(e) showsthe estimated depth using the adaptive tilt method, assumingthe source model is a horizontal sheet (a = 1). The southernpart of the interpreted cap rock is shallow (about 169 m) withrespect to the northern part (about 211 m). The depth esti-mates suggest that the interpreted cap rock is characterized byan approximately flat surface in the E-W direction. The overallrelief of the interpreted cap rock agrees with drilling informa-tion, which suggests that the depth of the cap rock deepensfrom approximately 200 m in the south to up to 360 m inthe north, with a generally planar geometry (Thompson andEichelberger 1928). The agreement between the depth resultsand the drilling information supports the use of a horizontalsheet model and an adaptive tilt value of 1, for this exam-ple. This case study further demonstrates that the method canprovide good estimates of the depth to gravity sources, whensupplemented with geologic constraints.

Faeroe-Shetland basalt

In the second example, we demonstrate the application ofthe method in the estimation of layer thickness using FTGdata over basalt flows in Faeroe-Shetland basalt (Figure 9a).The Tertiary flood basalts in this region extend over 250 000km2 and were emplaced during break up between Green-land and the Faeroe Islands (Andersen 1988; White et al.2003). They originated in the rift zone to the west of theFaeroe Islands and flowed for up to 150 km eastwards andsouthwards (White et al. 2003). Richardson et al. (1999)demonstrated that the basalt flows are over 3000 m thickon the Faeroe shelf immediately east of the Faeroe Islands andpinch out within the Faeroe-Shetland Trough. They overlieEarly Tertiary and Mesozoic sediments that were accumulatedduring earlier episodes of lithospheric stretching (Fliednerand White 2003). These sub-basalt sediments remain poorlyimaged by conventional seismic profiles because the highlyreflective basalts degrade the quality and coherency of anysub-basalt arrivals.



Figure 8 a) Tzx, b) Tzy and c) Tzz. d) Adaptive tilt angle calculated for the Vinton Salt Dome survey. Dashed white lines show 0◦ contours,which indicate the boundaries of the cap rock (labelled A) and enhance related structures at the margins of the salt dome (labelled B). e) Depthcolour map of the Vinton Salt Dome.

FTG data were acquired in the Faeroe-Shetland Basin areain 1999 for the purpose of resolving basalt complexity andimaging sub-basalt geology (Murphy et al. 2005). The tensorcomponents and bathymetry were acquired simultaneously.Bathymetry was measured using a Swath Fathometer to anaccuracy of ±2% of water depth. Survey line spacing was750 m and oriented NW-SE orthogonal to the dominant struc-tural trend. Tie lines were acquired at 2250 m spacing andoriented NE-SW. The recorded FTG data contain informa-tion about all responses that relate to sub-surface geology.Regional interpretation of this FTG data set by Murphy, Mu-

maw and Zuidweg (2005) indicated that sub-basalt imageryis possible and identified a number of basement ridges andsedimentary structures. They used filtering in the frequencydomain to extract part of the signal arising from the basaltinterval and other parts arising from the basement. Here, weused the same filtering approach and found FTG anomalieswith wavelengths of 7–30 km that exhibit trends that may beassociated with basalt structures. Figure 9(a) shows the fil-tered Tzz component as an example of the filtered FTG data(filtered Tzx and Tzy are not shown). The map highlights adominant trend in the NE-SW direction, which is associated



Figure 9 a) Vertical tensor component Tzz from FTG data over the Faeroe-Shetland Basin survey area; b) adaptive tilt angle calculated fromFTG data using a thin sheet model and an adaptive value of 1; c) estimated depth to the top of the basalt, calculated from c); d) profile A-A’(located in c), showing the top and base of the basalt from White et al. (2003) and estimated top (black dots) and bottom (dashed line) from thepresent method.



with the development of the Faeroe-Shetland Basin. This trendis clearly seen in the depth to basalt figures published by Whiteet al. (2003) based on interpretation of seismic data. We com-puted the adaptive tilt angle from the filtered tensor gravitydata (Tzx, Tzy and Tzz) using an adaptive value of 1 and as-suming a thin sheet model (Figure 9b). The depth to the top ofthe basalt was then estimated between tilt contours of ±25◦

(Figure 9c). We compared our estimates of depth to the topof the basalt with the seismic depth interpretations publishedby White et al. (2003) (Figure 9d). Generally the estimateddepths using the present method correlate very well with seis-mic depths toward the east and are overestimated toward thewest. The good agreement in the east suggests that the adap-tive tilt value of the thin sheet model is an appropriate valueand the disagreement in the west indicates higher adaptive tiltvalues are required to retain the correct depth when the basaltis thick.

We then used the seismic results as a constraint for thecorrect depth to the top of the basalt and estimated the thick-ness of the basalt following equation (8). Where the depth tothe basalt top was overestimated by the adaptive tilt method,we utilized the seismic depth values. The dashed line inFigure 9(d) shows a tentative surface of the base of the basaltbased on the present method. The result supports the seismicinterpretation in the east and suggests the thickness of thebasalt may reach more than 5 km in the west. This interpre-tation agrees well with the work of Richardson et al. (1999),who concluded that the basalt thickness decreases from 7 kmon the Faeroe Islands (and 3 km thick on the Faeroe shelf) tozero some 150 km away, midway across the Faeroe-ShetlandBasin.

An important consideration in the interpretation of thisregion is the limitations imposed by low-density contrastsbetween the flood basalts of the Faeroe-Shetland Basin andunderlying volcaniclastics. Such volcaniclastics have been en-countered during drilling projects within our study area, atleast on a local scale. In the event that they are regionallyextensive, our methodology may, in fact be sensitive to un-derlying Mesozoic sub-basalt ridges associated with the EastFaeroes High.

DISCUSS ION AN D C ON C LUSI ON S

In this paper we demonstrated a semi-automatic method toefficiently interpret FTG data using an adaptive tilt angle ap-proach. The primary advantages of such an approach overpreviously proposed methods are the direct use of the three

components of FTG data (Tzx, Tzy and Tzz) and the speed withwhich initial results can be obtained without the need for agood estimate of a starting model. We explored the influenceof noise within the FTG data and demonstrated that it is pos-sible to successfully reproduce depth estimates by applyingappropriate filters in order to clean the data prior to applyingour method. We also discussed the interference arising fromnon-isolated sources, which skew both location and depth es-timation results; this presents an interesting opportunity toexplore future extensions of our methodology.

We demonstrated the application of our method in the es-timation of both the depth and layer thickness of a gravitysource, in the context of two examples. Depth estimates forthe Vinton Salt Dome example are consistent with results fromdrilling information when a horizontal sheet model and anadaptive tilt angle value of 1 is invoked within our methodol-ogy; this highlights the benefit of supplementing the method-ology with geologic constraints. In the Faeroe-Shetland floodbasalt example, we incorporated seismic constraints on thedepth to the top of the basalt layer in order to map the layerthickness. Our results are in agreement with the seismic inter-pretation to the east (where the adaptive tilt value is consistentwith a thin sheet model) and show a significant thickening ofthe basalt to the west, consistent with other published works.It must be considered, however, that the resultant filtered FTGgravity map might also retain source information from sub-basalt geology that has an influence upon the results.

In conclusion, our method allows the exploitation of theexisting strengths of FTG data in identifying edges of geologicstructures to provide a rapid way to measure the depth andthickness of anomalous bodies. The method provides good re-sults over simple and well isolated gravity bodies. Complicatedsource geometry, or interference will affect the results. Thesuccess of the method is significantly enhanced by the integra-tion of an independent geologic constraint and the applicationof appropriate data filtering in order to isolate causative grav-ity anomalies. Future integration of this efficient and informa-tive method with other geophysical and geologic explorationtechniques will be a powerful tool in subsurface imaging andinterpretation.

ACKNOWLEDGEMENTS

The authors greatly appreciate constructive and thoughtfulcomments from two reviewers, Dr Alan Reid, the AssociateEditor Prof. Horst Holstein and Deputy Editor Prof. MaurizioFedi.



REFERENCES

Andersen M.S. 1988. Late Cretaceous and early Tertiary extensionand volcanism around the Faeroe Islands. In: Early Tertiary Vol-canism and the Opening of the NE Atlantic, Vol. 39 (eds A.C.Morton and L.M. Parson), pp. 115–122. Geological Society, Lon-don, Special Publication.

Beiki M. 2010. Analytic signals of gravity gradient tensor andtheir application to estimate source location. Geophysics 75,I59–I74

Cooper G.R.J. 2010. A Modified Tilt-depth Method for Kimber-lite Exploration. Expanded Abstract, 72nd EAGE Conference &Exhibition.

Cooper G.R.J. 2011. The Semi-Automatic Interpretation of GravityProfile Data. Computers and Geosciences 37, 1102–1109.

Dickinson J.L., Brewster J.R., Robinson J.W. and Murphy C.A. 2009.Imaging Techniques for Full Tensor Gravity Gradiometry Data.11th SAGA Biennial Technical Meeting and Exhibition, Swaziland,Expanded Abstracts, 84–88.

Dickinson J.L., Murphy C.A. and Robinson J.W. 2010. AnalysingFull Tensor Gravity Data with Intuitive Imaging Techniques. 72nd

EAGE Conference & Exhibition, Barcelona, Spain, 14–17 June2010.

Fliedner M.M. and White R.S. 2003. Depth imaging of basalt flows inthe Faeroe-Shetland Basin. Geophysical Journal International 152,353–371.

Li Y. 2001. 3D inversion of gravity gradiometer data. 71st AnnualInternational Meeting, SEG, Expanded Abstract 20, 1470–1473.

Mikhailov V., Pajot G., Diament M. and Price A. 2007. Tensor de-convolution: A method to locate equivalent sources from full tensorgravity data. Geophysics 72, 61–69.

Miller H.G. and Singh V. 1994. Potential field tilt – A new concept forlocation of potential field sources. Journal of Applied Geophysics32, 213–217.

Murphy C. and Brewster J. 2007. Target Delineation using Full Ten-sor Gravity Gradiometry data. ASEG 2007, Expanded Abstracts.

Murphy C.A., Mumaw G.R. and Zuidweg K. 2005. Regional targetprospecting in the Faroe Shetland Basin area using 3D FTG Gravitydata. 67th EAGE Conference & Exhibition, Expanded Abstracts,P503.

Pedersen L.B. and Rasmussen T.M. 1990. The gradient tensor ofpotential field anomalies: Some implications on data collection anddata processing of maps. Geophysics 55, 1558–1566.

Phillips J.D., Hansen R.O. and Blakely R.J. 2007. The use of curvaturein potential field data. Exploration Geophysics 38(2), 111–119.

Richardson K.R., White R.S., England R.W. and Fruehn J. 1999.Crustal structure east of the Faroe Islands. Petroleum Geoscience5, 161–172.

Salem A., Williams S., Fairhead J.D., Ravat D. and Smit R. 2007. Tilt-depth method: A simple depth estimation method using first-ordermagnetic derivatives. The Leading Edge 26, 1502–1505.

Salem A., Williams S., Samson E., Fairhead D., Ravat D. and BlakelyR.J. 2010. Sedimentary basins reconnaissance using the magneticTilt-Depth method. Exploration Geophysics 41, 198–209.

Thompson S.A. and Eichelberger O.H. 1928. Vinton salt dome, Cal-casieu Parish, Louisiana. AAPG Bulletin 12, 385–394.

Verduzco B., Fairhead J.D., Green C.M. and MacKenzie C. 2004.New insights into magnetic derivatives for structural mapping. TheLeading Edge 23, 116–119.

Zhang C., Mushayandebvu M.F., Reid A.B., Fairhead J.D. andOdegard M.D. 2000. Euler deconvolution of gravity tensor gra-dient data. Geophysics 65, 512–520.


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Interpretation of tensor gravity data using an adaptive tilt angle method

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