Coseismic deformation induced by the Sumatra earthquake
E. Boschi a, E. Casarotti a, R. Devoti a, D. Melini a,A. Piersanti a, G. Pietrantonio a, F. Riguzzi a,b,∗
a Istituto Nazionale di Geofisica e Vulcanologia, via di Vigna Murata 605, Roma, Italyb Department of Earth Sciences, University of Roma ‘La Sapienza’, Italy
Received 20 December 2005; received in revised form 3 May 2006; accepted 30 May 2006
Abstract
The giant Sumatra-Andaman earthquake of December 26, 2004 caused permanent deformations effects in a region of previouslynever observed extension. The GPS data from the worldwide network of permanent IGS sites show significant coseismic displace-ments in an area exceeding 107 km2, reaching most of South-East Asia, besides Indonesia and India. We have analyzed long GPStime series histories in order to characterize the noise type of each site and, consequently, to precisely assess the formal errors ofthe coseismic offset estimates.
Keywords: Sumatra earthquake; Coseismic deformations; GPS time series
1. Introduction
The devastating megathrust earthquake of December 26, 2004 off the west coast of northern Sumatra has beenprobably the largest since the 1960 Chile event. Its moment magnitude has been estimated to be 9.0 (correspondingto a seismic moment release of 4 × 1022 N m) using surface wave data but some researchers suggest that about two-third of the elastic energy has been emitted aseismically exciting only extremely low frequency normal modes (Steinand Okal, 2005; Park et al., 2005). This event was probably energetic enough to have detectable effects on Earthrotational parameters. Very preliminary calculations, taking into account only the high frequency energy emission andconsequently underestimating global effects show that the Sumatra earthquake should have produced a pole shift largeenough to be identified in the observed data series, a small change in the length of the day and a change in the oblatenessof the Earth (Chao, 2005).
Though there have been, in the last years, several numerical results indicating that the permanent deformation fieldassociated with giant earthquakes could be detectable on extremely large scale (comparable with plate dimension),until now, extremely far field post-earthquake deformations have never been detected except for a single controversial
∗ Corresponding author.E-mail address: [email protected] (F. Riguzzi).
E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62 53
observation associated with the Alaska 1964 event (Press, 1965; Piersanti et al., 1997). Now, the Sumatra eventrepresents a unique candidate to test this hypothesis. Indeed, our goal here is to look for evidence of far field coseismicresidual deformation in the time series of the permanent GPS station located in the Asian–Australian region. Afterthe present development of our analysis (Boschi et al., 2005) three other works (Banerjee et al., 2005; Vigny et al.,2005; Catherine et al., 2005) concerning the deformation field associated with the Sumatra event has been published.Banerjee et al. (2005) obtained coseismic displacements from static offsets recorded at continuously operating GPSstations, by differentiating the mean positions in the 5 days before and after the earthquake. All but five of the stationsare located at distances greater than 1000 km from the source. This dataset has been used by Banerjee et al. (2005)to model the earthquake geometry and slip distribution; their findings suggest that a fraction from 25% to 35% of thetotal moment release occurred at periods greater than 1 h, without the emission of seismic waves.
Vigny et al. (2005) took advantage of 49 GPS network SEAMERGES, 7 campaign GPS and 30 global stations ofIGS to create a very dense geodetic dataset, covering the near field (Thailand, Malaysia, Indonesia) and the far field (upto 4000 km from the epicenter). They focused their work on the near-field deformation. By means of a static inversionof the slip against the GPS data they proposed a source model characterized by a considerable amount of slip releasedon a 1000 km long trench. Moreover, thanks to an outstanding kinematic analysis, they ruled out the possibility of acompletely silent aseismic rupture on the Northern part of the fault.
Catherine et al. (2005) used the recordings of nine permanent GPS sites to infer the slip on a rupture plane. Theyfound a good fit to the data with an average slip of about 10 m, even if they modeled the deformation with an elastichalf-space approach, not taking into account Earth sphericity.
As we will describe in detail in the next section, our approach in the GPS data analysis is rather different withrespect to that of previously published solutions allowing for a better statistical accommodation of GPS data fluctu-ations not associated with the coseismic effects of the earthquake. The noise analysis of the GPS time series revealssignificant periodic components from seasonal up to quarterly or bi-monthly periods superimposed on a characteristiclow frequency flicker noise that could easily bias the coseismic signal. Analyzing multi-year time series will allow usto eventually separate low frequency signals from the sudden coseismic transient. Our displacement field differs up to10 mm with respect to previous solutions based on very short time series analysis and the uncertainties in the estimatesare generally reduced by a factor of 2 or more.
Using a spherical model of coseismic deformation we compared the GPS deformations with the predictions ofa refined source model based on seismological recordings (Ammon et al., 2005), finding a rather poor agreementbetween modeled and observed displacements. An inversion strategy based on a complex source model optimizing anindependent displacement dataset led to an improvement in the quality of the fit in the near and moderate-far field butnot in the very far field indicating that some numerical limitations could affect our preliminary modeling approach.
2. GPS data and time series analysis
In order to evaluate the coseismic displacement field associated with the great Sumatra earthquake, we analyzed theweekly coordinates of 42 permanent GPS sites located in a vast region of approximately 5000 km radius, centered onthe earthquake epicenter. Our analysis takes into account not only the small time window centered in the earthquakeoccurrence time but, in order to average out periodic signals in the GPS time series, we considered long datasets,covering nearly 8.5 years of continuous GPS observations, including all weekly determinations from January 1997(GPS week 886) to March 2005 (GPS week 1315). About half of the sites span more than 8 years of continuous obser-vations, a further 10 sites supply 3–5 years of data and a few recent sites only 2–3 years. The coordinate time serieswere obtained from the weekly quasi-observation files available at the SOPAC data center (ftp://garner.ucsd.edu/). Thequasi-observation solutions contain coordinate estimates of nearly 200 sites of the global IGS network, solved on aweekly basis (i.e. every weekly solution comes from a combination of seven daily determinations) and the referenceframe is only loosely constrained at 1 m level. The term ‘quasi-observation’ reflects the idea of projecting the rawdata information content into the coordinate space without imposing any external constraint. Thus, the coordinatesolution is free to adjust itself as close as possible to the raw observations and is minimally distorted by inconsis-tent constraints. As a consequence, the entire network can be rigidly translated, rotated and scaled with respect to achosen reference frame, at different amounts from week to week (Davies and Blewitt, 2000; Herring et al., 1991).For Gaussian distributed residuals, the formal error decreases as 1/
√n where n is the number of daily solutions, but
the complex noise content sets a limit on the achievable standard deviation associated to the estimates that strongly
54 E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62
depends on the particular site history. The GPS time series are affected by unpredictable noise caused mainly bythe monument setting and mismodeling biases due to the processing stage, causing a noise level up to several mil-limeters in the computed time series (Williams et al., 2004). It is therefore worthy to analyze long time series inorder to characterize the noise type of each site and, consequently, to precisely assess the formal errors of the offsetestimates.
The main steps of this analysis can be summarized as follows: apply inner constraints to each weekly solution inorder to get the intrinsic variance-covariance matrix; transform the weekly solution into the fiducial reference frame(ITRF2000); detrend, filter and estimate offsets, and finally, perform residual noise analysis in order to properly scalethe formal errors.
Minimal inner constraints were applied to the weekly loose-constrained solutions, projecting the variance-covariancematrix into the relative error subspace constraining translations, scale and rotations to 1 mm (Davies and Blewitt, 2000).
Each weekly network is then transformed into a fiducial reference frame defined by 30 globally distributedsites extracted from the IGS cumulative solution (IGS04P51.SNX, available e.g. at ftp://cddisa.gsfc.nasa.gov/gps/products/1302/). Sites that could be affected by coseismic displacements associated with the Sumatra event havebeen discarded and do not contribute to the reference frame definition. After the reference frame definition, the weeklytime series have been detrended and filtered from seasonal and Chandler cycles. This procedure has been accomplishedby means of a least squares fit of the network time series, estimating a linear trend, occasional offsets, annual andsemiannual sinusoid amplitudes and a Chandler wobble amplitude when appropriate. We estimated simultaneously allthe selected parameters (drifts, steps and sinusoidal amplitudes) and used the full variance-covariance matrix associatedto the weekly solutions. For sites very close to each other we constrained their secular drifts in order to get a singletectonic response, this is true for the following couples of sites: TNML and TCMS (Hsinchu, Taiwan, few metersapart), BAN2 and IISC (Bangalore, India, 6.5 km apart), YAR1 and YAR2 (Yarragadee, W. Australia, coincident).
Since instrumental and/or environmental changes could cause significant steps in the GPS time series, we decidedto estimate an offset each time a known change has been reported in the site-log and the offset itself exceed the 1-sigmaconfidence region. At the epoch December 26, 2004 a common 3-D offset has been estimated at all the considered sites,in order to get the amount of displacement after the seismic event had occurred. Since the flicker noise is predominantin GPS time series (Williams, 2003), we could expect large undulations, lasting several weeks and randomly distributedthat, in principle, could alias the instantaneous coseismic displacement measured at each site. Therefore, we chooseto include all site positions after the seismic event until GPS-week 1315 (March 20, 2005) measuring in fact the3-month average site displacement due to the Sumatra earthquake. Fig. 1a and b show the improved time series ofsome representative GPS sites selected from a set of 42 sites.
The formal standard deviations associated with the estimates are likely to be underestimated depending on thedeviation from normality of the detrended residuals. Williams et al. (2004) showed that in many GPS permanentsites, the colored noise component has the effect of increasing the Gaussian errors by a factor up to several units,depending on the length of the time series and the noise spectral index. We recomputed realistic errors associatedto the estimated offsets using the maximum-likelihood estimation scheme proposed by Williams et al. (2004). In afirst step, assuming an a-posteriori power-law noise covariance matrix, we compute the appropriate colored noisemodel, estimating the spectral index κ and the amplitudes of the white and colored noise and subsequently we re-compute the covariance of the estimates using the estimated noise model. In this study, the effect of colored noiseon the coseismic displacement error is to enhance the standard deviation by a scale factor ranging from 1.5 to 6,depending on the specific site. The estimated spectral indexes range typically from −1 to nearly 0, i.e. from flickernoise to the fractional white noise region, in agreement with analogous findings for global GPS networks (Williamset al., 2004). Table 1 shows the estimated offsets for the North and East components and the associated re-scalederrors.
Besides the analysis carried out on the GPS weekly quasi-observations, we analyzed GPS observations of a stationlocated on the northern Sumatra island (SAMP) whose data are provided by the online SOPAC databank, since thisstation is not included in the weekly solutions previously mentioned.
We processed a network of seven IGS stations (BAKO, COCO, DGAR, KARR, KUNM, NTUS and SAMP) fromGPS week 1294–1305 by the BERNESE software v. 5.0 (Hugentobler et al., 2005) using the final IGS orbits andfollowing the “standard” procedure adopted by the Centre of Orbit Determination in Europe (CODE) analysis centreof IGS. The loose-constrained daily solutions were analyzed as described above to obtain the daily time series of SAMP(Fig. 2) and then to estimate the co-seismic steps and the re-scaled errors (see Table 1).
E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62 55
Fig. 1. (a) Weekly GPS time series of the East (grey) and North (black) components for some representative sites: BAKO, BAN2, COCO, DGAR,HYDE IISC. (b) Weekly GPS time series of the East (grey) and North (black) components for some representative sites: KUNM, LHAS, NTUS,TNML, USUD and WUHN.
Fig. 2. Daily GPS time series of the East (grey) and North (black) components for SAMP (northern Sumatra island).
3. GPS displacement field
The displacement field after the Sumatra main shock is shown in Fig. 3. In general, short time series show system-atically higher error ellipses, occasionally long lasting sites, such as GUAM (high spectral index), DGAR, PIMO andNTUS (high noise amplitudes), show also higher errors, roughly at the 3–4 mm level, caused mainly by the particularnoise content of the time series.
We compared our displacement field with three already published solutions (Banerjee et al., 2005; Vigny et al., 2005;Catherine et al., 2005), all of which based on very short time series (about 1 week before and 1 week after the event)
56 E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62
Table 1GPS analysis sites, estimated offsets and re-scaled errors
Site Longitude (◦) Latitude (◦) E (mm) σE (mm) N (mm) σN (mm)
that correspond to two points in our plots. Even though our solution is statistically consistent with the three publisheddisplacement fields, differences, generally on the order of a few millimeters may occasionally reach 10 mm (e.g. SAMP,NTUS and PIMO). We notice a better agreement (3.7 mm WRMS) with the Vigny et al. (2005) solution, whereas theagreement with the other two, Catherine et al. (2005) (WRMS = 4.9 mm) and Banerjee et al. (2005) (WRMS = 4.9 mm)is slightly worse. Fig. 4 shows the differences of the modules and azimuths between different geodetic displacementfields, the residuals are computed with respect to our values, such that negative values indicate shorter displacementswith respect to this study, the error bars represent the square sum of the modulus errors. The set of commonly analyzedsites are ordered with increasing distance from the epicenter, the nearest site being SAMP on the left corner. Majordifferences are reported at the near-distance sites (SAMP and NTUS), in which Banerjee et al. reports shorter offsetmagnitude of about 10 mm, whereas Catherine et al. and Vigny et al. show a substantial consistency, given the highassociated errors. The site PIMO (Manila observatory, Philippines) show an anomalous residual with respect to theother solutions, its magnitude seems to be underestimated by this study by an amount in the order of 4–8 mm, but asabove, the high uncertainties do not clearly separate the estimated offset. We explain this difference as caused by ananomalous wiggling observed especially in the north component, originated after the main shock and lasting about 3months. Since its high frequency nature could hardly be interpreted as a post-seismic event, we choose to filter outquarterly waves that smoothed somewhat the instantaneous offset.
All discrepancies could be explained by the significant flicker noise content or the weekly stochastic fluctuationsthat can easily bias the offset estimate. In this respect, the present analysis is more robust since the analysis schemeoutlined above estimates the coseismic offsets as an average value of the weekly solutions following the seismic event.
E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62 57
Fig. 3. GPS coseismic and modeled displacements associated with the Sumatra-Andaman earthquake. The displacements at SAMP are rescaled bya factor 0.25 for presentation requirements.
Fig. 5 shows the planar (2-D) offset standard deviations at common sites, on an average our uncertainties are a factorof 2 lower than the other published errors, and all restricted in the 2–3 mm region. Given the dominant flicker noisein the GPS time series, a standard deviation near 2 mm on the offset estimation should be considered as the limitingprecision of this type of estimates.
4. Deformation field modeling
In order to infer the details of the seismic source from the geodetic deformation data, we attempted a preliminarymodeling of the residual permanent deformation associated with the Sumatra earthquake using a semi-analytical modelof global coseismic deformation (Piersanti et al., 1997, 2001). The model adopts a spherical, layered, incompressibleself-gravitating approach. We employed a four-layer stratification with an 80 km thick lithosphere, a 200 km astheno-sphere, a uniform mantle and a fluid inviscid core. All the elastic parameters were obtained by volume-averaging thereference PREM values.
We computed the predicted coseismic offsets using the seismic source model given by Ammon et al. (2005). Thismodel is obtained with seismological data and gives a rupture area extending 1200 km along the Andaman trough. Peakslip values are distributed along a 600-km segment offshore northwestern Sumatra. In Fig. 3 we compare the observedGPS displacements with the computed offsets. In near-distance sites there is generally good agreement between themodel and the observations; for instance the static offset recorded at station SAMP is well reproduced both in absolute
58 E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62
Fig. 4. Modulus (panel a) and azimuth (panel b) differences between GPS solutions. Sites are ordered with increasing distance from the epicenter,the nearest site being on the left side. Negative values indicate shorter displacements with respect to this study and the error bars represent the squaresum of the modulus errors.
value and in direction. As the distance increases the fit is less satisfactory especially in Indian sites (HYDE, IISC) andAustralian sites, where the lack of agreement affects both magnitude and azimuth.
To ascertain whether the lack of agreement between modeled and observed displacements may be imputable to slowaseismic slip on the fault plane, we constructed a slip distribution model by inverting the coseismic field.
Since most of the GPS offsets obtained in this work are located at large distances from the source area, they arenot suitable for an inversion of the detailed structure of the slip distribution. Vigny et al. (2005) has performed a slipinversion by means of the very near-distance GPS data, demonstrating that their dense dataset is appropriate to thiskind of analysis. The authors underline that one possible limitation of their inversion is the assumed constant azimuthof the slip along the rupture fault plane.
E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62 59
Fig. 5. GPS offset standard deviations as estimated by different groups. The uncertainties of this study are on the average a factor of 2 lower thanthe other published errors. The sites are ordered with increasing distance from the epicenter.
To avoid this limitation we used the very near-distance GPS data provided by Vigny et al. (2005) but we computedthe best-fitting slip distribution on a fault geometry composed of multiple single seismic sources, each of them withdifferent slip orientations (Ammon et al., 2005). In addition, we consider also the GPS offsets of the Indian stations,as provided by the dataset of Vigny et al. (2005). The slip distribution resulting from our inversion is shown in Fig. 6;the associated deformation field is depicted in Fig. 7. The associated normalized χ2 is 3.4, which implies that theinverted slip distribution model gives an acceptable agreement with the GPS offsets of Vigny et al. (2005). Because ofthe latter differences, our inversion model produces a slip distribution different than Vigny et al. and Ammon et al. Inparticular, there is a consistent amount of compressional slip on the northern segment of the fault area, due principallyto the addition at the inversion of the Indian data. If we compare Fig. 6 with the slip distribution obtained by Ammonet al. with seismological data, we can see that the main difference is that the source model provided by Ammon et al.has the largest slip values near the epicenter, i.e. where most of the seismic energy release is expected to have beenreleased. In our model we get a considerable seismic moment release in the epicentral area, but most of the energy isreleased along the northern segment of the fault. This energy release, which is needed to account for the orientation ofthe Indian sites, but is absent from seismological models, may be interpreted as the effect of a slow slip which occurredaseismically.
Using the slip distribution obtained from inversion of near-distance GPS stations we computed the expected defor-mations on far-distance stations; the results are shown in Fig. 3. From the comparison of the results of forward andinverted models we can see that the offsets computed with the inverted source show generally better agreement withdata, as can also be seen from the reduction of about 35% in the normalized chi-square values, from 15.3 for the forwardmodel to 9.7 of the inverted model; in particular there is a satisfactory fit in Indian sites. Moreover the reduction reachesabout 70% considering the nine nearest GPS sites (SAMP, NTUS, COCO, BAKO, BAN2, HYDE, KUNM, DGAR andLHAS), from 13.4 for the forward model to 3.9 for the inverted model. When we look at extremely far-distance siteswe see that the inverted and forward modeling yield similar results, generally in poor agreement with data. At distancesconsiderably larger than the physical dimensions of the seismic source, the modeled displacements are not sensible tothe detailed structure of the fault, such as the distribution of energy release. Therefore, the lack of agreement betweenmodel and observations for distant stations cannot be ascribed to the slip distribution model and is presumably causedby intrinsic limitations of our modeling approach.
60 E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62
Fig. 6. Seismic moment release distribution associated with the best-fitting seismic source resulting from our inversion procedure.
In general, many sites where the fit is not good, display a smaller amount of observed displacement with respect tothe computed one. Considering the difference between modeled and observed displacements in Indian and Indochinasites we see that observed data indicate a substantial amount of compressional deformation northwards the ruptureplane. This could confirm the hypothesis of a considerable amount of deformation energy released aseismically (Steinand Okal, 2005). However, the lack of agreement between model and observation in far-distance sites should probablybe ascribed mostly to modeling limitations. Indeed, our approach assumes a laterally homogeneous stratification whileit has been shown in various papers that in subduction zones the lateral heterogeneities, which are supposed to be quitestrong, may have a crucial role in assessing the deformation field (see, for example, Masterlark, 2003). Moreover,our approach does not account for topography which is likely to play an important role in Himalayan region. Indeed,the great differences between the GPS displacements registered at KIT3 and POL2 with respect to that registered atURUM and IRKT (Fig. 3) suggests that some effects connected with 3D Earth structure are possibly relevant in thisarea. Another limitation can be found in our radial stratification that may be too simplified, Banerjee et al. (2005) foundthat a more refined radial layering has just the effect of giving smaller displacements in the very far field where ourmodel gives apparently too much large values.
5. Conclusions
Our main goal in this work was to evidence the presence of a static offset associated with the cosesismic effectsof the giant Sumatra-Andaman earthquake of December 26, 2004 in the records of many GPS permanent stations inSouth-East Asia, India and Australia, in the extremely far field of the seismic source.
E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62 61
Fig. 7. Horizontal deformation field in absolute value (color scale) and direction (vectors) associated with the seismic source obtained from theinversion of geodetic data.
Our analysis is based on the definition of a reliable datum to project the weekly loose solutions and on the removalof biases to obtain improved time series of 42 permanent GPS sites. This procedure allowed us to estimate highlyreliable coseismic offsets characterized by small errors, in an area, not covered by previous analysis, exceeding107 km2.
From the comparison of modeled and observed deformation in the near- and moderate far-field, we have the indicationof a large energy release in a fault plane similar to that obtained by Ammon et al. (2005) and Vigny et al. (2005) butwith a larger amount of compressional slip on the northern segment of the fault area.
The relevant differences between modeled and observed data in the very far-distance sites may be ascribable tointrinsic modeling limitations. Although very much numerical modeling effort in the future is needed to preciselydescribe the residual permanent deformation field caused by this giant event and to assess the role played by aseismicenergy release and long term postseismic displacements, the observations and numerical modeling already availableallow us to affirm that the Sumatra earthquake excited a permanent detectable deformation field on such a great spatialscale that its effects can be considered as almost global.
Acknowledgments
We thank the SOPAC team for providing the GPS weekly combined solutions publicly. We are grateful to L. Biagi,M. Crespi, C. Doglioni and F. Sanso’ for the fruitful discussions and encouragements.
62 E. Boschi et al. / Journal of Geodynamics 42 (2006) 52–62
References
Ammon, J., Ji, C., Thio, H.K., Robinson, D., Ni, S., Hjorleifsdottir, V., Kanamori, H., Lay, T., Das, S., Helmberger, D., Ichinose, G., Polet, J., Wald,D., 2005. Rupture process of the 2004 Sumatra-Andaman earthquake. Science 308, 1133–1139.
Banerjee, P., Pollitz, F.F., Burgmann, R., 2005. The size and duration of the Sumatra-Andaman earthquake from far-field static offsets. Science 308,1769–1772, doi:10.1126/science.1113746.
Boschi, E., Casarotti, E., Devoti, R., Melini, D., Piersanti, A., Pietrantonio, G., Riguzzi, F., 2005. Global permanent deformations triggered by theSumatra earthquake, arXiv.org/physics/0506003.
Catherine, J.K., Ghalaut, V.K., Sahu, V.K., 2005. Constraints on rupture of the December 26, 2004, Sumatra earthquake from far-field GPSobservations. Earth Planet. Sci. Lett. 237, 673–679.
Chao, B.F., 2005. Did the 26 December 2004 Sumatra, Indonesia, Earthquake Disrupt the Earth’s Rotation as the Mass Media Have Said? Eos 86,01.
Davies, P., Blewitt, G., 2000. Methodology for global geodetic time series estimation: a new tool for geodynamics. J. Geophys. Res. 105 (B5),11083.
Herring, T.A., Dong, D., King, R.W., 1991. Sub-milliarcsecond determination of pole position using Global Positioning System data. Geophys. Res.Lett. 18 (10), 1893.
Hugentobler, U., Dach, R., Fridez, P., 2005. Bernese GPS Software v. 5. 0. Astronomical Institute University of Bern.Masterlark, T., 2003. Finite element model predictions of static deformation from dislocation sources in a subduction zone: Sensitivities to homo-
geneous, isotropic, Poisson-solid, and half-space assumptions. J. Geophys. Res. 108, 2540, doi:10.1029/2002JB002296.Park, J., Song, T.R.A., Tromp, J., Okal, E., Stein, S., Roult, G., Clevede, E., Laske, G., Kanamori, H., Davis, P., Berger, J., Braitenberg, C., Van
Camp, M., Lei, X., Sun, H., Xu, H., Rosat, S., 2005. Earth’s free oscillations excited by the 26 December 2004 Sumatra-Andaman Earthquake.Science 308, 1139–1144.
Piersanti, A., Spada, G., Sabadini, R., 1997. Global postseismic rebound of a viscoelastic Earth: Theory for finite faults and application to the 1964Alaska earthquake. J. Geophys. Res. 102, 477.
Piersanti, A., Nostro, C., Riguzzi, F., 2001. Active displacement field in the Suez-Sinai area: the role of postseismic deformation. Earth Planet. Sci.Lett. 193, 13.
Press, F., 1965. Displacements, strains, and tilts at teleseismic distances. J. Geophys. Res. 70, 2395.Stein, S., Okal, E., 2005. Speed and size of the Sumatra Earthquake. Nature 434, 581–582.Vigny, C., Simons, W.J.F., Abu, S., Bamphenyu, R., Satirapod, C., Choosakul, N., Subarya, C., Socquet, A., Omar, K., Abidin, H.Z., Ambrosius,
B.A.C., 2005. Insight into the 2004 Sumatra-Andaman earthquake from GPS measurements in southeast Asia. Nature 436, 201–206.Williams, S.D.P., 2003. The effect of coloured noise on the uncertainties of rates estimated from geodetic time series. J. Geod. 76, 483.Williams, S.D.P., Bock, Y., Fang, P., Jamason, P., Nikolaidis, R.M., Prawirodirdjo, L., Miller, M., Johnson, D.J., 2004. Error analysis of continuous
GPS position time series. J. Geophys. Res. 109 (B03412), doi:10.1029/2003JB002741.
