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GRACE gravity data help constraining seismic models of the 2004 Sumatran earthquake

2011; American Geophysical Union; Volume: 116; Issue: B10 Linguagem: Inglês

10.1029/2010jb007848

2156-2202

Gabriele Cambiotti, Andrea Bordoni, R. Sabadini, Lorenzo Colli,

Geological and Geophysical Studies

Journal of Geophysical Research: Solid EarthVolume 116, Issue B10 Geodesy and Gravity/TectonophysicsFree Access GRACE gravity data help constraining seismic models of the 2004 Sumatran earthquake G. Cambiotti, G. Cambiotti [email protected] Department of Earth Sciences, University of Milan, Milan, ItalySearch for more papers by this authorA. Bordoni, A. Bordoni Department of Earth Sciences, University of Milan, Milan, ItalySearch for more papers by this authorR. Sabadini, R. Sabadini Department of Earth Sciences, University of Milan, Milan, ItalySearch for more papers by this authorL. Colli, L. Colli Department of Earth and Environmental Sciences, Munich University, Munich, GermanySearch for more papers by this author G. Cambiotti, G. Cambiotti [email protected] Department of Earth Sciences, University of Milan, Milan, ItalySearch for more papers by this authorA. Bordoni, A. Bordoni Department of Earth Sciences, University of Milan, Milan, ItalySearch for more papers by this authorR. Sabadini, R. Sabadini Department of Earth Sciences, University of Milan, Milan, ItalySearch for more papers by this authorL. Colli, L. Colli Department of Earth and Environmental Sciences, Munich University, Munich, GermanySearch for more papers by this author First published: 08 October 2011 https://doi.org/10.1029/2010JB007848Citations: 40AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] The analysis of Gravity Recovery and Climate Experiment (GRACE) Level 2 data time series from the Center for Space Research (CSR) and GeoForschungsZentrum (GFZ) allows us to extract a new estimate of the co-seismic gravity signal due to the 2004 Sumatran earthquake. Owing to compressible self-gravitating Earth models, including sea level feedback in a new self-consistent way and designed to compute gravitational perturbations due to volume changes separately, we are able to prove that the asymmetry in the co-seismic gravity pattern, in which the north–eastern negative anomaly is twice as large as the south–western positive anomaly, is not due to the previously overestimated dilatation in the crust. The overestimate was due to a large dilatation localized at the fault discontinuity, the gravitational effect of which is compensated by an opposite contribution from topography due to the uplifted crust. After this localized dilatation is removed, we instead predict compression in the footwall and dilatation in the hanging wall. The overall anomaly is then mainly due to the additional gravitational effects of the ocean after water is displaced away from the uplifted crust, as first indicated by de Linage et al. (2009). We also detail the differences between compressible and incompressible material properties. By focusing on the most robust estimates from GRACE data, consisting of the peak-to-peak gravity anomaly and an asymmetry coefficient, that is given by the ratio of the negative gravity anomaly over the positive anomaly, we show that they are quite sensitive to seismic source depths and dip angles. This allows us to exploit space gravity data for the first time to help constraining centroid-momentum-tensor (CMT) source analyses of the 2004 Sumatran earthquake and to conclude that the seismic moment has been released mainly in the lower crust rather than the lithospheric mantle. Thus, GRACE data and CMT source analyses, as well as geodetic slip distributions aided by GPS, complement each other for a robust inference of the seismic source of large earthquakes. Particular care is devoted to the spatial filtering of the gravity anomalies estimated both from observations and models to make their comparison significant. Key Points GRACE data help constraining seismic models of the 2004 Sumatran earthquake 1. Introduction [2] Co-seismic gravitational perturbations are visible from gravity space mission data [Mikhailov et al., 2004; Sabadini et al., 2005; Han et al., 2006; de Linage et al., 2009]. We herein analyze co-seismic geoid and gravity anomalies from the 2004 Sumatran earthquake by means of a new, compressible self-gravitating Earth model, that is fully realistic as it builds on PREM [Dziewonski and Anderson, 1981] and represents the elastic limit of viscoelastic models, recently used for post-glacial rebound studies [Cambiotti et al., 2010] and developed for co-seismic studies by Smylie and Mansinha [1971] and Sun and Okubo [1993]. In this sense, our approach differs from that followed by Gross and Chao [2006] and de Linage et al. [2009], the latter using compressible models based on a free-oscillation scheme. The gravitational part of the phenomenon is dealt with self-consistently and, in this respect, our modeling is similar to that used by Pollitz et al. [2006] for the study of post-seismic relaxation following the 2004 Sumatran earthquake, even though we implement PREM without volume averaging of its elastic parameters. Furthermore, differently from Smylie and Mansinha [1971] and Sun and Okubo [1993], we decompose the Poisson equation in order to discriminate between gravitational perturbations due to volume and topography changes; we can thus address the style of deformation, dilatational versus compressional, without the limitations suffered by plane half-space models, as in the work of Han et al. [2006]. In the end, instead of the compressible model used by Sabadini et al. [2007] to quantify the effects of the 2004 Sumatran earthquake on the Earth's rotation, based on the Gilbert and Backus [1968] analytical approximation of compressibility [Cambiotti et al., 2009], our model now fully accounts for the effects of compressibility, both in the initial state and during the perturbations [Cambiotti and Sabadini, 2010; Cambiotti et al., 2010], on the basis of Runge-Kutta integration in the radial variable of the differential equations describing momentum conservation and self-gravitation. Thus, it also overcomes the limitation of assuming incompressibility in co-seismic studies [Sabadini et al., 2005; Melini et al., 2010]. [3] Because the gravitational effect of sea level feedback has been important for the 2004 Sumatran earthquake [de Linage et al., 2009], we also add a self-consistent treatment of the global ocean layer of PREM. In this way, we refine the approaches used by Han et al. [2006] and de Linage et al. [2009] although, from a quantitative point of view, our approach does not significantly change the results presented by them. [4] This novel theoretical treatment in the modeling is accompanied by new efforts in the treatment of the GRACE data time series that are aimed at optimizing the estimate of the co-seismic gravitational component of the 2004 Sumatran earthquake and providing a realistic comparison between observations and models. The 2004 Sumatran earthquake was one of the strongest non-periodic gravity variations that occurred at the Earth's surface in the last decade. However, the analysis of the earthquake signature in GRACE data is quite challenging because of the step-like shape of the phenomenon. Additional contamination may originate from other phenomena occurring in the Sumatran region, such as hydrological and residual ocean circulation cycles. Moreover, the peculiar noise associated with GRACE data is particularly strong at equatorial latitudes, and its north–south shape is troublesome. We devote particular attention to removing those signals other than the co-seismic jump from GRACE data time series to quantify the asymmetry between the negative co-seismic gravity anomaly north–east of the Sumatran trench and the positive one south–west, which is ascribed to the co-seismic dilatation within the crust by Han et al. [2006] or to the sea level feedback by de Linage et al. [2009]. [5] We then discuss the physical process that is responsible for this spatial asymmetry, and, similar to the concept suggested by Gross and Chao [2006] for space-based Earth rotation measurements, we exploit gravity data from the GRACE space mission to help constrain the seismic source model of the 2004 Sumatran earthquake obtained by the multiple centroid-momentum-tensor (CMT) source analysis of Tsai et al. [2005]. 2. Gravitational Perturbations Due to Co-Seismic Volume Changes [6] To evaluate co-seismic perturbations and at the same time separate the contribution due to volume changes within the different layers of the Earth in the total gravitational perturbation, we propose an alternative approach to the classic definition of the gravitational potential in terms of the volume integral of the ratio of the density distribution over the distance from the observation point. In addition to computational advantages, our approach allows to point out an important aspect of the way in which the seismic source is taken into account that, if neglected, can lead to erroneous interpretations of the style of deformation (dilatational versus compressional) as we will discuss in sections 5 and 10. [7] After the expansion in spherical harmonics, the gravitational potential ϕℓm(1) of harmonic degree ℓ and order m due to volume changes within a shell of the Earth defined by the radial interval I ⊂ [0, a], with a being the Earth's radius, is usually obtained as follows [Gross and Chao, 2006] where G, r, ρ and χℓm are the gravitational constant, the radial distance from the Earth's center, the initial density and the degree-ℓ order-m volume change with Uℓm and Vℓm being the degree-ℓ order-m radial and tangential displacements. [8] Instead of this approach, equation (1), let us consider the Poisson equation after the expansion in spherical harmonics where ϕℓm is the degree-ℓ order-m total gravitational perturbation and Then, in order to distinguish the gravitational perturbation ϕℓm(1) due to the volume changes, within the chosen radial interval I ⊂ [0, a], from the remaining gravitational perturbation ϕℓm(2), we split the Poisson equation (3) as follows such that where HI is the characteristic function of the interval I Note that the right-hand side (RHS) of equation (6) describes the density perturbation due only to volume changes within the interval I, whereas the RHS of equation (7) is the remaining density perturbation. In order to define proper boundary conditions, we introduce the relevant gravitational fluxes such that where qℓm is the total gravitational flux Both qℓm(1) and qℓm(2), equations (10)–(11), must be continuous at the internal interfaces between the layers of the Earth model. The free Earth surface boundary conditions are while, for point-like surface loading at the north pole, the boundary conditions at the Earth surface are with δ0m being the Kronecker delta, selecting only order-0 harmonic coefficients. After some straightforward algebra, equations (6)–(7), together with the radial and tangential components of the momentum equation, can be cast in the following linear differential system where yℓm is the spheroidal 8–vector solution with T standing for the transpose and σℓm(rr) and σℓm(rθ) being the degree-ℓ order-m radial and tangential stresses, while Aℓ is the block 8 × 8–matrix composed of two 4 × 8–matrices Aℓ(U) and Aℓ(L) that we report in equations (A1)–(A3). Note that the form of the lower matrix Aℓ(L) (r) depends on whether r is within or outside of the interval I, equations (A2) and (A3), respectively. Here fℓm is the 8-vector describing the forcing that, for seismic sources located at the radial distance from the Earth's center rs, is given by with rs and δ(r − rs) being the radius of the seismic source and the Dirac delta. The expressions for fℓm(0) and fℓm(1) are given by equations (30)–(31) of Smylie and Mansinha [1971], together with the additional terms provided by Mansinha et al. [1979, equations (20)–(21)]. In Appendix B we report their complete expressions, equations (B1)–(B8). [9] Note that to obtain the system of 8 differential equations, equation (16), we have substituted into the momentum equation the sum of the gravity perturbations due to volume and topography changes −∇ (ϕℓm(1) + ϕℓm(2)) for the total gravity perturbation −∇ ϕℓm. The momentum and Poisson equations are thus unaffected by the splitting of the Poisson equation (3) into equations (6)–(7), which are solved simultaneously and self-consistently for the gravitational potential perturbations ϕℓm(1) and ϕℓm(2), and for the displacement and stress fields. [10] The solution of the seismic problem, equation (16), yields with rC, H and bℓm being the core radius, the Heaviside function and the 8-vector given by P1 and IC are the projector for the 3-rd, 4-th, 6-th and 8-th components and the 8 × 4 − matrix defining the core-mantle boundary conditions that we discuss in the next section and that we report in equation (A4). Πℓ (r, r0) is the fundamental 8 × 8–matrix that solves the homogeneous differential system with the Cauchy datum at r0 given by the unit 8 × 8–matrix 18 By choosing r0 as the core, rC, and the seismic source, rS, radii, we then obtain the propagators Πℓ (r, rC) and Πℓ (r, rS) used in equations (20) and (21), respectively. 3. Core-Mantle Boundary Conditions [11] Let us now discuss how to obtain the core-mantle boundary conditions for the 8-vector solution yℓm, equation (17). As pointed out by Longman [1963], volume changes χℓm are allowed within the inviscid core only for compressional stratifications that satisfy the Williamson-Adams equation with g and κ being the initial gravity and the bulk modulus. On the contrary, compositional stratifications do not satisfy equation (24), and volume changes must be null in this case, χℓm = 0. However, for both compressional and compositional stratifications, the Poisson equation can be cast as follows Here, for the sake of simplicity and because we are more interested in the volume changes within the mantle and the lithosphere rather than in the Longman [1963] paradox, we decided not to discriminate the gravitational potential due to volume changes in the core, I ∩ [0, rC] = ∅. Thus, equations (6)–(7) and (10)–(11) become In view of the regularity conditions at the center of the Earth, r = 0, we know that with A and B being two constants. Then, the gravitational fluxes qℓm(1) and qℓm(2), equations (28)–(29), have to satisfy the following regularity conditions where we have utilized This way, following Longman [1963], Smylie and Mansinha [1971], and Chinnery [1975], we impose the core-mantle boundary conditions where IC and C4 are the 8 × 4–matrix, that we report in equation (A4), and the 4-vector of constants that must be determined by means of the Earth surface boundary conditions. 4. The Self-Consistent Global Ocean [12] In order to take into account in a physical self-consistent way the global ocean layer of PREM [Dziewonski and Anderson, 1981], we now derive how the Earth surface boundary conditions should be modified. We assume that the ocean behaves as an inviscid fluid and that its initial density ρw does not depend on the radial variable r, drρw = 0. Then, from equations (26)–(27), the Poisson equations for ϕℓm(1) and ϕℓm(2) become the Laplace equations within the ocean while the relevant gravitational fluxes ϕℓm(1) and ϕℓm(2) are still given by equations (28)–(29), substituting ρ with ρw. The solution of equation (36) can be expressed as where Aj and Bj, with j = 1, 2, are four constants of integration and Because, for the seismic problem, the top surface of the ocean is a free surface on which the radial displacement follows the geoid, we impose the following boundary conditions at the top of the ocean r = b (6371 km) Thus, from equations (39)–(40) evaluated at r = b, we obtain where for brevity we have defined α as Then equations (37)–(40) yield In order to determine B1 and B2, we must consider proper boundary conditions at the bottom of the ocean, namely at the interface r = a (6368 km) between the solid Earth and the ocean. Following Longman [1963], Smylie and Mansinha [1971], and Chinnery [1975], we impose with IO and O4 being the 8 × 4–matrix that we report in equation (A5), and the 4-vector of constants The two constants B1 and B2 describe the gravitational perturbations ϕℓm(1) and ϕℓm(2) within the ocean via equations (46)–(47), while B3 and B4 take into account the free slip and loading due to the water redistribution coming from the gap between the geoid and the radial displacement at the solid-fluid interface. [13] Let us now consider that the spheroidal 8-vector solution yℓm is determined with the four constants of integration C4 of the core-mantle boundary conditions (35) Then, equation (50) can be recast in the following block matrix equations which allow us to obtain the eight constants of integration C4 and O4 The case of perturbations of harmonic degree ℓ = 1 must also be considered in order to discriminate between gravitational perturbations due to volume, ϕℓm(1), and topography, ϕℓm(2), changes that can be non-zero, though the total degree-1 gravitational perturbations ϕℓm must be zero in view of the conservation of the center of mass [Farrell, 1972, pp. 774–777; Sun and Okubo, 1993]. In Appendix C, we discuss the additional considerations that this case requires. [14] We have now fully determined the perturbations both within the solid Earth and within the inviscid ocean. At the same time, we have accounted for the interaction between the ocean and solid Earth consisting of the oceanic water redistribution and its loading effect. It is noteworthy that for an infinitesimally thin ocean layer, in the limit of b → a, our approach reproduces exactly the sea level feedback discussed by Farrell and Clark [1976] in the case of a global ocean. Nevertheless, the present approach cannot be extended to a non spherically symmetric ocean; thus, it cannot consider the continents. On the other hand, it allows a correct description of the effect of the thickness of the ocean layer, which instead is neglected by the sea level theory of Farrell and Clark [1976]. For all intents and purposes, the effects for the Earth are small, because b − a = 3 km, and can be ignored. 5. Localized Volume Changes Due to Dip-Slip Faults [15] Owing to the approach to co-seismic volume changes discussed in section 2, it is possible to clearly point out a specific feature of dip-slip faults. Let us consider the different cases of the seismic source radius rS being within or outside of the interval I, where we evaluate the gravitational perturbations due to co-seismic volume changes. It is well known from Smylie and Mansinha [1971], Takeuchi and Saito [1972] and equation (20) that the seismic source is equivalently described by the step-like discontinuity of the spheroidal 8-vector solution yℓm at r = rS where [X(r)]−+ is the jump of the field X across the radial interface r If the seismic source is outside of the shell defined by the radial interval I, rS ∉ I, the gravitational fluxes qℓm(1) and qℓm(2) are continuous across rS in view of equation (A3) and of the fact that the only non-zero components of fℓm(0) and fℓm(1) are the 3-rd and 4-th components, equations (B1)–(B8). In contrast, if the seismic source is within the shell defined by the radial interval I, rS ∈ I, the gravitational fluxes qℓm(1) and qℓm(2) are discontinuous across rS in view of equations (A2) and (B6). Here, δ, γ and δ0m are the dip and slip angles of the seismic source and the Kronecker delta selecting only order-0 harmonic coefficients, while β is given by with μ and λ being the two parameters of Lamé. Note that the discontinuities of qℓm(1) and qℓm(2) compensate for each other, equation (58), reflecting that the total gravitational flux qℓm, equation (12), is indeed continuous across rS [Smylie and Mansinha, 1971]. [16] This peculiar behavior of the gravitational fluxes qℓm(1) and qℓm(2) can be explained by considering that the discontinuity in the radial displacement Uℓm yields a volume change, χℓmS, that is localized exactly at the seismic source due to the radial derivative of the radial displacement, ∂rUℓm, entering the geometric definition of volume changes χℓm, equation (2). As reflected by the dependence of equation (60) on the slip angle γ, it should be noted that for reverse and thrust faults, such as that of Sumatran, equation (61) describes a localized dilatation because γ ∈ [0°, 180°]. On the contrary, for normal faults, equation (61) describes a localized compression because γ ∈ [180°, 360°]. [17] In order to compute the gravitational perturbation ϕℓm(1) due to volume changes without including the effects of the volume change χℓmS localized at the fault discontinuity, we have to neglect the discontinuities of the gravitational fluxes qℓm(1) and qℓm(2), equations (57)–(58). This means that equation (A3) should be used instead of equation (A2) for the matrix Aℓ(rS) when we compute equation (21), even if rS ∈ I. This alteration of Aℓ(rS) entering equation (21) only has the effect of removing from ϕℓm(1) and ϕℓm(2) the contributions due to the opposite discontinuities in the relevant gravitational fluxes, equations (57)–(58), without altering the radial, Uℓm, and tangential, Vℓm, displacements and the total gravitational perturbation ϕℓm. Indeed, the gravitational perturbations due to these discontinuities cancel each other out and they then do not involve any effective volume force in the momentum equation. [18] As we will show in section 10, the gravitational effect of the volume change localized at the fault discontinuity can mask the typical style of deformation and, if not properly accounted for, causes the local dilatation associated with the seismic source to be erroneously interpreted as crustal dilatation, thus leading to the erroneous interpretation [Han et al., 2006] that reverse and thrust faults, as that of Sumatran, cause an overall dilatation within the solid Earth. 6. Sea Level Feedback [19] In order to gain further insight into the physics of the co-seismic gravitational perturbations due to the 2004 Sumatran earthquake, particularly regarding the asymmetry between the negative and positive gravitational anomalies observed in GRACE data [Han et al., 2006; de Linage et al., 2009], we begin by considering geoid anomalies ΔG rather than those in gravity δg. This way, we can directly compare geoid anomalies ΔG and radial displacements U in terms of sea level variations ΔS describing the water redistribution responsible for the sea level feedback on the geoid anomalies. [20] We present the results obtained by using the seismic source model of Tsai et al. [2005], which is composed of five point-like sources with total seismic moment NS = 1.17 × 1023 N · m, and with the use of an isotropic 350 km Gaussian filtering [Wahr et al., 1998]. Although more realistic slip distributions over the fault are typically used to explain seismic waves and ground motions from GPS [Ammon et al., 2005], in the present work we use the along strike five seismic source model used by Tsai et al. [2005]. However, at the limited spatial resolution of GRACE data, the difference with respect to the use of a more realistic slip distribution is expected to be small. Slip distribution along dip instead affects the long-wavelength seismic signal, a sensitivity that we will use in section 9 to obtain information about the depth at which the largest seismic moment has been released, by considering different source depths. [21] To better isolate the main features of the co-seismic phenomenon, we focus on the maximum, ΔGmax, and minimum, ΔGmin, geoid anomalies and we investigate the main physical processes affecting the asymmetry coefficient AS, that we define as the ratio between the absolute values of the maximum positive, ΔGmax, and negative, ΔGmin, geoid anomalies [22] Figure 1 shows the co-seismic geoid anomalies for compressible self-gravitating Earth models based on PREM [Dziewonski and Anderson, 1981], both eliminating (Figure 1a) and including (Figure 1b), as discussed in section 4, the 3 km thick ocean layer. We refer to these models as S-PREM (Solid PREM) and O-PREM (Ocean PREM), respectively. For S-PREM, we obtain maximum and minimum geoid anomalies of +2.57 mm and −2.28 mm, respectively, and the asymmetry coefficient is AS = 0.88. The bipolar shape of the geoid anomalies of S-PREM closely resembles that of the gravity anomalies of Sun and Okubo [1993, Figure 7] for a dip-slip source within a spherically symmetric, self-gravitating Earth model as in our case. A detailed comparison is beyond the scope of our study because of different spatial resolutions and differing materials and seismic source parameters that were used in the quoted paper. The positive geoid anomaly results slightly greater in absolute value than the negative one. This indicates that, even if crustal dilatation occurred for co-seismic perturbations due to the 2004 Sumatran earthquake, as suggested by Han et al. [2006], it is not sufficiently large to explain the spatial asymmetries by GRACE. On the contrary, for O-PREM, we obtain maximum and minimum geoid anomalies of +1.24 mm and −2.52 mm, respectively, and the asymmetry coefficient is AS = 2.03. Indeed, as shown in Figure 2, the sea level feedback to the geoid anomalies, which is obtained by subtracting the geoid anomalies for O-PREM (Figure 1b) from those for S-PREM (Figure 1a), is negative almost everywhere and of the same order of magnitude of the geoid anomalies for S-PREM, with a minimum value of −1.36 mm. Figure 1Open in figure viewerPowerPoint Co-seismic geoid anomalies for compressible (a) S-PREM and (b) O-PREM, after the 350 km Gaussian filtering. Figure 2Open in figure viewerPowerPoint Co-seismic geoid anomalies due to the sea level feedback, obtained by subtracting compressible O-PREM and S-PREM geoid anomalies shown in Figure 1, after the 350 km Gaussian filtering. [23] In order to better understand this issue, in Figure 3 we show the radial displacements at the solid Earth surface, r = a, for both S-PREM (Figure 3a) and O-PREM (Figure 3b), after the 350 km Gaussian filtering for the sake of comparison with the geoid anomalies shown in Figure 1. Note that the predicted maximum uplift, +93.1 mm, has an absolute value that is much larger than the maximum downdrop, −18.3 mm, by about a factor 5 for S-PREM. Furthermore, the loading due to water redistribution has a negligible effect on the radial displacement because the maximum uplift, +97.0 mm, and downdrop, −18.6 mm, for O-PREM differ from those for S-PREM by less than 3 per cent. These differences are, however, comparable with the geoid anomalies shown in Figure 1. The fact that the radial displacement is larger than the geoid anomaly by almost two order of magnitude indicates that the co-seismic sea level variation, equation (62), is mainly characterized by the variation of the topography rather than that of the geoid, and, thus, the uplifted crust displaces away ocean water, reducing the geoid anomalies in the near field of the Sumatran earthquake. Figure 3Open in figure viewerPowerPoint Co-seismic radial displacements for compressible (a) S-PREM and (b) O-PREM, after the 350 km Gaussian filtering for the sake of comparison with the geoid anomalies shown in Figure 1 in terms of sea level variations, equation (62). [24] Thus, we agree with de Linage et al. [2009] in saying that the asymmetry toward the negative pole of the co-seismic gravity anomalies observed in GRACE data is due the sea level feedback and we will exploit this information in section 9 to help constraining seismic source models of the Sumatran earthquake obtained by CMT source analyses of Tsai et al. [2005]. As it concerns the large crustal dilatation obtained by Han et al. [2006], it will be considered in more detail in sections 10 and 11. 7. GRACE Data [25] The peculiar step-like shape of the signature due to an earthquake is quite difficult to resolve in gravitational data analyses using standard approaches. The time resolution of the GRACE data is the highest ever achieved by a satellite-only campaign on gravity variations, but it still poorly resolves co-seismic phenomena in detail. The 1-month time resolution is adequate, but it does not allow discrimination of very short time-scale phenomena and the co-seismic signal is clearly contaminated by post-seismic effects and by any other phenomena that occurred in the same geographical area during and immediately after the earthquake. Moreover, the peculiar noise of GRACE data, the so-called stripes, is particularly strong at equatorial latitudes; thus, its typical north–south shape can make data in the Sumatran region less clear. A good treatment of the stripes is therefore important. Among the various solutions proposed recently, we choose to rely on the anisotropic filtering described by Kusche [2007] and Kusche et al. [2009]. Indeed, at present, this decorrelation filter is the most accurate treatment of the stripe problem, and, because it is based on the analysis of the orbital characteristics of the GRACE space mission, it does not suffer from the bias