Geodetic observations detecting coseismic ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, B05408, doi:10.1029/2011JB008849, 2012

Geodetic observations detecting coseismic displacements and gravity changes caused by the Mw = 9.0 Tohoku-Oki earthquake Xin Zhou,1 Wenke Sun,1 Bin Zhao,2,3 Guangyu Fu,4 Jie Dong,1 and Zhaosheng Nie2 Received 4 September 2011; revised 4 February 2012; accepted 22 March 2012; published 12 May 2012.

[1] This paper reports coseismic displacements and gravity changes caused by the Tohoku-Oki earthquake (Mw 9.0), as observed respectively using GPS in Japan and China and its surrounding area, and as observed by GRACE. To interpret geodetic observation data, we must choose a reasonable model among the slip models presented for the event. For this purpose, we first calculated the displacements using three slip models from USGS, UCSB, and ARIA respectively, with different dislocation theories. Then we compared the results with the displacements observed in Japan and China. Results show that the modeled coseismic displacements calculated using the slip model of Wei et al. (ARIA) and the spherically layered dislocation theory under the PREM model agree well with the observed ones, indicating that the Earth’s layer-structural and curvature effects should be considered. Then, we computed the coseismic geoid and gravity changes on the earth surface and at a space-fixed point using the three slip models and the spherically layered dislocation theory. Results show that the maximum coseismic geoid change reaches 2.5 cm and that the coseismic gravity changes are about 1000–600 mgal for a solid Earth. Furthermore, we processed GRACE data to extract coseismic changes with decorrelation and a Gaussian filter of 350 km. The gravity changes observed by GRACE were dominated by a decrease over the back-arc region, with 5 mgal reflecting coseismic crustal dilatation of the landward plate, which agrees well with the theoretically modeled values from the three finite fault models. After the 2004 Sumatra–Andaman and 2010 Central Chile (Maule) earthquakes, this study presents the third case of clear detection of coseismic gravity changes by GRACE. Citation: Zhou, X., W. Sun, B. Zhao, G. Fu, J. Dong, and Z. Nie (2012), Geodetic observations detecting coseismic displacements and gravity changes caused by the Mw = 9.0 Tohoku-Oki earthquake, J. Geophys. Res., 117, B05408, doi:10.1029/ 2011JB008849.

1. Introduction [2] The Tohoku-Oki earthquake (Mw = 9.0), which occurred near the east coast of Honshu on 11 March 2011, was the strongest earthquake in the modern seismic record of Japan. It is the fourth-largest recorded in the world during the last century. This earthquake generated huge tsunami (10 m high) and caused an unprecedented catastrophe for Japan, with damage including about 19 thousand people dead and missing, and the destruction of nuclear power facilities. 1 Key Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing, China. 2 Institute of Seismology, China Earthquake Administration, Wuhan, China. 3 GNSS Research Center, Wuhan University, Wuhan, China. 4 Institute of Earthquake Science, China Earthquake Administration, Beijing, China.

Corresponding author: X. Zhou, Key Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing 100049, China. ([email protected]) Copyright 2012 by the American Geophysical Union. 0148-0227/12/2011JB008849

The seismic ruptures extend more than 500 km along the fault in the subduction zone, where the Pacific plate subducts beneath the North American/Eurasian plate by 8 cm/yr. The GPS data show that the powerful earthquake permanently changed Honshu’s surface, coastline, and coordination. The east coast moved eastward with a maximum value of more than 4 m and sank about 1 m (http://www.gsi.go.jp/ chibankansi/chikakukansi_tohoku.html). Moreover, according to theoretical calculations reported by R. Gross (http://www. nasa.gov/topics/earth/features/japanquake/earth20110314. html), this quake caused a global redistribution of mass and changed the axis of maximum inertia of the Earth. [3] Near-field deformations are known to be detectable by geodetic measurements. Distinct coseismic deformations caused by great earthquakes have also been reported frequently in recent years, such as those for the 1999 Chi-Chi earthquake (Mw = 7.6) [Yang et al., 2000; Yu et al., 2001], the 2001 Kunlun earthquake (Mw = 7.8) [Lin et al., 2002], and the 2003 Tokachi-Oki earthquake (Mw = 8.0) [Irwan et al., 2004]. In addition, coseismic deformations in the far field caused by huge earthquakes were observed using

B05408

1 of 20

B05408

ZHOU ET AL.: DEFORMATION OF THE TOHOKU-OKI EARTHQUAKE

B05408

Figure 1. Three fault slip models for the Tohoku earthquake respectively given by (a) Hayes [2011], (b) Shao et al. [2011], and (c) Wei et al. [2011]. Black stars show epicenters of the three models. modern geodetic techniques. For example, the coseismic horizontal displacement changes caused by the Sumatra– Andaman Earthquake (Mw = 9.3) were detected using GPS data in Japan about 4500 km distant from the epicenter [Banerjee et al., 2005; Khan and Gudmundsson, 2005; Vigny et al., 2005; Fu and Sun, 2006]. [4] To interpret the observed coseismic deformations such as displacement, strain, tilt, and gravity change, one often computes the corresponding theoretical values using a dislocation theory [Okada, 1985; Okubo, 1991, 1992] for a halfspace media model. However, to compute coseismic deformations in a far field, a more realistic Earth model such as the PREM model [Dziewonski and Anderson, 1981] should be used. Sun and Okubo [1993, 1998] studied the surface potential and gravity changes generated by an internal dislocation in a symmetrical Earth model. Sun et al. [1996] further presented formulations for computing coseismic displacements. Their results showed that the effect caused by Earth’s stratified structure might be as large as a 25% difference compared to the half-space [Sun and Okubo, 2002], which should be considered globally. Sun et al. [2009], after summarizing their previous work, presented a completed set of formulations for computing coseismic deformation. Wang et al. [2010] compared the horizontal and vertical displacements of the 2008 Wenchuan earthquake (Ms 8.0) in the near field using the two theories. They found the spherical dislocation theory’s results agree well with GPS measurements, but they did not compare the differences in a far field. [5] Except for the displacements, the coseismic gravity field changes are similarly detectable using gravity measurements. For example, coseismic gravity changes generated by the Tokachi-Oki earthquake in 2003 were detected using superconducting gravimetry [Tanaka et al., 2001; Imanishi et al., 2004]. Furthermore, according to Gross and Chao [2001] and Sun and Okubo [2004], the satellite gravity mission GRACE is theoretically able to detect the coseismic gravity changes caused by a giant earthquake with magnitude of 8 or greater. Subsequently, the coseismic and postseismic gravity changes caused by 2004 Sumatra–Andaman Earthquake (Mw 9.3) were detected by GRACE [e.g., Han et al., 2006; Panet et al., 2007; Ogawa and Heki, 2007; Chen et al., 2007; De Linage et al., 2009]. To interpret

GRACE observation signals, some reports have described seawater redistribution effects on modeled coseismic gravity and geoid changes and concluded that these should not be ignored [De Linage et al., 2009; Cambiotti et al., 2011; Broerse et al., 2011]. Recently, the coseismic gravity changes reportedly caused by the 2010 Chile earthquake (Mw = 8.8) were detected again by GRACE [Han et al., 2010; Heki and Matsuo, 2010; Zhou et al., 2011]. [6] After the 2011 Tohoku-Oki earthquake (Mw 9.0) occurred, some researchers presented different fault slip models that had been inferred from seismic waveform data, GPS observation deformations or both data combination, such as models by Hayes [2011], Shao et al. [2011], and Wei et al. [2011]. Although the seismic moments of the three models are similar, the slip distributions differ greatly. To interpret the geodetic and geophysical coseismic and postseismic data, a proper seismic slip model is necessary. Therefore, in this study, we compare the three slip models using GPS data in both the near field (Japan) and the far field (China). Simultaneously, we compare the coseismic deformations using dislocation theories for half-space and spherical Earth models. Then we compute the coseismic geoid, and the gravity changes in Japan and China caused by the Tohoku earthquake using the best fault slip model and dislocation theory. These results provide a theoretical reference for researchers who are interested in fault slip inversion and gravity data interpretation. [7] The magnitude of 2011 Tohoku-Oki earthquake was intermediate of the 2004 Sumatra earthquake and the 2010 Chile earthquake, which provided another good chance for GRACE to detect coseismic gravity changes. We extracted the coseismic gravity changes observed by GRACE and used model-determined data at space-fixed points to interpret those signals.

2. Fault Slip Models of the Tohoku-Oki Earthquake [8] To interpret observed coseismic deformations, we must choose a proper fault slip model. To date, many fault models have been presented by different organizations and researchers. The selection of fault models here is based on

2 of 20

B05408


B05408

Figure 2. Coseismic displacements observed using GPS: (a, b) Horizontal and vertical displacements in Japan. (c) The horizontal displacement in China and surrounding areas. The two stations in China and the two in Korea with large displacements are denoted by red diamonds. the different data, i.e., two models are inversed from seismic wave data and another is from seismic and geodetic data, and different maximum slips for comparison with models from the similar data. For this purpose, we choose three original fault slip models presented by Hayes [2011], Shao et al. [2011], and Wei et al. [2011]. The slip distributions of the three models are all shown in Figure 1. [9] The Hayes [2011] model is an updated version of the USGS model for the Tohoku earthquake (Mw 9.0), with the epicenter located at (38.32 N, 142.37 E). The other two models give the same epicenters at (38.05 N, 142.8 E). To obtain the finite slip model, Hayes used the GSN broadband

waveforms downloaded from the NEIC to analyze 39 teleseismic broadband P waveforms, 22 broadband SH waveforms, and 55 long-period surface waves. The inversed finite fault comprises 25 13 sub-faults, each of which has a 25 km 20 km cell size, with a strike angle of 195 and a dip angle of 10 (Figure 1a). Shao et al. [2011] presented a different finite fault model (available at: http://www. geol.ucsb.edu/faculty/ji/big_earthquakes/2011/03/0311_v3/ Honshu.html) consisting of 19 10 sub-faults (25 km 20 km cell size) with strike angles of 198 and dip angles of 10 (Figure 1b) using GSN broadband waveforms downloaded from the IRIS DMC and 28 teleseismic broadband

3 of 20

B05408


B05408

Figure 3. Comparisons of observed and calculated coseismic horizontal displacements in four Japanese regions shown by yellow frames in Figure 2a. The modeled displacement values are calculated for the slip models by (a1–a4) Hayes [2011], (b1–b4) Shao et al. [2011], and (c1–c4) Wei et al. [2011] using a process described for the spherical Earth model [Sun et al., 2009]. The blue and green vectors show the GPS observations; the red and orange vectors show the modeled data. P waveforms, 25 broadband SH waveforms, and 54 longperiod surface waves. Wei et al. [2011] used the GSN broadband data downloaded from the IRIS DMC and GPS data preliminary solution provided by the ARIA team at JPL and Caltech to inverse the finite slip distribution model. They analyzed 27 teleseismic P waveforms and 21 SH waveforms. Subsequently, they inverted a finite fault model constrained using GPS observations. The model comprises 25 14 subfaults (25 km 20 km cell size) with a strike angle of 201 and a dip angle of 9 (Figure 1c). [10] As described above, although the fault size determined by Shao et al. [2011] is smaller than that reported by the others, the seismic moment is slightly larger because the

slip is larger than those of the other two models (Figure 1). The moment magnitude determined using Shao et al.’s model reaches 9.1, whereas those of the other two models are 9.0. The maximum slips of the Hayes [2011], Shao et al. [2011], and Wei et al. [2011] models are 33 m, 60 m, and 31 m, respectively. All occurred at the oceanic crust (Figure 1), which implies that the fault slip models are different because of their different data and fault size, although the same inversion method, similar strike, and dip angles are used. To determine the best model among them, it is necessary to compare the modeling results with the observation data. For this purpose, we compare the predicted coseismic displacements based on the three models

4 of 20

B05408


B05408

Figure 3. (continued)

using different theories with GPS observations in Japan and China.

3. Coseismic Displacements Observed Using GPS [11] To compare the three fault slip models, coseismic displacements obtained using GPS data are used. We choose two sets of GPS data. One is for the near field: Japan. The other is for a far field: China and its surroundings (Figure 2). The observed displacements in Japan were obtained using GEONET, provided by the ARIA team at JPL and Caltech. The ARIA coseismic displacement field version 0.3 is based on estimations from 6 min before to 9 min after the event, and includes fewer postseismic contaminants. The continuous GPS data in China were provided by Crust Movement

Observation Network of China. We obtained the coseismic offsets in ITRF-2005 by estimating the differences of mean positions measured 3 days before and 3 days after this event (detailed processing is explained by Zhao et al. [2012]). The GPS deformations in the two fields are depicted in Figure 2. Figures 2a–2c show the coseismic horizontal and vertical displacements in Japan and horizontal displacements in China caused by the Tohoku event. The 1232 GPS sites’ data in Japan show remarkable horizontal displacements, of which almost all are southeastward, extending 5.2 m; the large vertical deformations are almost all downward, reaching 1.1 m. [12] We also make use of 86 GPS stations’ observation in a far-field over 1000 km distant from the epicenter, including 2 sites in South Korea, 2 sites in Taiwan, and 82 sites in

5 of 20

B05408


B05408

Figure 3. (continued) mainland China. Figure 2c shows marked horizontal deformations at two points JLYJ (129.5 E, 42.87 N) and SUIY (130.91 E, 44.43 N) in Jilin province in northeastern China, reaching over 3 cm, and at two points, DAEJ (127.37 E, 36.4 N) and SUWN (127.05 E, 37.28 N) on the Korean Peninsula, with displacements reaching about 2 cm. Like the local deformations in Japan, the horizontal displacements in the regions described above are eastward. Vertical displacements are not used because of the large deviations. In the following section, we use the GPS data presented above to verify the fault slip models.

4. Comparison of Fault Models in Coseismic Displacements [13] To compare the modeling coseismic displacements with the GPS data in near and far fields, we use two dislocation theories for half-space [Okada, 1985] and spherically

stratified [Sun et al., 2009] Earth models. The processing for the half-space Earth model is described simply in the Appendix A. A dislocation theory in a spherical, non-rotating, elastic, and isotropic (SNREI) Earth model is used to compare the half-space. When we apply the spherical dislocation theory in the PREM model [Dziewonski and Anderson, 1981] to compute the deformations, spherical coordinates are used instead of Cartesian coordinates. According to Sun et al. [2009], the coseismic displacements are calculated using integrating the displacement Green’s functions over all subfaults, which are treated as point sources. Herein, the Green’s functions of four independent sources at arbitrary depths can be derived by spline interpolation of the Green’s functions at special depths. The coseismic displacements that were calculated using the two dislocation theories with three fault models in Japan and China are shown in Figures 3–5 and A1–A3. [14] Figures 3 and A1 portray the predicted maximum horizontal displacement in Japan with the Hayes [2011]

6 of 20

B05408


B05408

Figure 4. As shown in Figure 3, but for vertical displacement. model, which is smaller than the observed value. However, the results obtained using the other two models are larger. A similar phenomenon occurs with the vertical displacement depicted in Figures 4 and A2. The vertical displacements calculated at a few stations with the Hayes model are upward and opposite to observations. The results calculated using half-space and spherical dislocation theories shown in Figures 3, 4, A1, and A2 are fundamentally similar. However, the coseismic deformations in the near field with the Shao et al. [2011] and Wei et al. [2011] models fit the observed ones better than those computed using the Hayes model. The situation differs in the far field, China. Figures 5 and A3 show that the horizontal displacements calculated using the half-space theory are remarkably larger than those calculated using spherical dislocation; the predicted results are not different among the three models with spherical theory. [15] To elucidate the differences among the three fault model and between the two theories, we use a statistical method––root-mean square––for quantitative comparison. The RMS of these results is obtainable using the following formula. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi n X 2 i i n s^ ¼ uobs ucal

ð1Þ

i¼1

The numerical RMS errors for GPS stations in near and far fields are presented in Tables 1 and A1. Tables 1 and A1 show that deformation by spherical dislocation fits the GPS data better than the half-space deformation does. Therefore, the spherical theory is effective for coseismic deformation in the near and far fields, and the effects of earth’s curvature and layer structure cannot be ignored. A similar result is derived by Pollitz et al. [2011] through comparison of the coseismic displacements in half-space, homogeneous spherical model, and layered spherical model. For the half-space theory, the Hayes [2011] model agrees with observations in the far field better than either of the other two models does; but the Shao et al. [2011] model is

the best in the near field. Moreover, for the spherical theory, the Shao et al. [2011] and Wei et al. [2011] models are much better than Hayes both in horizontal and vertical displacements, and the Wei et al. model agrees best with the observation in the near field. In contrast, based on the three models, no significant differences exist in vertical in horizontal displacement in China. It can be inferred that the seismic moment, rather than the compact region of slip, mainly controls the coseismic deformations in the far field.

5. Coseismic Geoid and Gravity Changes 5.1. Coseismic Geoid and Gravity Changes on the Earth Surface [16] As discussed in section 4, the spherical theory with Wei’s fault slip model is the optimum strategy to calculate the coseismic deformations resulting from the Tohoku event. Based on this opinion, we calculate the coseismic geoid and gravity changes on the solid Earth surface caused by the Tohoku-Oki earthquake. The calculation procedure is the same as that for displacements, but it uses the geoid and gravity Green’s functions. We divide the central area (2 2 ) into grids of 0.1 0.1 , and the remaining area into 0.5 0.5 to guarantee computational accuracy. The calculated coseismic geoid and gravity changes for a solid Earth are depicted in Figure 6. [17] Figures 6a and 6b respectively portray the calculated coseismic geoid and gravity changes in the near field. It is apparent that the coseismic geoid changes are negative near land, reaching 2 cm, and positive in the ocean, reaching 2.5 cm, whereas coseismic gravity changes that are dominated by vertical crustal movement are opposite to the geoid. Results show that the gravity changes near the east coast of Honshu reach about 50–100 mgal. They are expected to be detected using ground gravity measurements. In the oceanic trench area, gravity decreases about 1000 mgal, but it increases about 600 mgal near land. Figures 6c and 6d portray the coseismic geoid and gravity changes in eastern China: the coseismic geoid change is less than 0.8 mm, and

7 of 20

B05408


B05408

Figure 5. Comparisons of observed and calculated coseismic horizontal displacements in the far-field, China, and surrounding areas are shown. Other areas are shown in Figure 3. the gravity does not change remarkably in China. Therefore, coseismic gravity changes might be difficult to detect in mainland China. [18] For comparison with the Wei et al [2011] model, we also compute coseismic geoid and gravity changes in near and far fields using the Hayes [2011] and Shao et al. [2011] finite fault models (Figures 7 and 8). Figures 7a and 8a show that the coseismic geoid changes are from 1 to +2.9 cm for Hayes’ model and from 2.5 to +5 cm for Shao et al.’s model. Coseismic gravity changes on the solid Earth surface vary from about 1600 to +300 mgal for Hayes’ model and from 2800 to +900 mgal for Shao et al.’s model, as shown in Figures 7b and 8b. The results show that coseismic geoid and gravity changes predicted by Shao et al.’s fault model are larger much than those obtained from Hayes’ or Wei

et al.’s model. Furthermore, the computed geoid changes lie between 1.2 to +2.7 cm [Broerse et al., 2011] and gravity changes lie between about 1300 and +600 mgal [Sun et al., 2009] for a solid Earth because of the 2004 Table 1. RMS Comparison of PREM Modeled and Observed Coseismic Displacements Near-Field Displacements (cm)

Far-Field Displacement (mm)

Fault Model

Horizontal

Vertical

Horizontal

Hayes [2011] Shao et al. [2011] Wei et al. [2011]

22.6 13.1 7.8

17.2 4.9 4.5

2.5 2.4 2.5

8 of 20

B05408


Figure 6. Coseismic geoid and gravity changes in Japan and eastern China calculated using the Wei et al. [2011] fault model with spherical dislocation theory [Sun et al., 2009]: (a) coseismic geoid changes in Japan; (b) coseismic gravity changes in Japan; (c) coseismic geoid changes in eastern China; and (d) coseismic gravity changes in eastern China. Units: mm for geoid, mgal for gravity.

9 of 20

B05408

B05408


B05408

Figure 7. As shown in Figure 6, but computed using the Hayes [2011] model. Sumatra Mw 9.3 earthquake. Therefore, it is inferred that the geoid height and gravity changes from Wei et al.’s and Hayes’ models are more reasonable than those from Shao et al.’s model. However, in the far field, coseismic geoid and gravity changes mutually agree for the three fault models (Figures 6c, 6d, 7c, 7d, 8c, and 8d).

5.2. Coseismic Gravity Changes Detected by GRACE [19] GRACE, which was launched by GFZ and NASA in 2002, has been used to detect coseismic gravity changes resulting from the 2004 Sumatra earthquake (Mw 9.3) and the 2010 Chile earthquake (Mw 8.8) [Han et al., 2006;

10 of 20

B05408


B05408

Figure 8. As shown in Figure 6, but computed using the Shao et al. [2011] fault model. Panet et al., 2007; Ogawa and Heki, 2007; Chen et al., 2007; De Linage et al., 2009; Han et al., 2010; Heki and Matsuo, 2010; Zhou et al., 2011]. In terms of magnitude, the Tohoku earthquake (Mw 9.0) is intermediate of the 2004 Sumatra and 2010 Chile earthquakes. Therefore, it is also expected to be detected by GRACE. In fact,

according to Matsuo and Heki [2011], the coseismic gravity changes caused by the Tohoku earthquake can be detected by GRACE. In this section, we coseismically compare the coseismic gravity changes obtained using different fault slip models shown in section 2 with GRACE data.

11 of 20

B05408


Figure 9. Time series of GRACE non-seasonal gravity changes at (138 E, 39 N), the triangular site in Figure 10, as observed by GRACE, including 102 months of data for October, 2002–May, 2011, the date in March on which the earthquake occurred was removed. For each month, the P3M6 and 350 km Gaussian smoothing are used. Seasonal (annual and semiannual) and long-term linear signals were removed using least squares fitting. Unit: mgal.

Figure 10. Distribution of coseismic gravity changes measured by GRACE. The P3M6 and 350 km Gaussian filters were applied. Unit: mgal. The black star shows the epicenter. The triangle shows the location of the time series of GRACE gravity changes shown in Figure 9. The gravity change contours are shown every 1 mgal and are shown for each 2 mgal. 12 of 20

B05408

B05408


B05408

Figure 11. Modeled coseismic gravity changes at space-fixed points calculated using the Wei et al. [2011] fault model with spherical dislocation theory [Sun et al., 2009]. (a) Coseismic gravity changes with seawater correction and the Gaussian averaging with radius 350 km. (b) As in Figure 11a, but removing degrees and orders higher than 60. (c) Same as Figure 11b, but with deccorrelation technique. Unit: mgal. 5.2.1. GRACE Measurements [20] We use the GRACE Level2 data sets composed of 60 degree Stokes’ coefficients, released by the Center for Space Research, Univ. Texas. The data sets include those of 103 months from October 2002 to May 2011. Because of poor accuracy of the Earth’s oblateness values (C20), we must replace them with those from Satellite Laser Ranging

[Cheng and Tapley, 2004]. Because geophysical effects such as ocean tides, solid Earth and ocean pole tides, and atmospheric effects have already been removed by modeling, the GRACE data sets presumably include coseismic deformation reflecting the redistribution of mass. The hydrological effects are significant in gravity changes mapped by GRACE. They can contaminate the coseismic change signals.

13 of 20

B05408


B05408

Figure 12. As shown in Figure 11c, but with computation using the (a) Shao et al. [2011] fault model and (b) Hayes [2011] fault model. Unit: mgal. To remove these effects from GRACE data, we exploit the Global Land Data Assimilation System (GLDAS) hydrological model, which effectively models the hydrological signals [Rodell et al., 2004]. The hydrological signals combine soil moisture, snow water equivalent, and canopy data of the GLDAS Noah monthly model, which is gridded by 0.25 0.25 excluding latitude 60 to 90 . The data are truncated to the same degree as GRACE through spherical harmonic analysis. To reduce the significant longitudinal ‘stripes’, we apply a filtering scheme with decorrelation filtering P3M6 (remove a polynomial of 3 deg fitting for order 6 and above of Stokes’ coefficients) [Swenson and Wahr, 2006] and 350 km Gaussian smoothing. Such a filter radius with 350 km is reasonable because of the relation of Stokes coefficients degree 20; 000 . and spatial resolution: l ≈ n [21] To extract coseismic jumps from GRACE data, we first remove seasonal and long-trend signals using least squares fitting. Figure 9 presents a time series of GRACE gravity changes at the point of (138 E, 39 N) in Figure 10. The gravity change at this point (located at subduction zone) is greater than 5 mgal. Postseismic change is impossible to determine because of the short data sets. The gravity change distribution is calculated and shown for the area of 130 – 155 E longitude and 25 –50 N latitude with a 0.5 0.5 grid, where each gravity time series is calculated using the same filtering scheme and least squares fitting. The distribution of coseismic jumps, which is mapped in Figure 10, shows dominant negative gravity changes with ca. 5 mgal maximum change in the subduction zone, although the positive changes in the uplift zone are too small to distinguish because of the oceanic disturbance. Similarly to the 2004 Sumatra earthquake and the 2010 Chile earthquake, the magnitude of change in subduction zone is more remarkable than that in the uplift zone.

5.2.2. Modeling Coseismic Gravity Changes [22] In theoretical computations, using Wei et al.’s [2011] fault parameters, we calculated coseismic gravity changes following the method reported by Sun et al. [2009]. The calculated gravity changes show significant short-wavelength gravity changes with the maximum change of ca. 1 mGal near the epicenter, which mainly reflects surface deformation. [23] To apply theoretical results to interpret GRACE observation, two points must be considered carefully: (1) GRACE data do not reflect the radial crustal uplift or subside, and the corresponding free-air contribution must be excluded from the conventional dislocation formulation. (2) Because most crustal uplift occurred in the ocean area, the seawater at the oceanic bottom is discharged, and the corresponding seawater correction should be made. De Linage et al. [2009] first discussed seawater redistribution effects on coseismic gravity and geoid changes using a zeroorder approximation. Cambiotti et al. [2011] first presented a physical self-consistent Earth model with a global ocean layer (PREM) and modified Earth surface boundary conditions to model the coseismic geoid and gravity changes and the sea level feedback. Broerse et al. [2011] studied ocean contribution to coseismic geoid changes by solving a sea level equation in spectral domain and taking seawater loading effects into consideration. According to their studies, the seawater loading contribution is at least one order of magnitude smaller than the ocean mass redistribution. Therefore we exploit the seawater correction approach presented by De Linage et al. [2009] considering only the gravitational perturbation attributable to seawater redistribution. In addition, because of the ‘strip’ effect, the theoretical results should be smoothed using a filter like that used for GRACE data.

14 of 20

B05408


B05408

Figure A1. As shown in Figure 3, but using a process described by half-space [Okada, 1985].

[24] Figure 11a portrays the coseismic gravity changes at fixed points in space after adding seawater migration and 350 km spatial filtering. Similar Green’s functions and integral strategy to those used in the previous section are used herein. Results respectively show the maximum gravity change signals of 10 mgal on land and 5 mgal in the ocean. Those are considerably larger than the GRACE results, mainly because of a significantly high degree of signals remaining in coseismic jumps. [25] To compare the modeled gravity change with the GRACE results presented above, those short-wavelength signals must be removed from coseismic gravity changes. For this purpose, we truncate the modeling gravity changes at 60 deg in spherical harmonics. Then we use a 350 km Gaussian filter to smooth the coseismic changes truncated at 60 deg. Subsequently, we plot the results as in Figure 11b.

The amplitudes of gravity changes are reduced to a range of 6 mgal to 2 mgal, which closely resembles the GRACE results. Careful comparison between Figures 10 and 11b reveals a slight difference in the ocean area, where the modeled gravity shows an approximately 2 mgal signal. This phenomenon might result from the decorrelation applied in GRACE measurements. To confirm this inference, the same techniques (P3M6 + 350 km Gaussian filter) are used as those for the modeled gravity changes in Figure 11b, obtaining the final coseismic gravity changes shown in Figure 11c. Results portrayed in Figure 11c show that the modeled gravity changes agree well with those of GRACE. [26] Additionally, we compute the coseismic gravity change decorrelation using Shao et al.’s [2011] and Hayes’ [2011] models respectively with the techniques described previously (Figure 12). Figure 12 shows that gravity changes

15 of 20

B05408


B05408

Figure A1. (continued) from the two slip models also agree well with GRACE and that they can be comparable with those from Wei et al.’s [2011] model. Similarly to displacement in the far field, differences of the compact slip region affect the smoothed coseismic gravity changes of low degrees inconspicuously.

6. Discussion and Conclusion [27] The 2011 Tohoku-Oki giant earthquake (Mw 9.0) occurred at the subduction zone near Japan, engendering remarkable coseismic deformations that were observed clearly using GPS, with approximately 5 m horizontal and 1 m vertical displacements in Japan, and with about 3 cm horizontal displacement in eastern China. To determine a reasonable fault slip model, we compared three fault slip models presented respectively by Hayes [2011], Shao et al.

[2011], and Wei et al. [2011] with GPS observation data in Japan and China using dislocation theories for half-space and spherical Earth models. Results show that the details in slip distribution affect the far field displacements only slightly. Compared to those of the half-space model, the results obtained using dislocation theory for the PREM Earth model agree well with GPS displacements in both near and far fields. Results show that the displacements calculated using spherical dislocation theory with Wei’s model agree with GPS data. Shao et al.’s model was inversed from seismic wave data, whereas Wei et al.’s model was obtained from seismic and geodetic data. However, the latter seems to fit GPS displacements better than the former because the latter was constrained by GPS data. Although coverage of GPS data is limited to the Japanese mainland

16 of 20

B05408


B05408

Figure A1. (continued) area, the large seafloor deformation might not be constrained fully by GPS. Additionally, Shao et al.’s model shows that the peak slip reached about 60 m, which is almost double that of Wei et al.’s model. [28] We also discussed the coseismic geoid and gravity anomalies, computed with the three fault models, on the solid Earth surface in the near and far fields. Results show that geopotential field changes from Hayes’ [2011] and Wei et al.’s [2011] models are more reasonable than from Shao et al. [2011] after comparison with the 2004 Sumatra gigantic earthquake. Overly large geoid and gravity changes for Shao et al.’s model might be attributable to its large peak slip. Combining coseismic displacement and geopotential field change, we conclude that geodetic data can improve the finite fault model to a great extent. Using Wei et al.’s model and the spherical theory [Sun et al., 2009], geoid coseismic gravity changes are obtained as about 50–100 mgal in the

land area of Honshu, and the maximum negative gravity change reaches about 1000 mgal in ocean areas; the coseismic geoid changes lie between 2 and +2.5 cm. Furthermore, we processed GRACE data and extracted coseismic gravity changes, which agree well with the predicted ones. Results show that the negative gravity changes dominate the epicenter area. The smoothed low degrees of geopotential field were examined for comparison with GRACE. The coseismic gravity changes for the three models show almost complete mutual agreement.

Appendix A: Modeled Coseismic Displacements in Half-Space [29] Okada [1985] summarized the preceding work and presented a set of convenient analytical formulas, but it is necessary to transform the spherical coordinate to the fault

17 of 20

B05408


Figure A2. As shown in Figure 4, but using a process described by half-space [Okada, 1985].

Figure A3. As shown in Figure 5, but using a process described by half-space [Okada, 1985]. 18 of 20

B05408


B05408

Table A1. RMS Comparison Between Half-Space Modeled and Observed Coseismic Displacements Near-Field Displacements (cm)

Far-Field Displacement (mm)

Fault Model

Horizontal

Vertical

Horizontal

Hayes [2011] Shao et al. [2011] Wei et al. [2011]

23.6 15.2 16.8

18.0 6.3 6.2

5.3 7.8 7.4

Cartesian coordinate system that he defined. The Poisson ratio n = 0.25 is used for the half-space calculation. Then we transform the displacements from the fault coordinate system to the local north–east system by rotating a strike angle. The modeled coseismic displacements in the near field are shown in Figures A1 and A2, and the horizontal components in China are shown in Figure A3. Differences between results of observations and the model are listed in Table A1 using formula (1). [30] Acknowledgments. We thank three anonymous referees and the Associate Editor for thorough, thoughtful reviews that helped to improve the paper. GPS data were provided by the ARIA team at JPL and Caltech. All original GEONET RINEX data were provided to Caltech by the Geospatial Information Authority (GSI) of Japan. This study was financially supported by National Nature Science Foundation of China (grant 41174063).

References Banerjee, P., F. F. Pollitz, and R. Burgmann (2005), The size and duration of the Sumatra–Andaman earthquake from far-field static offsets, Science, 308, 1769–1772, doi:10.1126/science.1113746. Broerse, D. B. T., L. L. A. Vermeersen, R. E. M. Riva, and W. van der Wal (2011), Ocean contribution to coseismic crustal deformation and geoid anomalies: Application to the 2004 December 26 Sumatra–Andaman earthquake, Earth Planet. Sci. Lett., 305, 341–349, doi:10.1016/j. epsl.2011.03.011. Cambiotti, G., A. Bordoni, R. Sabadini, and L. Colli (2011), GRACE gravity data help constraining seismic models of the 2004 Sumatran earthquake, J. Geophys. Res., 116, B10403, doi:10.1029/2010JB007848. Chen, J. L., C. R. Wilson, B. D. Tapley, and S. Grand (2007), GRACE detects coseismic and postseismic deformation from the Sumatra– Andaman earthquake, Geophys. Res. Lett., 34, L13302, doi:10.1029/ 2007GL030356. Cheng, M., and B. D. Tapley (2004), Variations in the Earth’s oblateness during the past 28 years, J. Geophys. Res., 109, B09402, doi:10.1029/ 2004JB003028. De Linage, C., L. Rivera, J. Hinderer, J. P. Boy, Y. Rogister, S. Lambotte, and R. Biancale (2009), Separation of coseismic and postseismic gravity changes for the 2004 Sumatran earthquake from 4.6 yr of GRACE observations and modelling of the coseismic change by normal mode summation, Geophys. J. Int., 176, 695–714, doi:10.1111/j.1365-246X.2008. 04025.x. Dziewonski, A. M., and D. L. Anderson (1981), Preliminary reference earth model, Phys. Earth Planet. Inter., 25, 297–356, doi:10.1016/ 0031-9201(81)90046-7. Fu, G., and W. Sun (2006), Global coseismic displacements caused by the 2004 Sumatra–Andaman earthquake (Mw 9.1), Earth Planets Space, 58, 149–152. Gross, R. S., and B. F. Chao (2001), The gravitational signature of earthquakes, in Gravity, Geoid, and Geodynamics 2000: GGG2000 IAG International Symposium, Banff, Alberta, Canada, July 31–August 4, 2000, vol. 123, edited by M. G. Sideris, pp. 205–210, Springer, New York. Han, S. C., C. K. Shum, M. Bevis, C. Ji, and C. Y. Kuo (2006), Crustal dilatation observed by GRACE after the 2004 Sumatran–Andaman earthquake, Science, 313, 658–662, doi:10.1126/science.1128661. Han, S.-C., J. Sauber, and S. Luthcke (2010), Regional gravity decrease after the 2010 Maule (Chile) earthquake indicates large-scale mass redistribution, Geophys. Res. Lett., 37, L23307, doi:10.1029/2010GL045449. Hayes, G. (2011), Finite fault model: Updated result of the Mar 11, 2011 Mw 9.0 earthquake offshore Honshu, Japan, report, Earthquake Hazards

B05408

Program, U.S. Geol. Surv., Reston, Va. [Available at http://earthquake. usgs.gov/earthquakes/world/japan/031111_M9.0prelim_geodetic_slip.php.] Heki, K., and K. Matsuo (2010), Coseismic gravity changes of the 2010 earthquake in Central Chile from satellite gravimetry, Geophys. Res. Lett., 37, L24306, doi:10.1029/2010GL045335. Imanishi, Y., T. Sato, T. Higashi, W. Sun, and S. Okubo (2004), A network of superconducting gravimeters detects submicrogal coseismic gravity changes, Science, 306, 476–478, doi:10.1126/science.1101875. Irwan, M., F. Kimata, K. Hirahara, T. Sagiya, and A. Yamagiwa (2004), Measuring ground deformations with 1-second sampled GPS data: The 2003 Tokachi-oki earthquake (preliminary report), Earth Planets Space, 56, 389–393. Khan, S. A., and O. Gudmundsson (2005), GPS analyses of the Sumatra– Andaman earthquake, Eos Trans. AGU, 86(9), 89, doi:10.1029/ 2005EO090001. Lin, A., B. Fu, J. Guo, Q. Zeng, G. Dang, W. He, and Y. Zhao (2002), Coseismic strike-slip and rupture length produced by the 2001 Ms8.1 central Kunlun earthquake, Science, 296, 2015–2017, doi:10.1126/ science.1070879. Matsuo, K., and K. Heki (2011), Coseismic gravity changes of the 2011 Tohoku-Oki earthquake from satellite gravimetry, Geophys. Res. Lett., 38, L00G12, doi:10.1029/2011GL049018. Ogawa, R., and K. Heki (2007), Slow postseismic recovery of geoid depression formed by the 2004 Sumatra–Andaman earthquake by mantle water diffusion, Geophys. Res. Lett., 34, L06313, doi:10.1029/2007GL029340. Okada, Y. (1985), Surface deformation caused by shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 75(4), 1135–1154. Okubo, S. (1991), Potential and gravity changes raised by point dislocations, Geophys. J. Int., 105, 573–586, doi:10.1111/j.1365-246X.1991. tb00797.x. Okubo, S. (1992), Gravity and potential changes due to shear and tensile faults in a half-space, J. Geophys. Res., 97(B5), 7137–7144, doi:10.1029/92JB00178. Panet, I., et al. (2007), Coseismic and post-seismic signatures of the Sumatra 2004 December and 2005 March earthquakes in GRACE satellite gravity, Geophys. J. Int., 171(1), 177–190, doi:10.1111/j.1365246X.2007.03525.x. Pollitz, F. F., R. Bürgmann, and P. Banerjee (2011), Geodetic slip model of the 2011 M9.0 Tohoku earthquake, Geophys. Res. Lett., 38, L00G08, doi:10.1029/2011GL048632. Rodell, M., et al. (2004), The global land data assimilation system, Bull. Am. Meteorol. Soc., 85, 381–394, doi:10.1175/BAMS-85-3-381. Shao, G., X. Li, C. Ji, and T. Maeda (2011), Focal mechanism and slip history of 2011 Mw 9.1 off the Pacific coast of Tohoku earthquake, constrained with teleseismic body and surface waves, Earth Planets Space, 63(7), 559–564, doi:10.5047/eps.2011.06.028. Sun, W., and S. Okubo (1993), Surface potential and gravity changes due to internal dislocations in a spherical Earth–I. Theory for a point dislocation, Geophys. J. Int., 114, 569–592, doi:10.1111/j.1365-246X.1993. tb06988.x. Sun, W., and S. Okubo (1998), Surface potential and gravity changes due to internal dislocations in a spherical Earth–II. Application to a finite fault, Geophys. J. Int., 132, 79–88, doi:10.1046/j.1365-246x.1998.00400.x. Sun, W., and S. Okubo (2002), Effects of Earth’s spherical curvature and radial heterogeneity in dislocation studies: For a point dislocation, Geophys. Res. Lett., 29(12), 1605, doi:10.1029/2001GL014497. Sun, W., and S. Okubo (2004), Coseismic deformations detectable by satellite gravity missions—A case study of Alaska (1964, 2002) and Hokkaido (2003) earthquakes in the spectral domain, J. Geophys. Res., 109, B04405, doi:10.1029/2003JB002554. Sun, W., S. Okubo, and P. Vanicek (1996), Global displacement caused by dislocations in a realistic earth model, J. Geophys. Res., 101, 8561–8577, doi:10.1029/95JB03536. Sun, W., S. Okubo, G. Fu, and A. Araya (2009), General formulations of global coseismic deformations caused by an arbitrary dislocation in a spherically symmetric earth model: Applicable to deformed earth surface and space-fixed point, Geophys. J. Int., 177, 817–833, doi:10.1111/ j.1365-246X.2009.04113.x. Swenson, S. C., and J. Wahr (2006), Post-processing removal of correlated errors in GRACE data, Geophys. Res. Lett., 33, L08402, doi:10.1029/ 2005GL025285. Tanaka, Y., S. Okubo, M. Machida, I. Kimura, and T. Kosuge (2001), First detection of absolute gravity change caused by earthquake, Geophys. Res. Lett., 28(15), 2979–2981, doi:10.1029/2000GL012590. Vigny, C., et al. (2005), Insight into the 2004 Sumatra–Andaman earthquake from GPS measurements in Southeast Asia, Nature, 436, 201–206, doi:10.1038/nature03937. Wang, W., W. Sun, and Z. Jiang (2010), Comparison of fault models of the 2008 Wenchuan earthquake (Ms8.0) and spatial distributions of

19 of 20

B05408


coseismic deformations, Tectonophysics, 491, 85–95, doi:10.1016/j. tecto.2009.08.035. Wei, S., A. Sladen, and the ARIA group (2011), Updated result 3/11/ 2011(Mw 9.0), Tohoku-oki, Japan, report, Calif. Inst. of Technol., Pasadena. [Available at http://www.tectonics.caltech.edu/slip_history/ 2011_taiheiyo-oki/.] Yang, M., R. Juin, J. Yu, J. Y. Yu, and T. T. Yu (2000), Geodetically observed surface displacements of the 1999 Chi-Chi, Taiwan earthquake, Earth Planets Space, 52, 403–413.

B05408

Yu, S. B., et al. (2001), Preseismic deformation and coseismic displacements associated with the 1999 Chi-Chi, Taiwan, earthquake, Bull. Seismol. Soc. Am., 91, 995–1012, doi:10.1785/0120000722. Zhao, B., et al. (2012), Far field deformation analysis after the Mw9.0 Tohoku earthquake constrained by cGPS data, J. Seismol., 16, 305–313. Zhou, X., W. Sun, and G. Fu (2011), Gravity satellite GRACE detects coseismic gravity changes caused by 2010 Mw 8.8 Chile earthquake (in Chinese), Chin. J. Geophys., 54(7), 1745–1749, doi:10.3969/j.issn.00015733.2011.07.007.

20 of 20