Simulation of surface displacement and strain field of the 2011 Japan Mw9. 0 earthquake

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1 Geodesy and Geodynamics 211,2(4) : jgg9. com Doi:1.3724/SP.J Simulation of surface displacement and strain field of the 211 Japan Mw9. earthquake Ch en Sh UJUn., W u J' Jane h ao, Le' 1 D ongrung., C m. Y ongpan.., L' 1 H eng an d Zhan g Xinli n 3 1 lnstituje of Seismology, Chi= Earthquake Administration, Wuhan 4371, Chi= 'InstituJe of Earthquake Engi=ering of Wuhan, Wuhan 4371, China 3 Earthquake &search lnstinae, University of Tokyo , Japan Abstract: Based on dislocation theory of Okada, we adopted a finite-element fault model inverted by Gavin Hayes from seismic data for the 211 Japan Mw9. earthquake, and obtained the corresponding surface displacement and strain fields. The calculated displacement field is consistent with the observed GPS results in the trend of changes. Also the surface displacement and strain fields both show large variations in space. Key words: finite fault model ; fault dislocation; displacement field; strain field 1 Introduction The magnitude 9. Japan earthquake which occurred near the northeastern coast of Honshu in Japan on March 11, 211 had a long duration of 15 s to 3 s and generated tsunami waves 1-meters-high[!J. The earthquake and the tsunami together caused many deaths and property losses[']. Several previous studies suggested that the earthquake was caused by an eastward thrust movement of the Eurasian plate, under which the Pacific plate dramatically subducted westward fron Japan Trench [ 3 J. However, according to Seno' s division of the Northeastern - Asian plate [ 4 l, we consider the earthquake to be a typical plate-margin event located in the Okhotsk micro-plate, which is part of the North America plate. At the latitude of this earthquake, the Pacific plate moves approximately westwards with respect to the North America plate at a rate of 83 mm/ a and begins Received: ; Accepted: Corresponding author:tel: ; public. wh.hb.cn This study was supported by the Director Foundation of Institute of Seismology, CEA(IS215688) its descent beneath Japan at the Japan Trench[S-!OJ. In this study, we used the latest finite-element model provided by the USGS on the basis of inversion of seismic data and the dislocation model of Okada to calculate the surface displacement and strain caused by this earthquake. 2 Calculation method Dislocation theory has been used to interpret the relationship between the distribution of dislocation along a discontinuous plane and the displacement field in the surrounding continuous medium. The complete set of analytical expressions derived by Okada[ll-!7] have been commonly used to calculate crustal-displacement field caused by a strike-slip, normal, or thrust fault. where,\ and p. are the Lame constants, v, is the included angle cosine of the normal line of point source surface. z/, is displacement component i caused by force F at point ( ~ 1, ~2, ~ 3 ) in direction j. This expression is applicable to analyzing both the static displacement and

2 No.4 Chen Shujun et al. Simulation of surface displacement and strain field of the 211 Japan Mw9. earthquake 29 the strain changes caused by an earthquake. 3 Finite-element fault model According to the USGS website, this earthquake had an epicentrallocation of ( N, E), a focal depth of 32 km, and a seismic moment of 3. 6 x 1 22 Nm. The strike and plrmge angles of the principal compressive stress axis are 115 and 32, respectively; the strike and plunge angles of the principal tensile stress axis are 36 and 58, respectively. The strike, dip and slip angle of the two nodal planes are 29, 77, 95 and 187, 14, 68, respectively. The parameters given by GCMT were somewhat different, but both showed that this earthquake was the result of a low-angle thrust faulting. Many studies have been carried out on the seismic rupture of this earthquake[ 18 ' 191, they all showed it to he bidirectional spreading to a breadth of 4 km in the south-north direction in 12 seconds. In this study, we used a finite-element model which had been inversed from GSN broadband seismic waveforms by Gavin Hayes[ 2 ' 211 This model consists of 364 nodes and 325 finite-element grids, with 25 x 13 along the strike and dip directions of the fault plane. The area of each elemental grid is about 5 km 2 The Poisson ' s ratio IL is. 25 and Young modulus E is 8 x 1 1 Pa. The friction coefficient/ is. 4 and the dip angle of the fault plane is about o. The top of the fault plane is at a depth of km and the bottom at km (Fig. 1). 4 Calculation results 4. 1 Displacement field The calculated horizontal-displacements on earth ' s surlace are oriented predominantly from west to east, pointing approximately to the epicenter ( Fig. 2). The displacements in the region north of 38 N ( latitude of the epicenter ) are larger than those south of 38 N and are pointing approximately toward southeast. The displacement increases gradually with decreasing epicentral distance, being, for example, about 5 em at Aomori and 1 em at Morioka, located 128 km SSE of Aomori. In the region SSE of 38 N, the horizontal displacements are smaller and show an approximately EW orientation, not pointing to the epicenter as much. This difference in direction may he due to non-symmetrical rupture propagation at the seismic source. The maximum horizontal displacement is 4 em, near the epicenter. The calculated vertical displacement field is more complicated than the horizontal ( Fig. 3 ). The results shows a downward displacement in the area between X(km) Figure 1 The finite fault model for the earthquake[ll]

3 3 Geodesy and Geodynamics Vol.2 eastern Houshu and the Trench of Japan, but an upward displacement in a wider area with a borderline approximately coincident with the coastline. The large displacements around the northern and southern boundaries are caused by boundary effect in the calculation; they should be neglected. 41"N 4"N 39"N 38"N 37"N 36"N - _,. -~ -- _, ~ loocm Horizontal ~spalcement 14" E 141" E 142" E 143" E 144" E 145" E Figure 2 Calculated horizontal displacement field The vertical-displacement contours distribute roughly in NNE direction, with displacement largely increasing from west to east. The maximum subsidence along the east coast of Japan is - 3 em. In the positive-displacement area, there exist three maxima along the west Japan trench, the most prominent being the one in the epicenter area, where the displacement reaches 5 em Strain field According to the surface dilatation-strain map that we obtained for the earthquake ( Fig. 4), some complicated co-seismic increases occurred in most region of the earthquake fault' s hanging wall. The calculated maximum dilatation strain reaches 4 X 1-4, appearing in a large region from the Japan trench to the east boundary of the fault model. As a result of the boundary effect of the fault model, there is an obvious negative dilatation strain belt in the NNE-SSW direction from Morioka to Tharaki in Honshu. The dilatation strain decreases from south to north. The negative strain belt has the same strike direction as the boundary of the fault model. There is a large range of positive strain area on both sides of the above-mentioned negative strain belt. The negative and positive strain areas present a characteristic of stable and transitional changes, reflecting the 6 4" 4 4"N 4 39" 38" 39"N 38"N A f"' 2 - 'a'.:.. '" l5 37" 36" "N 36"N " E 141" E 142" E 143" E 144" E 145" E Figure 3 Calculated vertical displacement field Figure 4 Calculated dilatation-strain field -6

4 No.4 Chen Shujun et al. Simulation of surface displacement and strain field of the 211 Japan Mw9. earthquake 31 viscous relaxation effect of the medium on the earthquake fault's hanging-wall side after the earthquake. The long axis of the positive strain area has the same extension direction NNE-SSW as the west boundary of the fault model. The dilatation strain changes are relatively complicated near the epicentral region. The dilatation is positive north of the epicenter but negative to the south. There is a large negative-strain area from the Japan Trenth to the east longitude 144. In a large region from east Honshu to the trench, there are many regions of maximum positive strain, all of them extending in NNE-SSW direction. The calculated dilatation strain reflects a process of rapid strain release in the epicentral and neighboring region. To the east of the trench, there is a large range of extension and contraction region on the foot-wall side of the earthquake fault, showing the slip effect of a thrust fault in the subduction zone between North A merica and Pacific plates. Figure 5 shows the change of dilatation strain field a- long the A-B cross section of the upper crust. We may see a large positive strain area on the hanging-wall side and a negative strain area on the foot-wall side, separated by the fault plane. The dilatation changes near the fault plane are very complicated. The expansion and contraction areas show conjugated characteristics across the fault plane, revealing the complexity of strain released by the earthquake. Figure 6 shows the change of dilatation strain field along the C-D cross section of the crust and upper mantle. The result shows that there is an obvious boundary in the crust, about 2 km deep, where the dilatation strain field is discontinuous and mutational. Due to the boundary conditions, the dilatation strain in the two ends of the section appears abnormal. In the middle of the section, the dilatation displays a complicated image from to 1 km depth. The positive and negative dilatation extreme area always occurs in the vicinity of the boundary plane. The dilatation strain is changeable in the vicinity of l-2 J-4 :a :$' -6 ' c 8-8 A -1 so Datance> (km) Figure 5 Prof:Ue A-B of calculated dilatation strain i j " -4 :6-6 ' -8 ~ Disllllll:e(km) 4 5 Figure 6 Profile C-D of calculated dilatation strain this plane. 5 Conclusions 1 ) The simulated swface displacement field is consistent with the co-seismic displacement field observed by the Japanese Geonet GPS network[ 22 J, and consistent with the seismogenic structure of being a huge low-angle thrust fault, as obtained from seismogenesis research[23j.

5 32 Geodesy and Geodynamics Vol. 2 2) The co-seismic displacement field reaches far a way from the epicenter. 3) The vertical displacement field is more non-niform in space than the horizontal displacement field. 4) The strain field shows discontinuous changes on the surface and in deep crust, as expected from the a dopted models. Acknowledgements: The author just witnessed this earthquake in Tokyo on 11 March, 211. We are grateful to Earthquake Research Institute, University of Tokyo for obtained vigorous help and some data from him for this article. References [ 1] Poster of the Great Toboku Earthquake (northeast Honshu, Japan) of Mareh 11, 211-M...,Utude9.. http,//earthquake....,. g<n! earthquakes/ eqarchives/poster/211/ php, 211. [2] Jopan earthquake rou6mred 11168!"'"Pie were killed. http,//www. cea. guv. cn/iiiilllbge /html/8a fa5& d183c 1_content/11_3/3/ html. (in Chinese) [ 3] Zou Daobua. Japan strong earthquake and plate movement. Geography Education,211,(4) : (in Chinese) [ 4] Seno T, Sakurai T and SteinS. Can the Okhotsk plate be discriminated from the North American plate? J Geophys Res., 1996, 11 ' [5] Yin Jiaao and Zhu Yuanqing. Preliminary discussion on distribution and diolacation mode of the fault for Ms9. earthquake in Honshu, Japan. Journal of Geodecy and Geodynamics, 211, 31 (2), (inChine e) [6] Magnitude 9. near the east coast of Honshu, Japan. earthquake....,. g<n! earthquake,.! eqinthenew&l211/ mdidi"!jp". [ 7] Chen shujun, Y ao yunsheng, Zeng zuoxun, et al. Study on numerical simulation of tectonic stress field before and after reservoir impounding the head area of the Three Gorges. Chinese Journal of Rook Mechanic ond Engineering, 25, 24(2), ( in Chinese) [ 8] Wu jianchao, Chen shujun and Chen junhua. Numerical simulation of total displacement field change after impoundment of Three Gorges resenroir. Journal of Geodesy and Geodynamics, 29,29 (6), (in Chi..,.,) [ 9] Zhang Keliang and Ma Jin. Numerical simulation of co-seismic deformation of 211 Japan Mw9. earthquake. Geodesy and Geodynamic, 21, 2 ( 3), doi, dc/,p. J , 16. [1] Bai Yuzhu, Xujie, Xuxiwei, etal. Simulations on displacement fields of aground surl'ace in 28 W enchuan earthquake : the case of inverse and right-lateral motion of Yingxiu-Beichuan fault. SeismolOf!Y ond Geology, 21,32( I),!6-27. (in Chin""') [ 11 ] Okada Y. Swface deformation due to shear and tensile faults in a half-space. Bell Seis Soc. Am., 1985,75: [ 12 ] Okada Y. Internal deformation due to shear and tensile faults in a half-space. Bull Seis Soc Am., 1992,82: [13] Wan Yongge. Displacement and strain caused by Wenchuan earthquake. I of Institute of Disaster-Prevention Science and Technology, 29, 11 (1 ) : 5-9. ( in Chinese) [ 14 ] Won Y nngge, Shen Zhengkang, et ol. The mechanical effects of the 28 Ms7. 3 Yutian, Xinjiang earthquake on the neighboring faults and its tectonic origin of normal faulting mechanism. Chi """' Joumol of Geoph)"ics, 21, 53 ( 2), ( in Chi """') [ 15] Chinnery M A. The stress changes that accompany strike-slip faulting. Bull Seism Soc Amer, 1963,53, [16] Chen Yuntai., Lin Banghui, et al. The focal mechanism of the 1966 Hsingtai earthquake as inferred from the ground deformation observations. Chinese Journal of Geophysics, 1975,18(3) : (in Chinese) [17] Bai Yuzhu, Xu Jie and Zhou Bengang. Simulation ofvertical and horizontal displacement fields of 28 Wenchuan Ms8. earthquake. Technology for Earthquake Disaster Prevention, 29, 4 (3), (in Chi"""') [18] Shao Guangfu, Li Xiangyu, Ji Chen,et al. Focal mechanism and slip history of 211 Mw 9. 1 off the Pacific coast of Tohok.u earthquake, constrained with teleseismic body and swface waves. Earth Planets Space, 211,63, [ 19] Charles Ammon. Seismicity animations, fault rupture model, etc. of the Great 211 Tohoku-oki earthquake sequence. I eqseis. geosc. psu. edu/- cammon/ Japan211EQ/, 211. [ 2] Gavin Hayes. Preliminary results for Mw9. earthquake offshore Honshu, Japan. earthquake. usgs. gov/ earthquakes/ eqarchives/ subduction_zone, 211. [ 21 ] Gavin Hayes. Finite fault model-updated resoult of the Mar 11, 211 Mw9. eartuquake ofihsore Honshu, Japan. usgs. gov/ earthquakes/ eqinthe news/211/usc1xgp /finite_fault. php, 211. [22] Sun Wenke. Scientific interpret of the Mw9. earthquake in Japan. 211, The symposium papers of the hot issues in China Scientific Institution, 211. (in Chinese) [23] Xu Xiwei. Introduction to the Mw9. earthquake in Japan. http,; /www. eq igl. ac. cnlhtmv 8a834a81158ol5aa1158alhbbd 43/keyan/japandz2. pdf211, 211. (in Chinese)

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