为对中国自主重力/重力梯度卫星在陆地地震研究中提供理论依据，本文选取了主喜马拉雅逆冲断层（MHT），模拟了断层在同震和震间滑移产生的大地水准面、重力变化和重力梯度变化。首先给出了大地测量数据反演断层滑动分布的马尔可夫链—蒙特卡洛方法，实际反演中，Markov链的总长度由4×10⁷个模型组成，燃烧阶段和采样阶段的长度均为2×10⁷个模型，重采样的间隔为1000，初始温度设为100，终止温度为0.1。再次给出了基于反向滑移模型估计震间断层的耦合度。利用GPS和InSAR数据，对2×10⁴个重采样的模型取平均后，反演得到MHT的同震滑移和震间耦合分布，结果表明：2015年M_w 7.8尼泊尔地震同震破裂并未达到地表，最大滑移量约为6 m，地震矩为1.02×10²¹ Nm，相当于M_w 7.9，与其他手段得到的结果一致；MHT的震间耦合模型表明MHT在中上地壳以上部分在震间均处于闭锁状态，积累的能量相当于每年一个M 7地震。基于以上反演的断层滑移/滑移亏损模型，模拟了MHT同震和震间的重力场变化。变形地表面的同震重力变化呈南北两极分布，范围为-261—125 μgal，理论上能够被陆地重力测量所检测到。长波长的震间空间重力/重力梯度变化信号难以被当前重力卫星观测到；对冰川等大尺度质量效应进行改正后的同震重力/重力梯度变化有望被提高测量精度的下一代重力卫星检测出。本研究成果对中国未来发射的自主重力卫星数据在地震发生和孕育方面的应用研究将提供有益的启示。

Low-low tracking gravimetric satellite Gravity Recovery and Climate Experiment (GRACE) with a spatial resolution of 330 km can detect gravity field change due to mass migration of the Earth. Numerous studies show that coseismic and postseismic gravity changes caused by several megathrust earthquakes (>M_w 8.8) in the ocean can be detected by GRACE. The gravity gradient satellite Gravity field and steady-state Ocean Circulation Explorer (GOCE) can provide a global gravity and geoid model with high accuracy and a high spatial resolution of 80 km. However, GOCE measurements cannot be used to detect gravity signals induced by any earthquake because of high-frequency noise. Previous studies focused only on the oceanic earthquake and gravity change but not fault creep during the interseismic period. In this paper, we simulate the gravity and gravity gradient changes caused by interseismic coupling of the Main Himalaya Thrust, as well as the coseismic rupture of the 2015 Nepal M_w 7.8 event.
The MHT, where most crustal deformation occurs, absorbs half of the total India-Eurasia convergence rate (~20 mm/yr). Large earthquakes that recur along the Himalaya front must be related to the MHT rupture, for example, the 2015 Nepal earthquake. We first jointly invert the coseismic slip distribution of the 2015 Nepal event, which occurred at the seismic gap between the 1505 M 8.5 and 1934 M 8.2 events, using Markov chain Monte Carlo approach from GPS and InSAR observations. The InSAR data from ALOS-2 are resampled by using the quadtree technique. Green’s function is computed by using a spherically layered dislocation theory. The inverted average slip model shows that the maximum slip is approximately 6±0.7 m, and the seismic moment is approximately 1.02×10²¹ Nm, which is equivalent to M_w 7.9. The result is similar to that of other studies.
Then, we invert the interseismic slip deficit of the MHT from GPS data that are post-processed by removing the block rotation effect based on the backslip model. The interseismic coupling model, which is converted from the slip deficit, shows that almost all 20 km of the uppermost MHT was locked during the interseismic period. It includes the coseismic slip region of the 2015 Nepal event. The seismic moment deficit is approximately 6.8×10¹⁹ Nm/yr, which is consistent with other studies.
We compute the gravity changes at the Earth surface with a full wavelength on a 3’×3’ grid on the basis of the coseismic slip and interseismic slip deficit models. After considering the gravity change by vertical deformation, coseismic gravity change at the deformed surface has a dipolar distribution of gravity increase at the north of the epicenter and a decrease at the south. The magnitude of gravity change ranges from -261 μGal to 125 μGal and can be detected by traditional land gravimetry. The gravity change at Lhasa is -0.12 μGal, which was detected by using a superconductor gravimeter. Unlike the coseismic gravity change, the interseismic gravity change rate of the MHT after free air correction around the MHT ranges from -0.65 μGal/yr to 1.4 μGal/yr, which is difficult for gravimeters to detect with an accuracy of 10 μGal.
We synthesize geoid, gravity, and gravity gradient tensor changes with long wavelengths caused by coseismic slip and interseismic slip deficit of the MHT by using spherical harmonic expansion of gravity changes. The truncation degrees of geoid and gravity are 60, and that of the gravity gradient tensor is 250, which is consistent with that of GRACE and of GOCE. In addition, similar to GRACE data post-process, geoid and gravity are smoothed by using a DDK3 filter, which is useful for damping the high-frequency noise. Gravity satellite is not sensitive to crustal vertical deformation; thus, gravity changes of the full wavelength without free air correction are used to expand into spherical harmonics. Results show that coseismic geoid and gravity changes with 60 degrees are distributed at the surface with a dipolar pattern. For the coseismic phase, the magnitude of geoid change is -0.2-0.3 mm, and that of gravity change is -0.9-1.2 μGal, which cannot be detected by GRACE with an observation accuracy of approximately 2 μGal. The synthetic interseismic geoid and gravity changes have an opposite pattern to the coseismic signals. The magnitudes of interseismic geoid and gravity are -0.026-0.014 mm/yr and -0.11-0.08 μGal/yr, respectively. The synthetic interseismic signals are much smaller than those values because of glacier melting on high mountains.
The space coseismic gravity gradient of T_rr has a dipolar pattern with a magnitude of -27-31 mE; components of T_rθ and T_θθ have a tripolar pattern, and the magnitudes are -27-20 mE and -22-19 mE. The signals of the other three components are weaker at approximately ±10 mE. Unlike coseismic signals, all components of the interseismic gravity gradient tensor have a tripolar pattern in the range of -4-4 mE.
Indubitably, gravity and gravity gradient changes with a low degree due to interseismic coupling of the MHT may not be detected by gravimetric satellite directly given their weaker signals compared with changes due to glacier mass migration or land water storage change. However, after careful correction for other sources, we can extract the gravity or gravity gradient change from next-generation gravimetric satellites, the measurement accuracy of which will be improved by new techniques such as laser ranging and an accurate gradiometer in the future.