The genetic algorithm method is combined with the finite‐element method for the first time as an alternative method to invert gravity anomaly data for reconstructing the 3D density structure in the subsurface. The method provides a global search in the model space for all acceptable models. The computational efficiency is significantly improved by storing the coefficient matrix and using it in all forward calculations, then by dividing the region of interest into many subregions and applying parallel processing to the subregions. Central Taiwan, a geologically complex region, is used as an example to demonstrate the utility of the method. A crustal block 120 × 150 km2 in area and 34 km in thickness is represented by a finite‐element model of 76 500 cubic elements, each 2 × 2 × 2 km3 in size. An initial density model is reconstructed from the regional 3D tomographic seismic velocity using an empirical relation between velocity and density. The difference between the calculated and the observed gravity anomaly (i.e., the residual anomaly) shows an elongated minimum of large magnitude that extends along the axis of the Taiwan mountain belt. Among the interpretive models tested, the best model shows a crustal root extending to depths of 50 to 60 km beneath the axis of the Western Central and Eastern Central Ranges with a density contrast of 400 or 500 kg/m3 across the Moho. Both predictions appear to be supported by independent seismological and laboratory evidence.

S U M M A R YForward computation of the gravity anomaly of a density model is often a necessary step in modelling the subsurface density of a region. For geologically complex regions, this step may be computationally demanding and become the bottleneck in gravity inversion. We present a fast finite-element method (FFEM) for solving boundary value problems of the gravitational field in forward computation of gravity anomaly in complex geological regions. Testing against analytical solutions show that the method is more accurate than the classical integration method in cases where density in the material body is highly heterogeneous. At the same time, FFEM is more efficient than the integration method by a factor between s/100 and s/10, where s is the number of stations at which gravity anomalies are computed. Since s is usually much greater than 10-100 in 3-D gravity inversion in geologically complex regions, FFEM may be significantly more efficient in gravity modelling of such regions. We illustrate the utility of this method by calculating the gravity anomalies in central Taiwan.

Many researchers calculated strain rate of significant differences from the same GPS measurement data. In this paper, we use the Kriging method in geostatistics to GPS velocity field. Interpolating the scattered GPS velocity data of Qinghai‐Tibetan plateau and its adjacent areas to grid point values by Kriging, we calculate the strain rates from these nodal values in each grid cell similar to derivative of shape functions (essentially Lagrange interpolation function) in finite element algorithm, and obtain the stable distribution of strain rate field in Qinghai‐Tibetan plateau. The results show that the main part of Qinghai‐Tibetan plateau is in the state of compression in north‐south direction, and extension in west‐east direction. On the contrary, in the eastern part of Tibet, the strain rate is compressive in west‐east and extensional in north‐south direction. The orientations of principal strain rates are consistent with those of the P axis and T axis in focal mechanism. The high values of maximum compressive principal strain rates are located in the Himalayan main boundary thrust zone (MBT) and the surrounded regions. The maximum extensive principal strain rates are higher than those of the compressive ones in the main part of the interior of Qinghai‐Tibetan plateau. Also, the surface dilation strain rate shows that it is in the state of surface compression in Himalayan and its surrounded areas, and in the state of surface extension in the interior of Qinghai‐Tibetan plateau. The distribution of maximum shear strain rate clearly displays the outlines of some main active fault zones. The result of the strain rate in this study suggests that the contemporary tectonic strain of Tibet inherits the long term geological deformation.

In Appling studies, the strain rate in China has been computed from using different methods, resulting in quite different estimates of the strain rate the geo-statistics from GPS velocity field of Chinese continent, we obtain the velocity value at each little regularly spaced grid point, by kriging interpolation and the component of strain rate for each volume element, using a method similar to the derivation of shape functions in the finite element algorithm. Therefore the distribution of the strain rate field in whole for the Chinese continent is presented. The result shows that the orientations of principal strain rates are consistent with those of the P and T axes of focal mechanisms. The distribution of maximum shear strain rate clearly delineates some major active fault zones surrounding the Tibetan Plateau. The maximum shear strain rate is comparable with that obtained from analysis of seismic moment release. In part of the Tibetan Plateau containing normal faults and pull-apart grabens, we obtain an extensional state of strain. The absolute value of the strain rate in West China is approximately 5 times larger than that of East China, and the pattern of the strain rate field in most of the Chinese continent is controlled by the India/Eurasia collision.

Seismic stress drop is a fundamental parameter for the investigation of earthquake mechanism. In general, it is indirectly predicted by fault slip based on the dislocation source model or seismic moment; inversion for the stress change on faults has not received the deserved attention. In this study, we propose a finite element method to invert the stress drop on fault, constrained by the observed coseismic deformation. Rupture termination and displacement on fault are automatically predicted from the model. Applying the method to the 2011 Mw9.0 Tohoku‐Oki earthquake, we find that the fault consists of two asperities with maximum shear stress drops of 11.7 and 10.1 MPa, respectively. The predicted maximum horizontal and vertical displacements on the hanging wall at the Japan Trench are 55.2 and 10.8 m, respectively, in good agreement with observation. The predicted total static moments of the mainshock and the Mw7.9 aftershock, 29 min after the mainshock, are 4.48 × 1022 and 1.46 × 1021 Nm, corresponding to moment magnitudes of Mw9.0 and Mw8.0, respectively, again in excellent agreement with the observationally determined Mw9.0 and Mw7.9 by the U.S. Geological Survey.