有限元模拟弹性位错的等效体力方法

计算地震位错造成的位移场和应力场,对于估计大地震引起的后续地震活动发展趋势十分重要.本文提出在弹性位错问题的有限元模拟中,用等效体力代替位错源,从而在构建几何模型时不用包含断层,却可以处理包含任意复杂断层的问题,极大降低建模的难度.使用此方法,本文计算并讨论了在球形地球模型下2011年日本Tohoku-Oki特大地震对华北地区断层的影响,结果表明此次地震使华北主要断层趋于稳定.

Equivalent-bodyforce approach on modeling elastic dislocation problem using finite element method

Dislocation theory is well applied to calculate coseismic and postseismic effects. A key signature of the theory is that the solution of displacement is discontinuous. Various numerical methods can handle such discontinuous problems using a mesh which includes the discontinuous plane explicitly. However, generating such a mesh could be challenging and time consuming. We introduce an equivalent-bodyforce approach to handle discontinuities appearing in elastic dislocation theory. This approach gets rid of meshing the fault plane explicitly and simplifies the FEM modeling process.Based on Burridge and Knopoff's work, we deduced a close-formed formula representing equivalent-bodyforce in FEM framework, and then compared our numerical results with Okada's analytical solution in a test case in order to check the correctness of our formula and codes. At last, the 2011 M_w9.0 Tohoku-Oki earthquake was studied. We compared our numerical results with GPS observations to check the correctness of our formula and codes again, and discussed the co-seismic effects in North China of this earthquake.In the test case, our numerical results differ from Okada's analytical solution by less than 3% in most computing regions. In modelling co-seismic effects of the 2011 M_w9.0 Tohoku-Oki earthquake, our numerical results of displacement field agree well with GPS observations in both direction and magnitude. The co-seismic stress changes in North China are in east-west tension with a magnitude about 1 kPa. The north-south compression is one order of magnitude smaller. The Coulomb failure stress changes on active faults in North China are negative which indicates more stable, except at the north end of the Tanlu fault zone where the Coulomb failure stress changes are about 100 Pa.Equivalent-bodyforce approach is applicable and accurate in FEM modeling. The 2011 M_w9.0 Tohoku-Oki earthquake makes faults in North China more stable except the north end of the Tanlu fault zone.