Three-dimensional finite-difference time-domain computation of the seismoelectric field generated by a slipping fault

A three-dimensional finite-difference time-domain (FDTD) algorithm is developed to solve Pride equations to obtain the seismic waves and the accompanying electromagnetic (EM) fields excited by an underground slipping fault. The seismic waves are calculated separately by solving Biot equations using a velocity-stress FDTD algorithm and the PML technique for the truncated boundary. The accompanying EM fields are calculated by the alternating-direction implicit method, which is unconditionally stable and requires much less computation time than ordinary implicit methods. Planar free-surface boundary condition, under which analytical solutions exist, is considered. Local grid refinement is applied to model the high attenuation of the electric field near the free-surface, which is caused by the high attenuation of the slow compressional wave converted at the free-surface. Seismoelectric fields exited by a double couple are calculated as an example. Good agreements between our numerical results and the analytical results show the validity of our FDTD algorithm.