Simultaneous Synthesis of Static and Dynamic Ground Motions Near a Finite Fault in a Layered Medium

Recent development of geophysical observation instruments such as GPS have allowed us to obtain precise broadband data in wide dynamic and wide frequency ranges, including static displacements in a large area. Since theoretical studies analyze dynamic motions and static displacements individually, this study attempts to synthesize not only dynamic motions but also static displacements simultaneously and estimate effects of a surface layer on displacements in a frequency range of 0 - 1.5 Hz. When we represent seismic waves by the discrete wavenumber method, we face a difficulty in the choice of two factors to obtain accurate seismograms including static displacement: (1) the truncation number of wavenumber integration and (2) the representation of a potential in zero horizontal wavenumber. To find a suitable value of the truncation number of wavenumbers, we utilize a spatial domain solution using the analytic formulation for a homogeneous half space of Okada(1985) and estimate a wavenumber region in which the majority of energy is concentrated. For a finite rectangular fault buried in a half space, we find that a suitable value of the truncation number of wavenumber is 4 km^-1 by comparing the the analytical solution of Okada for static deformation. Secondly we find a new kind of singularities for a finite rectangular fault when both horizontal wavenumbers, k_x and k_y, go to zero, or in a case corresponding to VTSE (vertically traveling plane S-wave element). In order to deal with VTSE from a finite fault, a new S wave potential is introduced to obtain a displacement whose polarization is restricted on a horizontal plane. In order to remedy these singularities, we take an asymptotic solution for k_x = k_y = 0. These devices make it possible to simulate accurate seismograms, including dynamic and static components, for any fault configurations and station locations by our method. Moreover, we can apply our procedure to layered media to estimate the effect of a soft surface layer on static displacement. In the case of vertical strike slip fault, if a soft surface layer exists above a fault, static displacement at the surface is amplified by twice of in the half space case.