Abstract
In this paper, we study seismic responses to an earthquake source in horizontally stratified transversely isotropic porous media with a vertical axis of symmetry that is, transversely isotropic porous media. We present a semi-analytical method to simulate the three-dimensional time–space–domain seismic wavefields. We obtain the solution in the frequency–wavenumber domain by the global matrix method and transform it to the time–space domain by the discrete wavenumber method and fast Fourier transform. Our method incorporates the moment tensor source so that it allows simulating seismic responses to an earthquake. We validate our method by degenerating the transversely isotropic porous media into the isotropic porous media and transversely isotropic solid media, respectively, and compare the results with the corresponding reference solutions. We then investigate the characteristics of seismic wavefields in the transversely isotropic porous media by considering an explosive source, a shear-wave source and a double-couple source. The results reveal interesting observations in the transversely isotropic porous media versus the isotropic porous media. For example, the
q
S
V
wave can have a response to the pore pressure during its propagation in a transversely isotropic porous medium while the shear-wave does not generate any disturbance of the pore pressure. Our method is semi-analytical and computationally efficient and it can be used for rapid evaluation of the seismic responses in transversely isotropic porous media.
Keywords
Anisotropy, Mathematical formulation, Modelling, Wave