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 $qSV$ 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.

中文翻译：

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层状横向各向同性多孔介质中震源的地震响应

在本文中，我们研究了对具有垂直对称轴的水平分层横向各向同性多孔介质（即横向各向同性多孔介质）中的地震源的地震响应。我们提出了一种半解析方法来模拟三维时空域地震波场。用全局矩阵法求频波数域的解，用离散波数法和快速傅立叶变换将其变换到时空域。我们的方法结合了矩张量源，因此它允许模拟对地震的地震响应。我们通过将横向各向同性多孔介质分别退化为各向同性多孔介质和横向各向同性固体介质来验证我们的方法，并将结果与​​相应的参考溶液进行比较。然后，我们通过考虑爆炸源、剪切波源和双耦合源来研究横向各向同性多孔介质中地震波场的特征。结果揭示了横向各向同性多孔介质与各向同性多孔介质的有趣观察结果。例如，$q秒伏$横波在横向各向同性的多孔介质中传播过程中对孔隙压力有响应，而横波不会对孔隙压力产生任何扰动。我们的方法是半解析的且计算效率高，可用于快速评估横向各向同性多孔介质中的地震响应。