The dynamic stiffness matrix method for seismograms synthesis for layered transversely isotropic half-space

Natural rocks and soils show significant anisotropic behavior owing to sedimentation and weathering, particularly apparent in the crust. However, seismograms synthesis for the anisotropic medium is scarce, especially bottlenecks for large-scale and broadband seismic wave propagation. In this paper, seismogram synthesis for a multi-layered transversely isotropic half-space due to seismic point sources is addressed by using a dynamic stiffness matrix method. The critical step of the proposed method lies in the construction of the global dynamic stiffness matrix in frequency-wavenumber domain, which avoids the accumulation of errors that appeared in the reflection and transmission matrix method. Exponential divergent terms related to wavenumber and layer thickness in dynamic stiffness matrix are extracted for fast simulating large-scale and high-frequency wavefield. The seismic point sources are equated to the external loads imposed at the introduced auxiliary surfaces, through which the dynamic stiffness matrix can be utilized to obtain the solutions. The accuracy is verified by comparing the proposed method results with three examples in the publications, involving different source types and depth scales. Two numerical examples regarding Thomsen parameters are given to illustrate the mechanism of wave propagation and ground motion in an anisotropic media. Numerical results show that the anisotropic characteristics affect the wave propagation time, waveform and wave-front energy distribution, further leading to shear wave splitting phenomena, which remarkably differ from the isotropic case. A case study using a simplified three-layered crustal structure model in Tibet elucidates that peak ground displacement and its distribution difference within the epicenter of 10 km by comparing with the equivalent isotropic model without considering anisotropic properties. The results show a 10.91% deviation in the location of the peaks, with amplitude differences of up to 120% due to a 45 degrees dip-slip source at different frequencies (from 1 Hz to 15 Hz).