Synthetic seismograms in transversely isotropic and elastic media below ocean floor

Earthquakes can occur onshore and offshore. When it occurs offshore, an analytical model is needed where both the water layers and rock layers have to be considered. In this paper, we develop such a new solution when a general dislocation source is located in any layer of the transversely isotropic and elastic rock media. This novel and comprehensive method is based on the Fourier-Bessel series system of vector functions combined with the unconditionally stable dual-variable and position method. Based on the new vector system, the discrete dislocation Love numbers are pre-calculated and saved for obtaining the Green's functions due to a general dislocation source in the water/rock layered system. The problem is first solved in the time-harmonic domain, and then transformed back to the time domain via the numerical Gaussian quadrature. After validating the accuracy of the proposed method, numerical examples are presented for the synthetic seismograms on the seabed (ocean floor) and the time-variation of the displacement and velocity on the ocean surface.