Structure-preserving modeling of teleseismic wavefield using symplectic SEM-FK hybrid method

Teleseismic full-waveform tomography can obtain high resolution velocity structure of upper mantle, and even the structure of mantle transition zone beneath the study area. It has been a vital tool in probing the Earth's internal structure and dynamic process. This method is based on effective forward simulation of seismic wavefield, which requires forward-modeling methods with high accuracy and long-term stability. Under this background, we present a structure-preserving scheme based on symplectic geometric theory, which is specially tailored for teleseismic wave modeling. The spectral element method (SEM) is used to discretize the study area. Without the consideration of the dissipation term, the discretized ordinary differential equation is transformed into a Hamiltonian system, which can be solved numerically by the symplectic-preserving partitioned Runge-Kutta (PRK) method. After adding an extra spatial discretization term into the PRK scheme, we developed a new symplectic scheme with fourth order temporal accuracy. We call the spatial-temporal discretized scheme symplectic SEM (SSEM). We combine SSEM with FK method, which calculates plane wave propagation in one-dimensional layered media. After that, we construct a hybrid method (SSEM-FK) to efficiently calculate teleseismic elastic wave propagation in regional heterogeneous model. Numerical experiments show that SSEM-FK can accurately simulate the propagation of high-frequency teleseismic wavefield in the study area. The advantage of this method in computational efficiency forms the foundation for high-efficient and high-accurate teleseismic full-waveform tomography.