Quasi-Cartesian finite-difference computation of seismic wave propagation for a three-dimensional sub-global model

Abstract A simple and efficient finite-difference scheme is developed to calculate seismic wave propagation in a partial spherical shell model of a three-dimensionally (3-D) heterogeneous global Earth structure for modeling on regional or sub-global scales where the effects of the Earth’s spherical geometry cannot be ignored. This scheme solves the elastodynamic equation in the quasi-Cartesian coordinate form similar to the local Cartesian one, instead of the spherical polar coordinate form, with a staggered-grid finite-difference method in time domain (FDTD) that is one of the most popular numerical methods in seismic-motion simulations for local-scale models. The proposed scheme may be a local-friendly approach for modeling on a sub-global scale to link regional-scale and local-scale simulations. It can be easily implemented using an available 3-D Cartesian FDTD local-scale modeling code by changing a very small part of the code. We implement the scheme in an existing Cartesian FDTD code and demonstrate the accuracy and validity of the present scheme and the feasibility to apply it to real large simulations through numerical examples. Graphical abstract