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Seismic waves radiated from an earthquake propagate in the Earth and the ground shaking is felt and recorded at (or near) the ground surface. Understanding the wave propagation with respect to the Earth's structure and the earthquake mechanisms is one of the main objectives of seismology, and predicting the strong ground shaking for moderate and large earthquakes is essential for quantitative seismic hazard assessment. The finite difference scheme for solving the wave propagation problem in elastic (sometimes anelastic) media has been more widely used since the 1970s than any other numerical methods, because of its simple formulation and implementation, and its easy scalability to large computations. This paper briefly overviews the advances in finite difference simulations, focusing particularly on earthquake mechanics and the resultant wave radiation in the near field. As the finite difference formulation is simple (interpolation is smooth), an easy coupling with other approaches is one of its advantages. A coupling with a boundary integral equation method (BIEM) allows us to simulate complex earthquake source processes.

Finite difference simulations of seismic wave propagation for understanding earthquake physics and predicting ground motions: Advances and challenges