Abstract
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.
Highlights
Seismic waves radiated from an earthquake propagate in the Earth, which is often considered as an elastic medium the waves attenuate due to some anelasticity
We focus on the fact that an extreme ground motion is found even at depth, and this should have originated from the source process
Each method always has its merits and limits so that it is waited that various methods are developed and utilized. Such numerical codes have become popular for engineering/industrial purpose such as the quantitative seismic hazard/risk assessments [19], guaranteeing the numerical performance on parallel computers and obtaining the physically reasonable solutions are difficult tasks
Summary
Seismic waves radiated from an earthquake propagate in the Earth, which is often considered as an elastic medium the waves attenuate due to some anelasticity. Partially-staggered grids were proposed [5] to combine all the stress components at one point and all the velocity components at another point separated by half a grid step Such a modified method gives a better estimation of the boundary conditions, but additional operations are necessary. Appropriate absorbing boundary conditions over a wide range of frequencies allow proper calculation of the wave propagation phase and the residual displacement field This feature becomes important when seismologists are interested in geodetic deformation of very long periods as well as short-period ground motions. FDM1 is calibrated in its absorbing condition so as to work better at around a period of 100 s, while FDM2 is our conventional simulation of wave propagation adopted for a period of 1 s This discrepancy is important to understand when applying finite difference schemes for longperiod deformation processes. New approaches using graphic card as well as the usual CPU (GPU-CPU) have been recently developed [10]
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