Efficiency and optimization of the 3-D finite-difference modeling of seismic ground motion

We present a tutorial introduction to the 3-D finite-difference modeling of seismic ground motion in elastic and viscoelastic media with special emphasis on its computational efficiency. We consider four basic types of the finite-difference schemes - the displacement-stress, displacement-velocity-stress and velocity-stress schemes on a staggered grid, and displacement scheme on a conventional grid. Their memory requirements in the case of perfectly elastic medium, elastic medium with aposteriori approximate attenuation correction, and realistic viscoelastic medium are reviewed. We also present application of the powerful optimization techniques to the 3-D fourth-order displacement-stress and displacement-velocity-stress modeling in the case of viscoelastic medium whose rheology is based on the generalized Maxwell body. Description of a medium using material cell types and use of a discontinuous grid with combined memory optimization makes it possible to simulate earthquake ground motion in realistic large-scale models.