Stable discontinuous staggered grid in the finite-difference modelling of seismic motion

We present an algorithm of the spatial discontinuous grid for the 3-D fourth-order velocity-stress staggered-grid finite-difference modelling of seismic wave propagation and earthquake motion. The ratio between the grid spacing of the coarser and finer grids can be an arbitrary odd number. The algorithm allows for large numbers of time levels without inaccuracy and eventual instability due to numerical noise inevitably generated at the contact of two grids with different spatial grid spacings. The key feature of the algorithm is the application of the Lanczos downsampling filter. The algorithm of the discontinuous grid is directly applicable also to the displacement-stress staggered-grid finite-difference scheme.