P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method

Abstract

I present a finite‐difference method for modeling P-SV wave propagation in heterogeneous media. This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid. The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson’s ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson’s ratio. Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid‐solid interface. Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results. The weathered‐layer and corner‐edge models show in seismograms the same converted phases obtained by previous authors. This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half‐space. The head wave preserves the correct amplitude. Finally, the corner‐edge model illustrates a more complex geometry for the liquid‐solid interface. As the Poisson’s ratio v increases from 0.25 to 0.5, the shear converted phases are removed from seismograms and from the time section of the wave field.