Extension of split perfectly matched absorbing layer for 2D wave propagation in porous transversely isotropic media

The perfectly matched layer (PML) has proven to be efficient in absorbing outgoing waves in elastic and poroelastic media. It has not, however, been applied for porous anisotropic media. We develop the velocity-stress formulation for propagation of seismic waves for fluid-saturated porous anisotropic media with Biot's equations. Then we extend the split perfectly matched absorbing layer (SPML) to these media and describe the staggered-grid finite-difference scheme. Using fourth-order spatial operators and a second-order temporal operator under 2D Cartesian coordinates, we numerically solve the equations for the solid and fluid particle velocity components, and for the solid stress components and fluid pressure. The energy decay curve we show demonstrates that the algorithm can run stably. Results from the horizontally layered model show that the SPML model absorbs the outgoing wave well, which illustrates the algorithm is efficient for modelling in porous transversely isotropic media.