Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media1

The velocity-stress formulation for propagation of elastic seismic waves through 2D heterogeneous transversely isotropic media of arbitrary orientation is presented. The equations are recast into a finite-difference scheme and solved numerically using fourth-order spatial operators and a second-order temporal operator on a staggered grid. Absorbing, free-surface and symmetry boundary conditions have been implemented. Test cases compare well with other published solutions. Synthetic seismograms are calculated over two idealized models: (i) vertical fractures in granite with a dolerite sill reflector and (ii) a dipping anisotropic shale. Comparisons with the isotropic counterparts show significant differences which may have to be accounted for in seismic processing in the future.