Acoustic VTI modeling using high-order finite differences

Two second-order wave equations for acoustic vertical transversely isotropic (VTI) media are transformed to six first-order coupled partial differential equations for a more straighforward numerical implementation of the derivatives. The resulting first-order equations have a more natural form for discretization by any finite-difference, pseudospectral, or finite-element method. I discretized the new equations by high-order finite differences and used synthetic seismograms and snapshots for anisotropic and isotropic cases. The relative merits of placing the source deep and close to a free surface are assessed, illustrating advantages of exciting the source inside or outside of a near-surface, thin, isotropic layer. Results show that traveltimes from deep seismic reflectors can remain virtually unaffected when near-surface isotropic layers are included in acoustic VTI media.