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Finite-difference (FD) modeling of seismic waves in the vicinity of dippinginterfaces gives rise to artifacts. Examples are phase and amplitude errors, aswell as staircase diffractions. Such errors can be reduced in two general ways.In the first approach, the interface can be anti-aliased (i.e., with ananti-aliased step-function, or a lowpass filter). Alternatively, the interfacemay be replaced with an equivalent medium (i.e., using Schoenberg \& Muir (SM)calculus or orthorhombic averaging). We test these strategies in acoustic,elastic isotropic, and elastic anisotropic settings. Computed FD solutions arecompared to analytical solutions. We find that in acoustic media, anti-aliasingmethods lead to the smallest errors. Conversely, in elastic media, the SMcalculus provides the best accuracy. The downside of the SM calculus is that itrequires an anisotropic FD solver even to model an interface between twoisotropic materials. As a result, the computational cost increases compared towhen using isotropic FD solvers. However, since coarser grid spacings can beused to represent the dipping interfaces, the two effects (an expensive FDsolver on a coarser FD grid) equal out. Hence, the SM calculus can provide anefficient means to reduce errors, also in elastic isotropic media.

geophysical journal international

Finite-difference modeling of 2-D wave propagation in the vicinity of  dipping interfaces: a comparison of anti-aliasing and equivalent medium  approaches