  Finite-difference (FD) modeling of seismic waves in the vicinity of dipping
interfaces gives rise to artifacts. Examples are phase and amplitude errors, as
well 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 an
anti-aliased step-function, or a lowpass filter). Alternatively, the interface
may 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 are
compared to analytical solutions. We find that in acoustic media, anti-aliasing
methods lead to the smallest errors. Conversely, in elastic media, the SM
calculus provides the best accuracy. The downside of the SM calculus is that it
requires an anisotropic FD solver even to model an interface between two
isotropic materials. As a result, the computational cost increases compared to
when using isotropic FD solvers. However, since coarser grid spacings can be
used to represent the dipping interfaces, the two effects (an expensive FD
solver on a coarser FD grid) equal out. Hence, the SM calculus can provide an
efficient means to reduce errors, also in elastic isotropic media.
