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Irregular terrain has a pronounced effect on the propagation of seismic andacoustic wavefields but is not straightforwardly reconciled with structuredfinite-difference (FD) methods used to model such phenomena. Methods currentlydetailed in the literature are generally limited in scope application-wise ornon-trivial to apply to real-world geometries. With this in mind, a generalimmersed boundary treatment capable of imposing a range of boundary conditionsin a relatively equation-agnostic manner has been developed, alongside aframework implementing this approach, intending to complement emergingcode-generation paradigms. The approach is distinguished by the use ofN-dimensional Taylor-series extrapolants constrained by boundary conditionsimposed at some suitably-distributed set of surface points. The extrapolationprocess is encapsulated in modified derivative stencils applied in the vicinityof the boundary, utilizing hyperspherical support regions. This method ensuresboundary representation is consistent with the FD discretization: both must beconsidered in tandem. Furthermore, high-dimensional and vector boundaryconditions can be applied without approximation prior to discretization. Aconsistent methodology can thus be applied across free and rigid surfaces withthe first and second-order acoustic wave equation formulations. Application toboth equations is demonstrated, and numerical examples based on analytic andreal-world topography implementing free and rigid surfaces in 2D and 3D arepresented.

A Novel Immersed Boundary Approach for Irregular Topography with Acoustic Wave Equations