Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference
(FD) methods used to model such phenomena. Accurate wavefield simulation is
paramount in subsurface imaging applications such as reverse-time migration (RTM)
and full-waveform inversion (FWI), requiring suitable topography handling. Methods currently detailed in the literature are generally limited in scope applicationwise or non-trivial to apply to real-world geometries. A general immersed boundary treatment capable of imposing a range of boundary conditions in a relatively equation-agnostic manner has been developed, alongside a framework implementing
this approach to complement emerging code-generation paradigms. The approach is
distinguished by the use of N-dimensional Taylor-series extrapolants constrained by
boundary conditions imposed at some suitably distributed set of surface points. The
extrapolation process is encapsulated in modified derivative stencils applied in the
vicinity of the boundary, utilizing hyperspherical support regions. This method ensures boundary representation is consistent with the FD discretization. Furthermore,
high-dimensional and vector boundary conditions can be applied without approximation prior to discretization. A consistent methodology can thus be applied across free
and rigid surfaces with first and second-order acoustic wave equation formulations.
Application to both equations is demonstrated, and numerical examples based on
analytic and real-world topography implementing free and rigid surfaces in 2D and
3D are presented. Numerical examples and convergence tests demonstrate the accuracy of boundary treatments devised by the prescribed approach, their suitability to
practical applications, and the feasibility of automatically generating treatments to
suit each case.