none 10.1190/geo2023-0515.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 160047241 5981 2025121212534693200 10.1190 2025-12-12T17:54:00Z 2024-04-22T10:12:06Z 9 Geophysics 0016-8033 1942-2156 01 07 2024 89 4 Edward Caunt Imperial College London 1 , Department of Earth Science and Engineering, London, UK. edward.caunt15@imperial.ac.uk (corresponding author) http://orcid.org/0009-0008-9479-7714 Rhodri Nelson Imperial College London 1 , Department of Earth Science and Engineering, London, UK. rhodri.nelson@imperial.ac.uk http://orcid.org/0000-0003-2768-5735 Tim MacArthur Thrust Belt Imaging 2 , Calgary, Canada. tim@tbi.ca Fabio Luporini Devito Codes 3 , London, UK. fabio@devitocodes.com http://orcid.org/0000-0001-7161-2942 Gerard Gorman Imperial College London 1 , Department of Earth Science and Engineering, London, UK. g.gorman@imperial.ac.uk http://orcid.org/0000-0003-0563-3678 ABSTRACT 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 and full-waveform inversion, requiring suitable topography handling. Methods currently detailed in the literature generally are limited in scope application-wise or nontrivial 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, using 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. 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