Elastic immersive wavefield modelling

Many modelling studies of wave scattering require repeated numerical simulations through models with properties that differ only in a small sub-domain. Hence, it is of interest to recompute the wavefields that account for wave propagation through the whole domain, using simulations that are performed only in the sub-domain. Immersive boundary conditions (IBCs) can be used to establish such a local wavefield modelling scheme which enables accurate wavefield recomputation, including all interactions between the locally-perturbed medium and the full domain. We develop IBC theory for elastic wave propagation, in which the boundary conditions are updated dynamically at each time step of a simulation in the local domain. These updates are calculated by wavefield extrapolation based on the Kirchhoff-Helmholtz integrals using Green's functions in the background medium. Wavefield recording and injection in IBCs can be implemented either using finite-difference (FD) injection methods, or using the method of multiple point sources (MPS). The latter method is significantly less computationally demanding in terms of both memory and number of calculations. We therefore both extend acoustic FD injection methods to elastic media, and propose a new second-order accurate MPS method to implement elastic IBCs, which is numerically exact. In higher-order FD modelling, the MPS method is not numerically exact but still produces highly accurate IBC wavefields when compared to global-domain simulations.