An analysis of the indirect boundary element method for seismic modelling

SUMMARY An indirect boundary element method has been used to compute seismic wavefields in layered media. The advantages of this technique over numerical grid methods are that it satisfies radiation conditions, incorporates free surface effects, solves viscoelastic problems and can handle arbitrary source types. The technique is more appropriate for models with high aspect ratios and a limited number of layers. The computational cost increases with the number of layers and frequency content. Examples are presented in this study to illustrate some of the features of the technique. Seismograms are computed for SH and P‐SV line sources in 2-D earth models. Finite-difference and the Cagniard‐ de Hoop methods are used to test the accuracy of the technique. Even though the computation time for the method is several times greater than finite differences, the technique becomes cost effective as the number of computed shot-gathers increases. The technique also allows computation of constant offset gathers at a small additional cost which is very expensive to do by using finite differences. Numerical grid methods (e.g. finite differences, finite elements and pseudospectral methods) have become the standard tool for seismic modelling. These techniques are extremely versatile in terms of model complexity that can be treated, although grid generation may still be problematic. These methods are also very demanding of computation time. They involve discretization of the entire model volume, at a grid spacing which is generally much shorter than the smallest wavelength present in the solution. The finite aperture of the grid also imposes difficulties in the approximation of radiation conditions on the solutions and thus the grid may need to be made much larger than the modelled region. A third set of difficulties is associated with the approximation of the solution in the vicinity of boundaries (both internal and free surface). All of the grid methods involve some smoothing of the solution that may be objectionable for some modelling purposes, but may in fact be an advantage in imaging or migration. Boundary methods, boundary integrals (BIM) and boundary elements (BEM) have emerged as alternatives to the grid methods in cases where better accuracy is required near boundaries and sources or where the domain is infinite in extent (Cruse 1980). Boundary methods discretize the model only on boundary surfaces, rather than throughout the model volume, so that advantages may be obtained for models with large aspect ratio