Elastic waves in continuous and discontinuous geological media by boundary integral equation methods: A review

• Review of boundary integral equation (BIE) based methods for elastic wave motion.
• Both naturally occurring media and man-made materials are examined.
• Emphasis is given to fundamental solutions, the various BIE formulations and hybrid methods.
• Material inhomogeneity, layering, anisotropy and the presence of surface relief are considered.
• Continuous and discontinuous medium structure is considered.

In this review paper, we concentrate on the use of boundary integral equation (BIE) based methods for the numerical modeling of elastic wave motion in naturally occurring media. The main reason for using BIE is the presence of the free surface of the earth, whereby large categories of problems involve continua with a small surface to volume ratio. Given that under most circumstances, BIE require surface discretization only, substantial savings can be realized in terms of the size of the mesh resulting from the discretization procedure as compared to domain-type numerical methods. We note that this is not necessarily the case with man-made materials that have finite boundaries. Thus, although the emphasis here is on wave motion in geological media, this review is potentially of interest to researchers working in other scientific fields such as material science. Most of the material referenced in this reviews drawn from research work conducted in the last fifteen years, i.e., since the year 2000, but for reasons of completeness reference is made to seminal papers and books dating since the early 1970s. Furthermore, we include here methods other than the BIE-based ones, in order to better explain all the constituent parts of hybrid methods. These have become quite popular in recent years because they seem to combine the best features of surface-only discretization techniques with those of domain type approaches such as finite elements and finite differences. The result is a more rounded approach to the subject of elastic wave motion, which is the underlying foundation of all problems that have to do with time-dependent phenomena in solids.