State-of-the-art for the BIEM

In this chapter, general remarks about the BIEM, fundamental solutions, and modern computational techniques for inhomogeneous 2D elastic domains are discussed, together with applications to seismic wave propagation problems. More specifically, a closer look with scales of hundreds of km reveals the Earth is both strongly inhomogeneous with a sharp gradient of variation of its material properties and also heterogeneous due to the existence of free and subsurface relief, non-parallel layers, cavities, inclusions, cracks and faults, and finally underground engineering constructions. The Earth’s varying surface geology, the existence of a geomaterial depth-dependent gradient, of topography, and of nonlinear stress–strain states in the general geological region of interest, is the cause of significant spatial variations of seismic ground motion that can lead to large amplifications during earthquakes. A quantitative prediction of strong ground motionmanifestation at a given site involves dealing with the source of seismic waves, their path to that site, and the effects of local conditions. A possible way of shedding some light on the understanding of the site-response phenomena and their sensitivity to the type and properties of the seismic source, of inhomogeneity and heterogeneity in thewave path, is in developing high-performance numerical methods for the simulation of seismicwave propagation phenomena. © Springer International Publishing Switzerland 2017.