Discrete wave number representation of elastic wave fields in three‐space dimensions

Abstract

We present the generalization to three dimensions of the discrete wave number representation method of Bouchon and Aki (1977). The method is developed to study the near field of a three‐dimensional seismic source embedded in a layered medium. The elastic wave fields are represented by a superposition of plane waves propagating in discrete directions. The discretization is exact and results from a periodic two‐dimensional arrangement of sources. The accuracy of the method is checked, in the case of a rectangular dislocation source radiating in an infinite medium, by comparing the results obtained with Madariaga's (1978) exact solution. Examples of the calculation of strong ground motion produced by a thrust fault and a strike slip fault are presented.

3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

“…These are in full agreement with the solution for moving loads given earlier by Pedersen et al [31] and Papageorgiou and Pei [49]. The potentials are written as a superposition of plane waves, according to the technique used first by Lamb [50] for the 2D case, and then by Bouchon [51] and Kim and Papageorgiou [22] for calculating the three-space dimension field by means of a discrete wave number representation.…”

Analytical evaluation of the acoustic insulation provided by double infinite walls

“…A similar procedure is followed to obtain the fluid pressure potential. These potentials are then expressed as a superposition of plane waves, with different wave numbers, k n ; along the x direction, following the technique used first by Lamb [24] for the two-dimensional case, and then by Bouchon [25] and Kim and Papageorgiou [26] to calculate the three-dimensional field by means of a discrete wave number representation. This formulation assumes the existence of an infinite number of virtual loads distributed along the x direction, at equal intervals L x ; permitting the definition of k n ¼ ð2p=L…”

Wave Propagation from a Line Source Embedded in a Fault Zone

“…This discretization results from a periodicity assumption in the description of the source (Bouchon & Aki, 1977).…”

“…Therefore, the displacement u s in wavenumber domain from the seismic source located at the origin of the coordinate system (x, y) can be written in the form, according to Bouchon & Aki (1977), where u ss is the displacement from periodically distributed sources and s l =2 l/Δx s . If the series converges, eq.…”