Amplification of elastic waves by a three dimensional valley. Part 1: Steady state response

Abstract

SUMMARYSteady state scattering of incident P, SV, SH and Rayleigh waves by general non-axisymmetric three dimensional dipping layers is investigated by using an indirect boundary integral equation method. Material of the half-space and the layer is assumed to be linear, weakly anelastic, homogeneous and isotropic.Systematic comparisons between three dimensional and two dimensional models demonstrate that the validity of a two dimensional approximation for a given basin shape may be affected strongly by changes in azimuthal angle of incidence, type of incident wave and frequency. The discrepancies of two dimensional modelling appear to be much more pronounced for the case of an incident SH wave. Another important feature of the results is the existence of strong coupling between P/SV and SH modes, which has no correspondence in two dimensional models. Such off-azimuthal mode conversions are particularly strong for an incident SB wave.

Multi-Level Fast Multipole BEM for 3-D Elastodynamics

“…The formulation is extended to problems featuring piecewise-homogeneous media via a multi-region FM-BEM whose unknowns feature displacements and tractions on interfacial boundary elements. The correctness and computational performances of the proposed singleand multi-region versions of the elastodynamic FMM are demonstrated here on numerical examples featuring up to O(2 × 10 5 ) DOFs run on a single-processor PC, including a 3-D site effect benchmark (semi-spherical empty canyon or sedimentfilled basin, with previously published results [15,17,20] for low-frequency cases allowing comparisons).…”

“…7). This configuration, has been studied in the frequency domain in [15] using a standard indirect BEM (using the half-space Green's functions) . The mechanical parameters are defined through µ 1 = c S1 = 1, c P1 = 2, µ 2 = 1/6, c S2 = 1/2 and c P2 = 1.…”

The method of fundamental solutions for three-dimensional scattering of elastic waves in layered half space

“…To verify the numerical precision of the method, figure 3 shows the surface displacement amplitudes around a hemisphere basin with radius a in homogeneous half-space compared with the results of Mossessian and Dravinski [3]. The surface displacement amplitudes of a layered hemisphere alluvial basin for P waves incident compared with the results of Chailat et al [8].…”

“…Compared with the BEM, this method has several advantages such as avoiding dealing with the singularity of the fundamental solution, and the meshless feature. Due to its excellent numerical accuracy and ease of implementing, it has been widely applied in the field of diffraction of elastic waves in elastic medium [1][2][3][4]. More related papers can be found in the survey articles [5][6].…”

Scattering of elastic waves by a 3D anisotropic basin

“…In general, the auxiliary surfaces C and C are de"ned inside and outside of the scatterer, respectively. They usually follow in shape the boundary of the scatterer and the distance from the scatterer and the auxiliary surfaces must be determined empirically [16,19] in order to produce the convergent results for smallest number of sources and collocation points. In this paper the auxiliary surfaces have been constructed by "rst scaling the interface C, and then by shifting the new surface in the vertical direction.…”