Scattering of elastic waves by a 3D anisotropic basin

Scattering of elastic waves by a three-dimensional transversely isotropic b asin of arbitrary shape embedded in a half-space is considered using an ind irect boundary integral equation approach. The unknown scattered waves are expressed in terms of point sources distributed on the so-called auxiliary surfaces. The sources are expressed in terms of the full-space Green's func tions with their intensities determined from the requirement that the bound ary and the continuity conditions are to be satisfied in the least-squares sense. Steady-state results were obtained for incident plane pseudo-P-, SH- , SV-, and Rayleigh waves. Using the Radon transform the Green's functions are obtained in the form of finite integrals over a unit sphere or a unit circle which can be numerica lly evaluated very efficiently. Detailed analysis of the method includes the discussion on the shape of the auxiliary surfaces and the distribution of the collocation points and sour ces. The convergence criteria is defined in terms of transparency tests, is otropic limit test, and minimization of a certain norm. The isotropic limit tests show excellent agreement with the isotropic results available in lit erature. For anisotropic materials the numerical results are given for a semispheric al basin. The results show that presence of an anisotropic basin may result in significant amplification of surface motion atop the basin. While the a mplitude of peak surface motion may be similar to the corresponding isotrop ic results, the difference in the displacement patterns may be quite differ ent between the two. Therefore, this study clearly demonstrates that materi al anisotropy may be very important for accurate assessment of surface grou nd motion amplification atop basins. Copyright (C) 2000 John Wiley & Sons, Ltd.