Scattering of elastic waves by a 3D anisotropic basin

✍ Scribed by Zheng, T.; Dravinski, M.

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 209 KB
• Volume: 29
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/(sici)1096-9845(200004)29:4<419::aid-eqe915>3.0.co;2-u

✦ Synopsis

Scattering of elastic waves by a three-dimensional transversely isotropic basin of arbitrary shape embedded in a half-space is considered using an indirect 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 functions with their intensities determined from the requirement that the boundary and the continuity conditions are to be satis"ed 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 "nite integrals over a unit sphere or a unit circle which can be numerically evaluated very e$ciently.

Detailed analysis of the method includes the discussion on the shape of the auxiliary surfaces and the distribution of the collocation points and sources. The convergence criteria is de"ned in terms of transparency tests, isotropic limit test, and minimization of a certain norm. The isotropic limit tests show excellent agreement with the isotropic results available in literature.

For anisotropic materials the numerical results are given for a semispherical basin. The results show that presence of an anisotropic basin may result in signi"cant ampli"cation of surface motion atop the basin. While the amplitude of peak surface motion may be similar to the corresponding isotropic results, the di!erence in the displacement patterns may be quite di!erent between the two. Therefore, this study clearly demonstrates that material anisotropy may be very important for accurate assessment of surface ground motion ampli"cation atop basins.