Generalized transfer matrix method for propagation of surface waves in layered azimuthally anisotropic half-space

Author： Liu Tianyun Zhao Chongbin Duan Yunling

ISSN： 0956-540X

Source： Geophysical Journal International, Vol.190, Iss.2, 2012-08, pp. : 1204-1212

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Abstract

SUMMARYThis paper presents a systematic and efficient method, namely the generalized transfer matrix method, for evaluating the dispersion curves and eigenfunctions of surface waves in multilayered azimuthally anisotropic half-space. Apart from avoiding the well-known numerical difficulties associated with the existing Thomson–Haskell method, the generalized transfer matrix method possesses the robust determination of independent polarization vectors by using the singular value decomposition (SVD) approach, the explicit inversion of the 6 × 6 eigencolumn matrix without any resort to numerical inversion and the efficient computation of eigenfunctions for layered azimuthally anisotropic media. By means of straightforward transformations, the generalized transfer matrix method leads to a twofold recursive algorithm: (1) for the recursive computation of phase velocities it starts from the bottom half-space to the top layer and (2) for the recursive solution of eigenfunctions it starts from the top layer to the bottom half-space. While keeping the simplicity of the Thomson–Haskell transfer matrix method, the generalized transfer matrix method is of unconditional stability and computational efficiency. The related numerical examples demonstrate that the generalized transfer matrix method is a powerful and robust tool for simulating the propagation of elastic surface waves in the layered azimuthally anisotropic half-space.