Elastodynamic Green's tensor in anisotropic medium
Li, Zhao 1988-
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This thesis is dedicated to study the elastodynamic Green’s tensor in anisotropic medium in order to understand the influence of anisotropy on the point source radiation. In the first part of this thesis, a new form of elastodynamic Green’s tensor in VTI medium is found based on the method of Tsvankin and Chesnokov (1990). I found the analytical asymptotic Green’s tensor for elliptical anisotropic medium. I propose a new form of approximated qP-qSV solution for weak TI medium while the solution of SH wave can always be found analytically. The new form of the Green’s tensor is uniform through all directions. The accuracy of the approximated results will decrease as Thomsen parameters increase. In the second part, I study the anisotropic effect due to initial stress on the Green’s tensor. A six-rank tensor introduced by Nikitin and Chesnokov (1981) is being used to describe the effect of deviatoric stress on the symmetry of the medium. The Green’s tensor in general anisotropic medium is calculated. I studied four types of uniaxial initial stress. The phase velocity and radiation patterns in the pre-stress medium are calculated. Last, I examine the error brought by the approximation in calculating the Green’s tensor.