Browsing by Author "Li, Zhao 1988-"
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Item Elastodynamic Green's tensor in anisotropic medium(2013-08) Li, Zhao 1988-; Chesnokov, Evgeni M.; Kouri, Donald J.; Li, AibingThis 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.Item Time-domain solution of poroelastic wave equation(2016-11-21) Li, Zhao 1988-; Chesnokov, Evgeni M.; Kouri, Donald J.; Goloshubin, Gennady M.; Zheng, YingcaiA new method is developed for solving the HF-regime poroelastic wave equation in the time-domain. The dynamic permeability is approximated in the frequency-domain by a rational series, which used the finite number of terms and allows three groups of fitting coefficients at each approximate order. Using this rational series, the HF-regime wave equation is transformed to the time-domain and solved by an explicit algorithm. Based on its desirable structure, the rational series requires fewer memory variables comparing to other existing methods. An order-by-order fitting scheme is used for efficiently computing the fitting coefficients while ensuring the numerical stability. The numerical stiffness caused by the diffusive compressional wave is resolved by using a second-order symmetric split-operator technique. The current method is able to provide a general solution for two- or three-dimensional heterogeneous porous medium. The numerical solutions displayed great agreements with analytic results in the isotropic porous media. The propagation and scattering of the slow P-wave can be accurately modeled. The LF-regime solution is employed to study the physical meaning of the friability, which is an empirical parameter introduced in general singular approximation. A series of numerical experiments show that the ratio of friability and Biot-Willis coefficient can be indicative to the microstructure of the pore space.