Seismic anisotropy analysis with Muir-Dellinger parameters

Seismic anisotropy, defined as the dependency of seismic-wave velocities on propagation direction, is an important factor in seismic data analysis. Neglecting anisotropy can lead to significant errors in the subsurface images. Even after decades of considerable research efforts, the topic of anisotropy remains at the center of attention of the research community. In this dissertation, I address the fundamental problem of choosing parameterization to characterize the effects of seismic anisotropy and propose an alternative approach based on the Muir-Dellinger (MD) parameters. I first give their definitions and discuss their properties with respect to the classic qP-wave phase velocity in transversely isotropic (TI) media in the second chapter. I show that, when expressed in terms of MD parameters, the exact expression of phase velocity in this case is controlled by the elliptical background and two anelliptic parameters (q1 and q3) defined as the curvature of the qP-wave phase velocity measured along the symmetry axis and its orthogonal. The wide range of possible values for the vertical shear-wave velocity (vS0) expressed under the conventional Thomsen parameterization translates to a considerably narrower range of the slope in the nearly linear dependence between q1 and q3. This discovery suggests a possibility of using such a relationship to characterize the complete stiffness tensor, infer more information about the subsurface directly from qP kinematics, and provide a physical basis for reducing the number of parameters in qP-wave analysis. Based on various experimental measurements of stiffness coefficients reported in the literature, I relate such properties in shales, sandstones, and carbonates with corresponding values of slope. I further investigate this empirical linear relationship in the third chapter and show that it can also gives additional rock physics implications about the type of pore fluids. I provide some supportive evidence of its reality from self-consistent rock physics modeling and Backus averaging for shale samples. In addition, I find that both the 2D MD parameterization and its 3D extension, suitable for studies of qP waves in orthorhombic media, also provide a convenient foundation for the parameter estimation process. I carry out a detailed study on the sensitivity of MD parameters to qP-wave kinematics in comparison with other known anisotropic parameterization schemes in the fourth chapter. In the last chapter, using the MD parameters, I propose novel analytical approximations for qP-wave phase and group velocities in 2D TI and 3D orthorhombic media. The novel approximations are highly accurate and possess an advantage of having similar functional form with reciprocal coefficients, which adds practical convenience to considering both phase (wave) and group (ray) velocities. Finally, I discuss known limitations of the MD parameterization and suggest possible future research topics.