Date of Award
Doctor of Philosophy (PhD)
Geology and Geophysics
Seismic anisotropy, the variation of seismic wave speed with direction, is an extremely important physical phenomena. When a certain type of seismic wave (shear wave) propagates in an anisotropic medium, the component polarized parallel to the fast direction (along which the speed is higher) begins to lead and the component polarized to the slow direction lags behind (analogous to the optical birefringence). This observation of seismic anisotropy may be used to infer several physical properties of the medium through which these waves are propagating. Fortunately, Earth's upper mantle shows significant seismic anisotropy due to preferred crystallographic orientation of the constituent minerals. Therefore, it can provide crucial information regarding the convective flow and stress patterns in the upper mantle. To be more precise, seismic anisotropy can shed light on detail inner working of several geodynamic processes which are inherently anisotropic in nature and therefore insensitive to isotropic seismology. \\Owing to its simplicity, the classical ray theory based formulation is widely used to infer anisotropic structures of the upper mantle. However, due to the lack of vertical resolution of infinite frequency ray theory based methods and its numerous other shortcomings even in the simplified studies assuming isotropy, it is undesirable to use a ray theory based method in a fully anisotropic framework. The major portion of this thesis is devoted to developing anisotropy tomography method in a perturbative framework where the `finite-frequency' or the full `wave' feature is taken into account. Such technique is proven to be a substantial improvement in terms of localization of the anisotropy of upper mantle. After benchmarking, it is applied to infer the anisotropic structures beneath the High Lava Plains of Oregon and as such was able to provide an avenue for reconciling apparently contradictory constraints on anisotropic structures from different measurements. \\ In the last part of the thesis, we briefly discuss a technique (slightly tangential to the main theme of anisotropy however seems to enjoy a connection at a more fundamental level) we develop to obtain an effective description of the physical properties of a general heterogeneous medium (including pure randomness). This is motivated by the fact that when propagating through small heterogeneities, seismic waves naturally average the elastic properties of the medium and therefore only an effective physics is realized.
Mondal, Puskar, "A Few Applications of Seismic Waves: Anisotropy Tomography and All That" (2021). Yale Graduate School of Arts and Sciences Dissertations. 379.