On relations of anisotropy and linear inhomogeneity using Backus average, 1-D tomography and two-parameter velocity inversion

Abu Sayed, Md (2019) On relations of anisotropy and linear inhomogeneity using Backus average, 1-D tomography and two-parameter velocity inversion. Masters thesis, Memorial University of Newfoundland.

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Abstract

We divide this thesis into three major parts. In the first part, we study three velocity models and corresponding traveltimes to obtain the inhomogeneity and anisotropy of a medium by comparing them to the field data. We derive an analytical relation that relates the linear inhomogeneity of a layered medium to the anisotropy parameter in an equivalent medium. For the analytic ease, we consider the P and S wave velocity gradients to be equal. We relax this constraint in the third part of the thesis, where the velocity gradients are independent of each other. We find that the obtained value of the anisotropy in the equivalent medium is in the same order of magnitude as the inhomogeneity parameter from the linearly inhomogeneous and elliptically anisotropic medium. This statement encourages us to do further investigation on the more general relationship between the inhomogeneity and anisotropy parameters in an equivalent medium. In the second part, we develop a 1-D traveltime tomography method to calculate the velocity of a medium. We use the results of 1-D tomography to obtain linear inhomogeneity parameters in a specific layer. To get the trustworthiness of the method, we perform several synthetic experiments. We show that the inverted model parameters are reasonably accurate and stable. To examine the results of linear inhomogeneity parameters using a different method, we also develop an inversion method based on a two-parameter velocity model. Finally, we apply both the methods to Vertical Seismic Profile (VSP) data and do a study comparing their results. In the third part, we derive an analytical relationship between the anisotropy, characterized by the Thomsen [1986] parameters, and the linear inhomogeneity parameters, which forms a system of three equations for nine unknowns. To obtain well-posedness, we constrain the problem by considering two seismological methods, 1-D tomography and two-parameter methods, applied to field data. Lastly, we compare the results that come from the application of each method to the analytical relationship, for a particular region of interest, to assess the validity of the theoretical relationship.

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