Examination of seismic models: inhomogeneity, anisotropy, and Backus averaging

Kaderali, Ayiaz (2025) Examination of seismic models: inhomogeneity, anisotropy, and Backus averaging. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

The thesis examines seismic models of the Earth in terms of inhomogeneity, anisotropy, and Backus averaging. Chapter One provides background information. Chapters two to four are described below. The fifth chapter provides concluding remarks. The common thread through all the chapters is the use of data acquired in the same borehole: Vertical Seismic Profiling (VSP) data and a sonic log. A study on the estimation of inhomogeneity and anisotropy parameters from walkaway VSP traveltime data, using a multi-layered mathematical model, is presented in the second chapter. Least-squares residuals between measured and modelled traveltimes are minimized to estimate the anisotropy parameter, χ, and inhomogeneity parameters, a and b, of the layers. A two-step optimization is performed, and an adaptation of the Nelder-Mead algorithm is used to estimate the parameters. The methodology is applied to synthetic data and then to real data. An assessment of the reliability of results subject to noise shows the noise threshold to be quite low. Beyond this threshold, parameter estimates have diminishing accuracy. Using synthetic data, parameters are reliably estimated. With real data, parameter estimations indicate anisotropy to be exhibited only in the bottom layer. The third chapter is on the use of the Bayesian Information Criterion (BIC) for the selection of a model that is most representative and has the fewest number of parameters to fit the data. Eight three-layer models, with different parameterizations, are considered that correspond to the medium in which the VSP data were acquired. The simplest model is inhomogeneous and isotropic with six parameters. The most complicated model is inhomogeneous and anisotropic and consists of nine parameters. BIC values indicate the best model as the one with seven parameters and anisotropy in the third layer. An adaptation of the Backus average to obtain more accurate traveltimes for obliquely propagating waves is presented in the fourth chapter. A weighting is applied that considers the distance travelled in each layer, with weights corresponding to source-receiver offsets. Traveltimes computed from the standard Backus average are compared to traveltimes computed using the modified Backus average in three cases. The first, a ten-layer synthetic model with a 30-degree take-off angle, the second, with an extreme distance of 7000 m, and the third, with real data. In all three cases, the modified Backus average performs better. All three objectives: estimation of inhomogeneity and anisotropy parameters, use of BIC to indicate the most representative model of the medium based on the fit of the data, and modification of the Backus average to correct for non-vertical raypaths to obtain more accurate traveltimes, were successfully achieved.

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