Full-waveform inversion (FWI) is a technique designed to produce a high-resolution model of the subsurface by using information contained in entire seismic waveforms. This thesis presents a methodology for FWI in elastic VTI (transversely isotropic with a vertical axis of symmetry) media and discusses synthetic results for heterogeneous VTI models.
First, I develop FWI for multicomponent data from a horizontally layered VTI model. The reflectivity method, which permits computation of only PP reflections or a combination of PP and PSV events, is employed to model the data. The Gauss-Newton technique is used to invert for the interval Thomsen parameters, while keeping the densities fixed at the correct values. Eigenvalue/eigenvector decompostion of the Hessian matrix helps analyze the sensitivity of the objective function to the model parameters. Whereas PP data alone are generally sufficient to constrain all four Thomsen parameters even for conventional spreads, including PS reflections provides better constraints, especially for the deeper part of the model.
Next, I derive the gradients of the FWI objective function with respect to the stiffness coefficients of arbitrarily anisotropic media by employing the adjoint-state method. From these expressions, it is straightforward to compute the gradients for parameters of 2D heterogeneous VTI media. FWI is implemented in the time domain with the steepest-descent method used to iteratively update the model. The algorithm is tested on transmitted multicomponent data generated for Gaussian anomalies in Thomsen parameters embedded in homogeneous VTI media.
To test the sensitivity of the objective function to different model parameters, I derive an an- alytic expression for the Fréchet kernel of FWI for arbitrary anisotropic symmetry by using the Born approximation and asymptotic Green’s functions. The amplitude of the kernel, which represents the radiation pattern of a secondary source (that source describes a perturbation in a model parameter), yields the angle-dependent energy scattered by the perturbation. Then the radiation patterns are obtained for anomalies in VTI parameters embedded in isotropic homogeneous media and employed to analyze the inversion results for the transmission FWI experiments.
To understand some of the challenges posed by data recorded in surface surveys, I generate the multicomponent wavefield for a model based on a geologic section of the Valhall Field in the North Sea. A multiscale approach is adopted to perform FWI in the time domain. For the available offset range, diving-wave energy illuminates the top 1.5 km of the section, with the updates in the deeper regions due primarily to the reflections. FWI is tested for three model parameterizations and the results are explained in terms of the P- and SV-radiation patterns described above. These parameterizations lead to different trade-offs, and the choice of parameterization for a given data set depends on the recorded offset range, the quality of the initial model, and the parameter that needs to be recovered most accurately.
|Commitee:||Hale, Dave, Krahenbuhl, Richard, Tenorio, Luis, Tutuncu, Azra|
|School:||Colorado School of Mines|
|School Location:||United States -- Colorado|
|Source:||DAI-B 77/10(E), Dissertation Abstracts International|
|Keywords:||Anisotropy, Elastic, Inversion|
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