dc.contributor.author Huang, Xingguo dc.date.accessioned 2020-04-27T12:41:33Z dc.date.available 2020-04-27T12:41:33Z dc.date.issued 2020-05-14 dc.date.submitted 2020-04-22T13:28:44.637Z dc.identifier container/cc/26/cb/05/cc26cb05-60ea-41da-b355-b0d87a881b7b dc.identifier.uri https://hdl.handle.net/1956/22015 dc.description.abstract Seismic scattering theory plays an important role in seismic forward modeling and is the theoretical foundation for various seismic imaging methods. Full waveform inversion is a powerful technique for obtaining a high-resolution model of the subsurface. One objective of this thesis is to develop convergent scattering series solutions of the Lippmann-Schwinger equation in strongly scattering media using renormalization and homotopy methods. Other objectives of this thesis are to develop efficient full waveform inversion methods of time-lapse seismic data and, to investigate uncertainty quantification in full waveform inversion for anisotropic elastic media based on integral equation approaches and the iterated extended Kalman filter. The conventional Born scattering series is obtained by expanding the Lippmann-Schwinger equation in terms of an iterative solution based on perturbation theory. Such an expansion assumes weak scattering and may have the problems of convergence in strongly scattering media. This thesis presents two scattering series, referred to as convergent Born series (CBS) and homotopy analysis method (HAM) scattering series for frequency-domain seismic wave modeling. For the convergent Born series, a physical interpretation from the renormalization prospective is given. The homotopy scattering series is derived by using homotopy analysis method, which is based on a convergence control parameter $h$ and a convergence control operator $H$ that one can use to ensure convergence for strongly scattering media. The homotopy scattering scattering series solutions of the Lippmann-Schwinger equation, which is convergent in strongly scattering media. The homotopy scattering series is a kind of unified scattering series theory that includes the conventional and convergent Born series as special cases. The Fast Fourier Transform (FFT) is employed for efficient implementation of matrix-vector multiplication for the convergent Born series and the homotopy scattering series. This thesis presents homotopy methods for ray based seismic modeling in strongly anisotropic media. To overcome several limitations of small perturbations and weak anisotropy in obtaining the traveltime approximations in anisotropic media by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory, this study applies the homotopy analysis method to the eikonal equation. Then this thesis presents a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system. The new traveltime approximations are derived by using the linear and nonlinear operators in the retrieved zero-order deformation equation. Flexibility on variable anisotropy parameters is naturally incorporated into the linear differential equations, allowing a medium of arbitrarily anisotropy. This thesis investigates efficient target-oriented inversion strategies for improving full waveform inversion of time-lapse seismic data based on extending the distorted Born iterative T-matrix inverse scattering to a local inversion of a small region of interest (e. g. reservoir under production). The target-oriented approach is more efficient for inverting the monitor data. The target-oriented inversion strategy requires properly specifying the wavefield extrapolation operators in the integral equation formulation. By employing the T-matrix and the Gaussian beam based Green’s function, the wavefield extrapolation for the time-lapse inversion is performed in the baseline model from the survey surface to the target region. I demonstrate the method by presenting numerical examples illustrating the sequential and double difference strategies. To quantify the uncertainty and multiparameter trade-off in the full waveform inversion for anisotropic elastic media, this study applies the iterated extended Kalman filter to anisotropic elastic full waveform inversion based on the integral equation method. The sensitivity matrix is an explicit representation with Green’s functions based on the nonlinear inverse scattering theory. Taking the similarity of sequential strategy between the multi-scale frequency domain full waveform inversion and data assimilation with an iterated extended Kalman filter, this study applies the explicit representation of sensitivity matrix to the the framework of Bayesian inference and then estimate the uncertainties in the full waveform inversion. This thesis gives results of numerical tests with examples for anisotropic elastic media. They show that the proposed Bayesian inversion method can provide reasonable reconstruction results for the elastic coefficients of the stiffness tensor and the framework is suitable for accessing the uncertainties and analysis of parameter trade-offs. en_US dc.language.iso eng eng dc.publisher The University of Bergen en_US dc.relation.haspart Paper 1. Huang X., Jakobsen M., and Wu R. S. (2020). On the applicability of a renormalized Born series for seismic wave modelling in strongly scattering media. Journal of Geophysics and Engineering, 17 (2): 277–299. The article is available in the main thesis. The article is also available at: https://doi.org/10.1093/jge/gxz105 en_US dc.relation.haspart Paper 2. Jakobsen M., Huang X. and Wu R. S. (2020). Homotopy analysis of the Lippmann- Schwinger equation for seismic wavefield modeling in strongly scattering media. Geophysical Journal International, 222 (2): 743-753. The article is available at: http://hdl.handle.net/1956/22014 en_US dc.relation.haspart Paper 3. Huang X. and Greenhalgh S. (2019). Traveltime approximation for strongly anisotropic media using the homotopy analysis method. Geophysical Journal International, 216 (3): 1648-1664. The article is available at: http://hdl.handle.net/1956/21870 en_US dc.relation.haspart Paper 4. Huang X., Jakobsen M., Eikrem K. S. and Nævdal G. (2020). Target-oriented inversion of time-lapse seismic waveform data. Communication in Computational Physics, 28(1): 249-275. The accepted version is available in the main thesis. The published version is available at: https://doi.org/10.4208/cicp.OA-2018-0143 en_US dc.relation.haspart Paper 5. Huang X., Eikrem K. S., Jakobsen M. and Nævdal G. (2020) Bayesian seismic full waveform inversion in anisotropic elastic media using an integral equation approach. Geophysics, 85(4), 1JA-Z18. The submitted version is available in the main thesis. The article is also available at: https://doi.org/10.1190/geo2019-0644.1 en_US dc.relation.haspart Appendix: Huang, X., Jakobsen, M., & Wuy, R. S. (2019). Taming the divergent terms in the scattering series of Born by renormalization. In SEG Technical Program Expanded Abstracts 2019 (pp. 5065-5069). Society of Exploration Geophysicists. The article is not available in BORA due to publisher restrictions. The article is available at: https://doi.org/10.1190/segam2019-3216450.1 en_US dc.rights In copyright eng dc.rights.uri http://rightsstatements.org/page/InC/1.0/ eng dc.title Modeling and inversion of seismic data using multiple scattering, renormalization and homotopy methods en_US dc.type Doctoral thesis dc.date.updated 2020-04-22T13:28:44.637Z dc.rights.holder Copyright the Author. All rights reserved en_US dc.contributor.orcid https://orcid.org/0000-0001-9719-6297 fs.unitcode 12-50-0
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