Fu, XinChen, Jiefu2022-06-17December 22021-12December 2Portions of this document appear in: Lu, H., Shen, Q., Chen, J., Wu, X. and Fu, X., 2019. Parallel multiple-chain DRAM MCMC for large-scale geosteering inversion and uncertainty quantification. Journal of Petroleum Science and Engineering, 174, pp.189-200; and in: Lu, H., Shen, Q., Wu, X., Chen, J. and Fu, X., 2018, January. MCMC for large-scale geosteering inversion with a scalable MPI implementation. In 2018 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM) (pp. 1-2). IEEE; and in: Lu, H., Khalil, M., Catanach, T., Chen, J., Wu, X., Fu, X., Safta, C. and Huang, Y., 2021. Generalized Transitional Markov Chain Monte Carlo Sampling Technique for Bayesian Inversion. arXiv preprint arXiv:2112.02180; and in: Lu, H., Chen, J., Wu, X., Fu, X., Khalil, M., Safta, C. and Huang, Y., 2020. Underground formation characterization and uncertainty quantification using transitional Markov chain Monte Carlo sampling with an efficient parallel implementation. In SEG Technical Program Expanded Abstracts 2020 (pp. 425-429). Society of Exploration Geophysicists; and in: Lu, H., Shen, Q., Chen, J., Wu, X., Fu, X., Khalil, M., Safta, C. and Huang, Y., 2020. Bifidelity Gradient-Based Approach for Nonlinear Well-Logging Inverse Problems. IEEE Journal on Multiscale and Multiphysics Computational Techniques, 5, pp.132-143; and in: Lu, H., Chen, J., Wu, X., Fu, X., Khalil, M., Safta, C. and Huang, Y., 2020, July. Efficient Bi-fidelity Gradient-Based Method for Non-Linear Inverse Problems. In 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting (pp. 1245-1246). IEEE; and in: Zeng, S., Lu, H., Fu, X. and Chen, J., 2019, May. GPU Acceleration for Triaxial Induction Logging Tool Responses in Layered Uniaixal Formation. In 2019 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO) (pp. 1-3). IEEE.https://hdl.handle.net/10657/9290Understanding the earth model from real-world measurements is critical in geophysical explorations. When the physical process of generating measurements is described as a nonlinear model, iterative processes are needed to determine the earth model parameters from the measurements, and the process is known as geophysical inversion. As the detection techniques improve, the measurements contain more information about the earth model, resulting in a growth in the earth model dimension. Meanwhile, a more advanced detection technique usually means a more complicated physical process of generating measurements, which corresponds to a forward model with higher nonlinearity. Both factors have placed more requirements on the inverse algorithms. Traditional gradient-based algorithms can solve the inverse problem in a relatively short time, however, they only find local minimums without uncertainty quantification. If uncertainty quantification is desired, Bayesian inference methods have emerged as a viable option. However, Bayesian inference methods are slower than gradient-based algorithms since they usually require sampling. Therefore, efficient Bayesian inference methods are necessary for robust geophysical inversion with uncertainty quantification. This dissertation focuses on efficient Bayesian inference methods for solving geophysical inverse problems using high-performance computing techniques. In this dissertation, two efficient Markov chain Monte Carlo (MCMC) sampling methods with parallel computing techniques, as well as one MCMC method taking into account varying problem dimensions are proposed. It also demonstrates a bi-fidelity deterministic inversion method, in which a smooth surrogate model is used to assist the inversion. The proposed methods are assessed using the electromagnetic (EM) well-logging inverse problem, which infers the earth model through measurements taken from subsurface sensors during the high-angle and horizontal well drilling. Besides the inversion algorithms, two HPC techniques are investigated and tested in this dissertation, and they show promise of solving geophysical inverse problems efficiently.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. UH Libraries has secured permission to reproduce any and all previously published materials contained in the work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Well logginginverse problemsBayesian inferencehigh-performance computing2022-06-17Thesisborn digital