Uncertainty Quantification in Geophysical Inversion and Geological Differentiation

Date

2022-12-03

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Abstract

Geophysical inversions are typically performed to reconstruct subsurface physical property models. However, assessing the uncertainty of inversion results is still largely underexplored due to prohibitive computational cost. Also, little attention has been paid to quantifying the uncertainty of geological units differentiated from physical property models. The goal of my dissertation is to efficiently quantify two types of uncertainties, namely, uncertainty of geophysical inversions and uncertainty of geological units identified from inversions.

In the deterministic inversion framework, I proposed a new method to generate a large sequence of physical property models that all reproduce the geophysical data equally well but display diverse model characteristics. This is achieved by randomly sampling two hyperparameters of the mixed Lp norm regularization. The diverse model features reflect the underlying uncertainty. The workflow I developed can handle millions of model parameters, as demonstrated by a real-world application in the Decorah area over northeast Iowa. In the Bayesian inversion framework, to improve the computational efficiency, I developed a novel method of sparse geometry parameterization, which employs simple geometries to approximate the complex shapes of single or multiple anomalous bodies. I also developed a method of imposing structural constraints in trans-dimensional Monte Carlo sampling. I designed multiple scenarios to understand how various constraints and data sets affect the posterior uncertainty. I conducted realistic synthetic studies using the modified 2D SEG-EAGE, Sigsbee, and Pluto salt models.

To quantify the uncertainty of differentiated geological units, I developed a novel joint inversion method, termed mixed Lp-norm joint inversion, to recover a set of equivalent models. Only those jointly recovered models that fall within the range of prior rock sample measurements are accepted, and used in the subsequent step of geology differentiation, leading to multiple 3D quasi-geology models. Uncertainty of geological units is then quantified based on the variability of spatial distribution of each unit across the multiple quasi-geology models.

My dissertation has a broad and immediate impact on other researchers. The resulting methods and tools can be readily applied to solve various geoscientific problems using multiple geophysical measurements, such as mineral exploration, basin modeling, and volcano studies, etc.

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Keywords

Uncertainty quantification, Geophysical inversion, Numerical modeling, Geology differentiation

Citation

Portions of this document appear in: Wei, Xiaolong, and Jiajia Sun. "Uncertainty analysis of 3D potential-field deterministic inversion using mixed Lp norms." Geophysics 86, no. 6 (2021): G133-G158; and in: Wei, Xiaolong, Jiajia Sun, and Mrinal K. Sen. "Quantifying uncertainty of salt body shapes recovered from gravity data using trans-dimensional Markov chain Monte Carlo sampling." Geophysical Journal International 232, no. 3 (2023): 1957-1978; and in: Wei, Xiaolong, and Jiajia Sun. "3D probabilistic geology differentiation based on airborne geophysics, mixed L p norm joint inversion, and physical property measurements." Geophysics 87, no. 4 (2022): K19-K33.