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Joint inversion has drawn considerable attention due to the availability of multiple geophysical data sets, ever-increasing computational resources, the development of advanced algorithms, and its ability to reduce inversion uncertainty. A key issue of joint inversion is to develop effective strategies to link different geophysical data in a unified mathematical framework, in which the information obtained from different models can complement each other. We have developed a deep learning-enhanced joint inversion framework to simultaneously reconstruct different physical models by fusing different types of geophysical data. Traditionally, structure similarity constraints are pursued by joint inversion algorithms using manually crafted formulations (e.g., cross gradient). The constraint is constructed by a deep neural network (DNN) during the learning process. The framework is designed to combine the DNN and a traditional independent inversion workflow and improve the joint inversion result iteratively. The network can be easily extended to incorporate multiphysics without structural changes. Numerical experiments on the joint inversion of 2D DC resistivity data and seismic traveltime are used to validate our method. In addition, this learning-based framework demonstrates excellent generalization abilities when tested on data sets using different geologic structures. It also can handle different sensing configurations and nonconforming discretization.

The physical property models obtained from geophysical inversions can be converted to a 3D quasi-geology model via a process called geology differentiation. Recent works indicate that the geology differentiation can help maximize the value of the information contained in geophysical data. However, it remains largely unexplored as to how to quantify the uncertainties of a 3D quasi-geology model. We approach this problem by using a recently developed mixed [Formula: see text] norm regularization and a priori physical property measurements. We use mixed [Formula: see text] norm joint inversion to construct a large sequence of physical property models based on the Gzz component of the airborne gravity gradient and magnetic measurements. The available physical property measurements are used to determine which physical property models to accept. We then construct a sequence of 3D quasi-geology models by performing the geology differentiation for all of the accepted models, which allows us to compute the probabilities of our geology differentiation results. We apply our approach to a set of field data collected over the Decorah area located in northeast Iowa. We successfully quantify the uncertainties of the spatial extents for the identified geologic units and compute probabilities of geologic units at any location in our study area. The proposed workflow has broad implications for 3D geologic model building based on multiple geophysical and/or rock sample measurements.

The nonuniqueness problem in geophysical inversion, especially potential-field inversion, is widely recognized. It is argued that uncertainty analysis of a recovered model should be as important as finding an optimal model. However, quantifying uncertainty still remains challenging, especially for 3D inversions in both deterministic and Bayesian frameworks. Our objective is to develop an efficient method to empirically quantify the uncertainty of the physical property models recovered from 3D potential-field inversion. We work in a deterministic framework in which an objective function consisting of a data misfit term and a regularization term is minimized. We perform inversions using a mixed [Formula: see text]-norm formulation in which various combinations of [Formula: see text] ([Formula: see text]) norms can be implemented on different components of the regularization term. Specifically, we randomly sample the [Formula: see text]-norm values in multiple times, and generate a large and diverse sequence of physical property models that all reproduce the observed geophysical data equally well. This suite of models offers practical insights into the uncertainty of the recovered model features. We quantify the uncertainty through calculation of standard deviations and interquartile range, as well as visualizations in box plots and histograms. The numerical results for a realistic synthetic density model created based on a ring-shaped igneous intrusive body quantitatively illustrate uncertainty reduction due to different amounts of prior information imposed on inversions. We also apply the method to a field data set over the Decorah area in northeastern Iowa. We adopt an acceptance-rejection strategy to generate 31 equivalent models based on which the uncertainties of the inverted models as well as the volume and mass estimates are quantified.

Mineral exploration under a thick sedimentary cover naturally relies on geophysical methods. We have used high-resolution airborne magnetic and gravity gradient data over northeast Iowa to characterize the geology of the concealed Precambrian rocks and evaluate the prospectivity of mineral deposits. Previous researchers have interpreted the magnetic and gravity gradient data in the form of a 2D geologic map of the Precambrian basement rocks, which provides important geophysical constraints on the geologic history and mineral potentials over the Decorah area located in the northeast of Iowa. However, their interpretations are based on 2D data maps and are limited to the two horizontal dimensions. To fully tap into the rich information contained in the high-resolution airborne geophysical data, and to further our understanding of the undercover geology, we have performed separate and joint inversions of magnetic and gravity gradient data to obtain 3D density contrast models and 3D susceptibility models, based on which we carried out geology differentiation. Based on separately inverted physical property values, we have identified 10 geologic units and their spatial distributions in 3D which are all summarized in a 3D quasi-geology model. The extension of 2D geologic interpretation to 3D allows for the discovery of four previously unidentified geologic units, a more detailed classification of the Yavapai country rock, and the identification of the highly anomalous core of the mafic intrusions. Joint inversion allows for the classification of a few geologic units further into several subclasses. We have demonstrated the added value of the construction of a 3D quasi-geology model based on 3D separate and joint inversions.