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Magnetic inversions constrained with geological information: An investigation using regularized inversion and machine learning approach
Liu, Zhuo
Liu, Zhuo
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2024
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2025-10-09
Abstract
Imaging the distributions of physical property values and the geometries of subsurface anomalies has been a central focus in geophysics for decades. Theoretically, geophysical data contains sufficient information about these distributions and geometries, as indicated by the mathematical expressions describing geophysical responses. However, recovering this information purely through geophysical approaches remains challenging due to the complex interplay between these two types of information in the data. Distinguishing the influence of physical properties from geometric factors in the data is difficult. Typically, this problem is circumvented by recovering only one type of information, with the other being substituted by known values from previous studies or simplifying assumptions. These practices, however, may not always be accurate, potentially reducing the fidelity of the subsurface models and missing valuable geological insights. To address this, I developed a set of inversion methods using both traditional Gauss-Newton-based minimizations and machine learning approaches, aiming to enhance the recovery of subsurface information.
First, I explored the recovery of anisotropic magnetic susceptibility through a clustering-constrained physical property inversion. Traditionally, anisotropy parameters are obtained from labor-intensive, time-consuming, and expensive laboratory measurements on oriented samples. Given that anisotropy influences the orientation of induced magnetization and is thus recorded in geophysical data, the initial goal was to assess the effectiveness of recovering anisotropy and inferring different geologic units from purely geophysical data. The study focused on layered sedimentary rocks, assuming principal susceptibilities are aligned with the structure. Synthetic tests demonstrated that anisotropic inversion improves accuracy over isotropic inversion, and the clustering results can distinguish different rock units. Field test results over the Wyoming Salient aligned well with previous sample measurements, revealing formation boundaries aligning with the boundaries of geologic ages where rock samples were unavailable.
Next, I addressed the influence of geometry on geophysical data. Incorrect assumptions can introduce errors into inversions, undermining results. Therefore, it is crucial to consider both geometries and physical properties in inversions. I developed a constrained simultaneous inversion method and corresponding workflow to recover basement depth and lateral magnetic susceptibility variations in basement rock by combining physical property and geometry inversions. Magnetotelluric data provided prior depth information to guide basement depth recovery, while susceptibility inversion was constrained by clustering. Both synthetic and field tests over the Illinois Basin showed that this method, allowing for varying susceptibility, better approximates true geology compared to existing methods assuming uniform physical properties. The clustering results also provided insights into differentiating different rock units and their boundaries.
Finally, I ventured into machine learning for inversion, leveraging neural networks' universal approximator capabilities to map intricate relationships between geologic anomalies and geophysical data for higher accuracy. A deep neural network was developed and trained as an inverse operator, incorporating descriptive prior information about geological faults. Trained and tested on synthetic datasets, the network was then applied to airborne magnetic data over the Illinois Basin. The inverted basement depth models show high accuracy and the ability to recover faults in the basement depth model. Despite overfitting issues, the inverted susceptibility models accurately represented the overall behavior of the truth and boundaries between sections of different susceptibility values. Field data validation demonstrated the method's feasibility, achieving superior accuracy in basement relief imaging compared to traditional methods, and revealing a mafic intrusion that is consistent with previous geological records.
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