Inversion of Magnetic Data using Learned Dictionaries and Scale Space

2025-02-08

AI Summary

Magnetic inversion suffers from inherent ill-posedness—non-uniqueness, depth ambiguity, and noise sensitivity—while conventional methods lack adaptability in complex geological settings. To address these challenges, this paper proposes a novel variational inversion framework integrating learnable dictionaries with a scale-space regularization scheme. The method innovatively couples iterative adaptive dictionary learning with scale-space regularization to progressively incorporate structural details while robustly suppressing noise. It supports both fixed and dynamic dictionary learning and employs multi-scale variational optimization to enhance the physical plausibility of the solution. Experimental results on synthetic geological models demonstrate that the proposed approach significantly outperforms conventional variational and static-dictionary methods, achieving higher reconstruction accuracy and superior noise robustness. This work establishes a new paradigm for stable, multi-scale magnetic susceptibility distribution reconstruction.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Magnetic data inversion is an important tool in geophysics, used to infer subsurface magnetic susceptibility distributions from surface magnetic field measurements. This inverse problem is inherently ill-posed, characterized by non-unique solutions, depth ambiguity, and sensitivity to noise. Traditional inversion approaches rely on predefined regularization techniques to stabilize solutions, limiting their adaptability to complex or diverse geological scenarios. In this study, we propose an approach that integrates variable dictionary learning and scale-space methods to address these challenges. Our method employs learned dictionaries, allowing for adaptive representation of complex subsurface features that are difficult to capture with predefined bases. Additionally, we extend classical variational inversion by incorporating multi-scale representations through a scale-space framework, enabling the progressive introduction of structural detail while mitigating overfitting. We implement both fixed and dynamic dictionary learning techniques, with the latter introducing iteration-dependent dictionaries for enhanced flexibility. Using a synthetic dataset to simulate geological scenarios, we demonstrate significant improvements in reconstruction accuracy and robustness compared to conventional variational and dictionary-based methods. Our results highlight the potential of learned dictionaries, especially when coupled with scale-space dynamics, to improve model recovery and noise handling. These findings underscore the promise of our data-driven approach for advance magnetic data inversion and its applications in geophysical exploration, environmental assessment, and mineral prospecting.

Problem

• Improves subsurface magnetic susceptibility inversion
• Addresses non-unique solutions and noise sensitivity
• Enhances adaptability to complex geological scenarios

Innovation

• Learned dictionaries enhance feature representation
• Scale-space framework reduces overfitting risks
• Dynamic dictionaries increase inversion flexibility