A Novel Bayesian Geophysical Inversion Method to Address Loss Function Bias: The Iterative Normalizing Flows Model

• Published in: Journal of geophysical research. Machine learning and computation Vol. 2; no. 1
• Main Authors: Liao, Binbin, Chen, Xiaodong, Xu, Jianqiao, Zhou, Jiangcun, Sun, Heping
• Format: Journal Article
• Language: English
• Published: Wiley 01.03.2025
• ISSN: 2993-5210; 2993-5210
• DOI: 10.1029/2024JH000479

Geophysical inversion plays a pivotal role in understanding the Earth's internal structure. Recently generative neural networks (GNNs), such as normalizing flows models (NFMs), have gained popularity for solving Bayesian inversion problems. However, the posterior probability density functions (PDFs) obtained by amortized GNN‐based methods often deviates from the target distribution. This discrepancy arises because traditional amortized methods use joint PDFs as the objective in loss functions, rather than the conditional PDFs of the observed data. To address this, we propose the Iterative Normalizing Flows Model (INFM), a novel approach that mitigates loss function bias by progressively narrowing the prior distribution's support set in each iteration, while ensuring that the posterior distribution accurately converges to the target distribution. Our experiment, validated on high‐dimensional Bayesian inversion tasks, shows that INFM significantly enhances inversion accuracy without increasing network complexity or computational cost. When applied to the Earth's 1‐D structure model inversion, our method revealed key insights, such as a lower core density compared to the Preliminary Reference Earth Model (PREM) model and the presence of anisotropy in both the mantle and core, consistent with previous studies. These findings suggest that the INFM method offer high computational efficiency and accuracy, making it well‐suited for large‐scale geophysical inversion problems. Plain Language Summary Understanding the Earth's internal structure from surface observations is a major challenge in Earth science. Recently, scientists have been using advanced computer methods, such as neural networks, to help with this task. However, traditional methods cannot always provide the most accurate results. To improve this, we developed a new approach called the Iterative Normalizing Flows Model (INFM). Rather than trying to figure out the Earth's structure all at once, this method makes small refinements over time, which helps reduce errors. In our tests, INFM performed better than previous methods without requiring more computer power. When we applied it to study the Earth's structure using real data about the Earth's structure, it revealed new details, such as a less dense core and signs of unusual properties in both the mantle and the core. Our method is both efficient and accurate, making it a valuable tool for scientists studying the Earth's interior on a large scale. Key Points We propose the Iterative Normalizing Flow Model to address loss function bias for Bayesian geophysical inversion The new method enhances convergence and accuracy over traditional Normalizing Flow Models while maintaining computational efficiency Applied to Earth's normal mode inversion, it provides accurate posterior pdfs for density and anisotropy in the Earth's interior