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

Abstract 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.