A Novel Bayesian Geophysical Inversion Method to Address Loss Function
Bias: The Iterative Normalizing Flow Model
Abstract
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Geophysical inversion plays a pivotal role in understanding the Earth’s
internal structure. Recently generative neural networks (GNNs), such as
normalizing flow models (NFMs), have gained popularity for solving
Bayesian inversion problems. However, their effectiveness is often
hindered by the loss function bias. This bias occurs due to the global
nature of loss functions in NFMs, which lead to inaccuracies when
applied to geophysical inversion, where the Earth model is unique. To
address this, we propose the Iterative Normalizing Flow 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. Our experiments, validated on high-dimensional Bayesian
inversion tasks, show 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 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.