In order to develop a geophysical earth model that is consistent with the measured geophysical data, two types of inversions are commonly used: a physics-based regularized inversion and a statistical-based machine learning inversion. In nonlinear problems, deterministic regularized inversion usually necessitates a good starting model to prevent possible local minima. The neural networks inversion requires large training data sets, which makes its generalizability limited. To overcome the limitation of physics-based regularized inversion and a statistical-based machine learning inversion and combine the benefits of both one inversion scheme, we developed a new physics-based neural network (PBNN) inversion algorithm. In our PBNN inversion, we include machine learning constraints into the regularized inversion using a coupling model objective function. The coupling objective function aims to minimize the difference between the recovered model through regularized inversion and the network-predicted reference model. We update the reference model using either a fully-trained network or an adaptively-trained network. The fully trained PBNN has the ability to collect all of the connections between data and models through a pseudoinverse operator. However, for geophysical inversion applications, particularly in the exploratory setting, this approach is unlikely to become feasible. Neural networks may struggle to extract complicated correlations from data when given insufficient data observations. The technique is impractical for practical usage due to the quantity of training required. In our novel adaptively PBNN algorithm, there is no need to prepare a training data set. At each iteration, the adaptively-PBNN algorithm retrains using the recovered models from the regularized inversion and their related data. The regularized inversion's recovered resistivity models are sufficient to guide neural network predictions towards the true model. One unique advantage is that the approach’s ability to fully use all intermediate models from the regularized inversion that were commonly discarded and apply them to the network training. When applied to synthetic MT data, we show that our technique is capable of reconstructing high-resolution resistivity models.

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