A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Network

Regularization is critical in solving the ill-posed geo-physical inversion problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effect inherently from a Neural Network structure. Researchers in Computer Vision (CV) have discovered that the Convolutional Neural Network (CNN) architecture inherently enforces a regularization that is advantageous for addressing diverse CV inverse problems, including de-noising and in-painting. In this study, we examine the applicability of this implicit regularization to geophysical inversions. The CNN maps an arbitrary vector to the model space (e.g. log-conductivity on the simulation mesh). The predicted subsurface model is then fed into a forward numerical simulation process to generate corresponding predicted measurements. Subsequently, the objective function value is computed by comparing these predicted measurements with the observed field measurements. The backpropagation algorithm is employed to update the trainable parameters of the CNN during the inversion. Note that the CNN in our proposed method does not require training before the inversion, rather, the CNN weights are estimated in the inversion algorithm, hence this is a test-time learning (TTL) approach. The results demonstrate that the implicit regularization provided by the CNN can be useful in DC resistivity inversions. We also provide a detailed discussion of the potential sources of this implicit regularization and some practical guides for applying the proposed method to other geophysical scenarios. The proposed approach for reparameterizing the inverse problem can be adapted to other Tikhonov-style geophysical inversions.