Enhancing Deep Learning based RMT Data Inversion using Gaussian Random Field

TL;DR

A DL-based inversion scheme for Radio Magnetotelluric data where the subsurface resistivity models are generated using Gaussian Random Fields enhances generalization in a data-driven supervised learning framework, suggesting a promising direction for OOD generalization in DL methods.

Abstract

Deep learning (DL) methods have emerged as a powerful tool for the inversion of geophysical data. When applied to field data, these models often struggle without additional fine-tuning of the network. This is because they are built on the assumption that the statistical patterns in the training and test datasets are the same. To address this, we propose a DL-based inversion scheme for Radio Magnetotelluric data where the subsurface resistivity models are generated using Gaussian Random Fields (GRF). The network's generalization ability was tested with an out-of-distribution (OOD) dataset comprising a homogeneous background and various rectangular-shaped anomalous bodies. After end-to-end training with the GRF dataset, the pre-trained network successfully identified anomalies in the OOD dataset. Synthetic experiments confirmed that the GRF dataset enhances generalization compared to a homogeneous background OOD dataset. The network accurately recovered structures in a checkerboard resistivity model, and demonstrated robustness to noise, outperforming traditional gradient-based methods. Finally, the developed scheme is tested using exemplary field data from a waste site near Roorkee, India. The proposed scheme enhances generalization in a data-driven supervised learning framework, suggesting a promising direction for OOD generalization in DL methods.

Figures (14)

• Figure 1: A schematic representation of a Convolutional block for each convolutional layer.
• Figure 2: Image showing the proposed network for the RMT data inversion. The network consists of a sequence of convolutional layers, a batch normalization layer and a ReLu activation layer. The input is a 4 channel data (apparent resistivity and phase for TE and TM mode) and output is the resistivity model.
• Figure 3: The synthetic GRF dataset. (a) and (c) represent random localized anomalies, (b) and (d) represent randomly distributed horizontal or nearly horizontal layered resistivity anomalies.
• Figure 4: Image showing model parameters for generating OOD dataset. The dataset consists of five different types of geometry. (a) Dataset of type-1: single block-shaped anomaly. (b) Dataset of type-2: double block-shaped anomalies. (c) Dataset of type-3: three block-shaped anomalies. (d) Dataset of type-4: single inclined shaped anomaly. (e) Dataset of type-5: double inclined shaped anomaly. The resistivity values for the anomalies are randomly generated in two different classes of resistivity, first H stands for high resistivity between (1000-2000) $\Omega~m$, and second one L stands for low resistivity which ranges between (10-20) $\Omega~m$ and the background is homogeneous with 500 $\Omega~m$. Each geometry is generated in a different amount the highest being the more complex geometry (c) and (e), while the lowest being the simplest among all (a).
• Figure 5: The statistical distribution shift between the checkerboard and GRF resistivity models. (a) represents the checkerboard sample, (b) is the corresponding histogram plot which consists of three peaks denoting background, low and high resistivity, (c) the GRF sample and (d) shows a distribution of GRF sample from high to low resistivity.