Inversion using adaptive physics‐based neural network: Application to magnetotelluric inversion

Abstract

A new trend to solve geophysical problems aims to combine the advantages of deterministic inversion with neural network inversion. The neural networks applied to geophysical inversion have had limited success due to the need for extensive training of datasets and the lack of generalizability to out-of-sample scenarios. Deterministic regularized inversion often requires a good starting model to avoid possible local minima in highly nonlinear problems. We have developed a physics-based neural network procedure that combines the advantages of deterministic and neural network inversions in a coupled inversion scheme. The new inversion algorithm is formulated as a constrained minimization problem with a composite objective function composed of data misfit, neural network training function and a coupling model objective function that links the two inversion schemes through a reference model. We investigate two strategies to update the reference model in the coupling model objective function using either a fully trained network or an adaptively trained network that keeps evolving and learning during the inversion. First, we propose a procedure to generate the training dataset required for the fully trained network to improve the network generalization. Second, we extend the analysis of the adaptively trained network inversion without preparing a training dataset, so it is suitable for most exploration scenarios. Our approach enables the network to learn only the relevant model distribution. Predictions from the network are used to constrain the deterministic inversion using a new predicted reference model. We demonstrate the convergence of our procedure in recovering high-resolution resistivity models when applied to synthetic magnetotellurics data. We compare the recovered resistivity model from a deterministic inversion, a neural network inversion and physics-based neural network inversions using fully and adaptively trained networks, respectively. The results indicate that the adaptive physics-based neural network is superior as it does not require preparing a training dataset but can still recover reliable resistivity models.

A novel approach for water reservoir mapping using controlled source audio‐frequency magnetotelluric in Xingning area, Hunan Province, China

“…Zhang et al., 2023). Moreover, in our approach, we invert the two‐dimensional resistivity model using local one‐dimensional models assuming that the resistivity model consists of$$\ {N}_l$$ layers of fixed thicknesses (Alyousuf & Li, 2022). As a good inversion is essential for better pseudostratigraphic (PS) maps, we upstream perform fast and efficient one‐dimensional inversion for all stations and then stitch the one‐dimensional smooth models to form a two‐dimensional pseudo‐inversion section.…”

Fast Initial Model Design for Electrical Resistivity Inversion by Using Broad Learning Framework

“…Global optimization algorithms, such as simulated annealing [9], genetic algorithms [10,11], and particle swarm optimization [12], play a crucial role in solving optimization problems with multiple local optima by thoroughly exploring the entire search space to identify the global optimum [13]. However, the high computational costs associated with global optimization algorithms limit their practical application in 3-D electrical resistivity inversion problems [11,14,15]. Deterministic methods such as the Gauss-Newton method [16], limited memory quasi-Newton method [17], and conjugate gradient method [18][19][20][21] are the popular approaches for the 3-D electrical resistivity inversion due to their promising performance in terms of result accuracy, stability, and convergence speed [8,11,22].…”