Fast forward modeling of magnetotelluric data in complex continuous media using an extended Fourier DeepONet architecture

The calculations of magnetotelluric (MT) responses play a fundamental role in the inversion and resolution analysis of MT problems. Conventional numerical methods for forward modeling involve solving a large system of linear equations. Although these methods provide accurate and stable solutions, they are computationally expensive as the model size increases. In this study, we develop an efficient forward-modeling network using an extended Fourier DeepONet (EFDO) architecture for fast MT forward modeling in complex continuous media. By efficiently learning the mapping of differential operators from the conductivity models to the MT responses, the EFDO framework can effectively approximate the MT forward operator. Once trained, it can instantaneously predict the MT responses for complex continuous resistivity models under identical model discretization conditions. We first compare the accuracy of the EFDO with a conventional finite volume (FV)-based forward-modeling solver and the existing deep-learning (DL)-based modeling schemes. Numerical experiments demonstrate that the MT responses predicted by the EFDO exhibit high conformity with the solutions computed by the FV method. Compared with other DL-based solvers, such as the extended Fourier neural operator and the UNet-Fourier neural operator, EFDO indicates superior prediction accuracy while significantly reducing training resource requirements. In addition, EFDO exhibits excellent generalization, maintaining outstanding prediction performance for the untrained frequencies of the same class samples. The EFDO can predict the MT responses at approximately 200 times the speed of the FV solver. The huge improvement in computational speed makes the EFDO a feasible solver for high-dimensional MT stochastic inversions, which require many forward evaluations.