A Fourier neural operator surrogate model for nonlinear electrical resistivity tomography

SUMMARY Electrical resistivity tomography (ERT) is used to infer the subsurface resistivity structure. ERT requires solving a nonlinear inverse problem that is often approximated as linear to reduce computational time. However, the approximation requires assumptions that cause limitations for the data analysis. Most of the computational time is due to the forward problem that requires solving the Poisson equation. Recently, similar forward problems have been shown to be replaceable with a surrogate model of lower computational cost. We present a geoelectric surrogate based on Fourier neural operators and demonstrate a successful application in nonlinear inversion. The standard deviation of the surrogate prediction error for unseen samples is $<$5 per cent. Furthermore, the surrogate reduces computational time by over three orders of magnitude per realization, enabling ERT for previously intractable settings. We apply the surrogate in Markov chain Monte Carlo inversion of simulated data. The results resolve sharp resistivity changes with plausible uncertainties.