Efficient Transdimensional Bayesian Inversion of 2D Magnetotelluric Data with Deep Learning based Surrogate Modelling

Efficient Transdimensional Bayesian Inversion of 2D Magnetotelluric Data with Deep Learning based Surrogate Modelling

Koustav Ghosal¹, Arun Singh² and Deepak K. Gupta³

¹Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad, India

²Indian Institute of Technology Roorkee, Uttarakhand, India

³Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad, India

Email id: koustav.20dr0066@agp.iitism.ac.in

Geophysical inverse problems are ill-posed and non-unique in nature, which makes the estimated model parameters prone to uncertainty. Uncertainty quantification is a vital step in geophysical inversion. Traditional gradient-based methods often struggle to provide reliable estimates of uncertainty with their single best fit model. Alternative approaches, such as the trans-dimensional Bayesian approach, have gained popularity for their ability to address this issue by generating an ensemble of models, which allows for uncertainty quantification. However, curating an ensemble for 2D magnetotelluric data inversion is computationally expensive and requires efficient sampling methods or rapid forward solvers to reduce the computation cost. The development of surrogate models has emerged as a promising solution to mitigate these computational challenges, enabling faster evaluations while maintaining accuracy in the inversion process. We proposed a 2D forward solver based on a convolutional neural network to accelerate the forward computation and integrate with trans-dimensional Bayesian framework. To enhance the generalization capabilities of the deep neural network, the subsurface resistivity models used for training were generated using Gaussian Random Fields (GRFs). This approach increased the network's robustness, even when dealing with unseen, out-of-distribution data.

The developed algorithm was tested on synthetic data, demonstrating that with surrogate modeling, the trans-dimensional inversion was ten times faster compared to the finite-difference-based forward solver, while producing similar results. Subsequently, the algorithm was applied to a subset of the CORPA dataset, covering a 200 km profile. The derived subsurface structure revealed a 5 km thick sedimentary layer sitting above a resistive basement. In the middle of the profile, the conductive North American conductor known as the Plain is clearly visible. The results not only align well with deterministic outcomes but also provide comprehensive uncertainty estimates.