Physics-Driven Deep Learning Inversion with Application to Magnetotelluric

Abstract

Due to the strong capability of building complex nonlinear mapping without involving linearization theory and high prediction efficiency; the deep learning (DL) technique applied to solve geophysical inverse problems has been a subject of growing interest. Currently, most DL-based inversion approaches are fully data-driven (namely standard deep learning), the performance of which largely depends on the training sample sets. However, due to the heavy burden of time and computational resources, it can be challenging to supply such a massive and exhaustive training dataset for generic realistic exploration scenarios and to perform network training. In this work, based on the recent advances in physics-based networks, the physical laws of magnetotelluric (MT) wave propagation is incorporated into a purely data-driven DL approach (PlainDNN) and thus builds a physics-driven DL MT inversion scheme (PhyDNN). In this scheme, the forward operator modeling MT wave propagation is integrated into the network training loop, in the form of minimizing a hybrid loss objective function composed of the data-driven model misfit and physics-based data misfit, to guide the network training. Consequently, the proposed PhyDNN method will take the advantage of the fully data-driven DL and conventional physics-based deterministic methods, allowing it to deal with complex realistic exploration scenarios. Quantitative and qualitative analysis results demonstrate that the PhyDNN can honor the physical laws of the MT inverse problem, and with other conditions unchanged, the PhyDNN outperforms the PlainDNN and the classical deterministic Occam inversion method. When processing field data, the PhyDNN method yields considerably impressive inversion results compared to the Occam method, and the corresponding simulated MT responses agree well with the real measurements, which confirms the effectiveness and applicability of the PhyDNN method.

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“…Physics-informed neural network (PINN) (Raissi et al, 2019;Gong and Tang, 2022) is one the most representative coupled physics-DL solutions. Recently, Liu et al (2022) embeds the forward operator into the network architecture. However, the loss of the partial differential equation is calculated by a traditional EM forward modeling scheme instead of the automatic differentiation of the neural network proposed by PINN.…”

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“…Geophysical inversion is a technique that uses observed data to infer the spatial distribution of subsurface physical parameters [40,41]. However, because the observed data are limited, the inverse problem is usually ill-posed, and the inversion results frequently have issues such as instability and non-uniqueness [40,41].…”

“…Geophysical inversion is a technique that uses observed data to infer the spatial distribution of subsurface physical parameters [40,41]. However, because the observed data are limited, the inverse problem is usually ill-posed, and the inversion results frequently have issues such as instability and non-uniqueness [40,41]. To minimize the ill-posed problem, Tikhonov et al [42] proposed a regularized inversion method to stabilize the model iteration process by adding a regularized model constraint term to the inversion objective function.…”

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“…For example, Ling et al embedded the Galilean invariance into the network to improve the accuracy in RANS turbulence modeling [23]. Liu et al integrated the forward operator model for magnetotelluric into the network training loop to reconstruct the subsurface resistivity model [24]. Huang et al incorporated the physics from the finite element mode into the network to guide the damage feature learning from measured data [25].…”