Three‐Dimensional Integrated Imaging of Gravity and MT Data Based on Deep Neural Network Constraints and Structural Constraints

ABSTRACT Joint inversion serves as an established strategy to mitigate non‐uniqueness in geophysical inversion. Current main coupling methods implement joint inversion of multiphysics parameters by introducing either rock‐physics relations or the structural similarity of the model parameters. In this study, we focus primarily on the performance of deep neural network (DNN) constraints while comparing them against other structural constraints in three‐dimensional joint inversion of gravity and magnetotelluric (MT) data. Tests on synthetic and field data demonstrate that, compared with standard cross‐gradient constraints, the summative gradient constraints introducing gradient polarity sign establish a stronger structural coupling, yielding better joint inversion results. Furthermore, we develop a DNN‐constrained three‐dimensional collaborative inversion algorithm. This algorithm eliminates the need for laborious weight adjustments of constraint terms, thereby avoiding additional computational costs on the inherently expensive three‐dimensional inversion process. By training neural networks to learn structural similarity and physical property correlations between model parameters, we generate enhanced initial models for inversion. Synthetic data experiments demonstrate that, compared with single‐method inversion and two joint inversion schemes based on structural constraints (cross‐gradients and summative gradients), the DNN‐constrained inversion more effectively integrates the respective advantages of gravity and MT, reconstructs subsurface target anomalies more accurately and achieves faster iteration convergence with lower data misfit. Application to field data from Yellowstone further validates the feasibility and practicality of this DNN‐constrained scheme.