Multimodal U-Net: A Novel Approach for 2-D Inversion of Magnetotelluric Data

Under the broad definition of multimodal data, data presenting different views and complementary information are classified as multimodal. Two-dimensional magnetotelluric (MT) responses, including apparent resistivity and phase of two polarization modes, reflect differing physical properties and offer complementary insights into the subsurface media. Traditional deep learning (DL) approaches often struggle to capture and integrate these complementary features effectively for accurate inversion. In this study, we treat $\rho _{S}^{\text {TE}} $ , $\varphi ^{\text {TE}}$ , $\rho _{S}^{\text {TM}}$ , and $\varphi ^{\text {TM}}$ of 2-D MT as multimodal data and introduce a data fusion method of multimodal DL (MDL), which enhances the accuracy of MT inversion by employing a multimodal U-net model to integrate various MT response features effectively. In detail, each MT response is processed in a different encoder to exploit its unique information better. It is densely connected within each encoder and across different encoders, facilitating the fusion of MT data across depths and response modalities. Our method maximizes complementary information from multiple response modalities, resulting in a more precise depiction of nonlinear processes in MT inversion. First, 2-D Gaussian random fields (GRFs) simulate the resistivity model. Then, the multimodal U-net is introduced and improved as the MT inversion framework and compared with the conventional U-net. Moreover, the anti-noise ability and generalization of the multimodal U-net are tested by introducing varying noise levels into the MT responses. Finally, we validate our proposed method with MT field data from the Yanggao area in the Datong Basin, Shanxi Province, China, showing that the performance of our model surpasses conventional U-net and traditional nonlinear conjugate gradient (NCG) inversion methods.