Two-dimensional deep learning inversion of magnetotelluric sounding data

Conventional linear iterative methods for magnetotelluric sounding (MT) suffer from considerable limitations related to difficulties in selecting the initial model and local optima. On the other hand, conventional intelligent nonlinear methods exhibit slow convergence and low accuracy. In this study, we propose an inversion strategy based on the deep learning (DL) deep belief network (DBN) to realise the instantaneous inversion of MT data. A scaled momentum learning rate is introduced to improve the convergence performance of the restricted Boltzmann machine during the DBN pre-training stage, and a novel activation function (DSoft) is introduced to enhance the global optimisation capability during the DBN fine-tuning stage. To address the difficulty in designing the sample data when prior information is lacking, we employ the k-means++ algorithm to cluster the MT field data and use the clustering results as the prior information to guide the construction of the sample dataset. Then, based on the proposed DBN, we ensure end-to-end mapping directly from the apparent resistivity to the resistivity model. We implement two groups of experiments to demonstrate the validity of both improvements on the DBN. We consider six types of geoelectric model from the test set to demonstrate the feasibility and effectiveness of the proposed DBN method for MT 2D inversion, which we further compare with the well-known least-square regularisation method for several extended geoelectric models and field data. The qualitative and quantitative analyses show that the DL inversion method is promising as it can accurately delineate the subsurface structures and perform rapid inversion.