Application of supervised descent method for 2D magnetotelluric data inversion

The supervised descent method (SDM) is applied to 2D magnetotellurics (MT) data inversion. SDM contains offline training and online prediction. The training set is composed of the models generated according to prior knowledge and the data simulated by MT forward modeling. In the training process, a set of descent directions from an initial model to the training models is learned. In the prediction, model reconstruction is achieved by optimizing an online regularized objective function with a restart scheme, where the learned descent directions and the computed data residual are involved. SDM inversion has the advantages of (1) being more efficient than traditional gradient-descent methods because the computation of local derivatives of the objective function is avoided, (2) incorporating prior uncertain knowledge easier than deterministic inversion approach by generating training models flexibly, and (3) having high generalization ability because the physical modeling can guide the online model reconstruction. Furthermore, a way of designing general training set is introduced, which can be used for training when the prior knowledge is weak. The efficiency and accuracy of this method are validated by two numerical examples. The results indicate that the reconstructed models are consistent with prior information, and the simulated responses agree well with the data. This method also shows good potential to improve the accuracy and efficiency in field MT data inversion.