Application of supervised descent method to transient electromagnetic data inversion

Inversion plays an important role in transient electromagnetic (TEM) data interpretation. This problem is highly nonlinear and severely ill posed. Gradient-descent methods have been widely used to invert TEM data, and regularization schemes containing prior information are applied to reduce the nonuniqueness and stabilize the inversion. During the inversion, the partial derivatives are repeatedly computed, which is time and memory consuming. Furthermore, regularization schemes can only provide limited prior information. Much prior information from knowledge and experience cannot be directly used in inversion. In this work, we applied the supervised descent method (SDM) to TEM data inversion. This method contains an offline training stage and an online prediction stage. In the training stage, a training data set is generated according to prior information. Then, the average descent direction between a fixed initial model and the training models can be learned by iterative schemes. In the online stage of prediction, the learned descent directions are applied directly into the inversion to update the models. In this manner, one can select models satisfying the data and model misfit. In this study, SDM is applied to model- and pixel-based inversion schemes. Synthetic examples indicate that SDM inversion can not only enhance the accuracy of inversion due to the incorporation of prior information but also largely accelerate the inversion procedure because it avoids the online computation of derivatives.