First arrival traveltime tomography using supervised descent learning technique

First arrival traveltime tomography is a highly non-linear inverse problem. Regularization is often used to constrain and stabilize the model reconstruction. It can be considered as adding prior information into the inversion. But not all prior information can be done this way because some cannot be expressed in rigorous mathematical forms. Moreover, the inversion algorithms based on gradient-descent arc often trapped in local minima. All these have a negative impact on the accuracy of reconstruction. In this work, we apply the supervised descent method (SDM) for 2D traveltime tomography. SDM is a machine-learning algorithm that contains two steps. In the training stage, SDM learns a set of descent directions from a training dataset containing prior knowledge. In the prediction stage, it uses both the learned descents and the data residual to accomplish model reconstruction. In this paper, we present the formulations of the training and prediction for SDM, and introduce two methods to solve the regularized objective function in the online prediction stage. The descent learning technique provides a new perspective to combine machine-learning-based inversion and classical gradient-based inversion, and offers a flexible way to incorporate both uncertain prior knowledge and physical modeling process into deterministic inversion. It can help the inversion to skip local minima and achieve fast convergence. The numerical results show that the accuracy and speed of SDM inversion can be enhanced compared with classical gradient-based methods. In addition, the learning ability of this descent learning technique is also validated.