Least-squares reverse time migration via deep learning-based updating operators

Abstract

Two common issues of least-squares reverse time migration (LSRTM) consist of the many iterations required to produce substantial subsurface imaging improvements and the difficulty of choosing adequate regularization strategies with optimal hyperparameters. We investigate how supervised learning can mitigate these shortcomings by solving the LSRTM problem through an iterative deep learning framework inspired by the projected gradient descent algorithm. In particular, we develop an image-to-image approach interlacing the gradient steps at each iteration with blocks of residual convolutional neural networks (CNNs) that capture the prior information in the training phase. By including the least-squares data-misfit gradient into the learning process, we force the solution to comply with the observed seismic data, while the CNN projections implicitly account for the regularization effects that lead to high-resolution reflectivity updates. After training with 900 randomly generated instances, our network ensemble can estimate accurate reflectivity distributions in only a few iterations. To demonstrate the effectiveness and generalization properties of the method, we consider three synthetic cases: a folded and faulted model, the Marmousi model, and the Sigsbee2a model. We empirically find that it is possible to obtain an improved reflectivity model for out-of-distribution instances by using the learned reconstructions as warm starts for the conjugate gradient algorithm and bridging the gap between the learned and conventional LSRTM schemes. Finally, we apply the proposed network with transfer learning on a 2D towed-streamer Gulf of Mexico field data set, producing high-resolution images comparable with traditional LSRTM but drastically reducing the required number of iterations.