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 (CNN) 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 nine hundred 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 show 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, bridging the gap between 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 to traditional LSRTM but drastically reducing the required number of iterations.

Sensing prior constraints in deep neural networks for solving exploration geophysical problems

“…Various DNN models, trained by synthetic datasets, have been successfully applied to solve multiple geophysical problems including seismic denoising ( 7 , 22 , 72 , 73 ), seismic migration ( 36 , 40 ), velocity model building ( 25 , 29 , 42 , 43 , 45 , 74 , 75 ), impedance inversion ( 62 , 76 ), and seismic interpretation ( 52 , 71 , 77 , 78 ). As shown in Fig.…”

“…During the past decade, DNNs have been widely used in various geophysical research areas ( 1 – 5 ), including seismology ( 6 – 14 ), atmospheric science ( 15 – 17 ), and planetary and space science ( 18 – 20 ). DNNs have been particularly intensively studied in exploration of geophysics to accelerate and advance the entire workflow of data processing ( 21 – 24 ), tomography ( 25 – 29 ), forward modeling ( 30 – 35 ), migration ( 36 – 40 ), velocity model building ( 41 – 47 ), and interpretation ( 48 – 53 ).…”

Deep decomposition learning for reflectivity inversion

“…Instead of using 1D models and noisy traces, the networks were trained with synthetically generated 2D reflectivity models and their corresponding noisy data slices to improve lateral continuity and robustness to noise. We follow Torres and Sacchi (2022a) to generate synthetic reflectivity models (as shown in Figure 5) considering the spatial correlation imposed by depositional processes while mimicking fractured, faulted and folded sedimentary structures that can take arbitrary shapes and orientations. The training samples reflect that physical, nonrandom processes produce the earth's geology, and subsurface layers can have many arbitrary orientations, including sharp discontinuities.…”

“…Such networks bypass the use of explicit physics operators but rely on a vast amount of training samples to learn the underlying physics of the problem. To reduce the dependency on training data, learned iterative schemes (Torres & Sacchi, 2022a) incorporate physics into the learning process and replace various components of unrolled iterative reconstruction algorithms with neural network computations. Alternatively, to avoid iterations, the learned post‐processing method first maps the measurements to the model space through a known physics operator (either the pseudo‐inverse $$\mathbf {L}^\dagger : \mathbb {R}^m\rightarrow \mathbb {R}^n$$ or an approximation to it) and then trains a neural network to learn a model perturbation that potentially improves this initial reconstruction (Kaur et al., 2020; Zhang et al., 2021).…”

Convolutional Neural-Network-Based Reverse-Time Migration with Multiple Reflections

“…[30] also used CNNs on dip-angle domain elastic reverse-time migration to improve image quality; Ref. [31] introduced the idea on minibatch LSRTM, and Torres and Sacchi [32,33] used blocks of residual CNN on LSRTM with a preconditioned conjugate gradient least-squares algorithm (CGLS) to enhance image resolution; Ref. [34] used deep learning for accelerating prestack correlative LSRTM.…”