We have developed a novel framework for combining physics-based forward models and neural networks to advance seismic processing and inversion algorithms. Migration is an effective tool in seismic data processing and imaging. Over the years, the scope of these algorithms has broadened; today, migration is a central step in the seismic data processing workflow. However, no single migration technique is suitable for all kinds of data and all styles of acquisition. There is always a compromise on the accuracy, cost, and flexibility of these algorithms. On the other hand, machine-learning algorithms and artificial intelligence methods have been found immensely successful in applications in which big data are available. The applicability of these algorithms is being extensively investigated in scientific disciplines such as exploration geophysics with the goal of reducing exploration and development costs. In this context, we have used a special kind of unsupervised recurrent neural network and its variants, Hopfield neural networks and the Boltzmann machine, to solve the problems of Kirchhoff and reverse time migrations. We use the network to migrate seismic data in a least-squares sense using simulated annealing to globally optimize the cost function of the neural network. The weights and biases of the neural network are derived from the physics-based forward models that are used to generate seismic data. The optimal configuration of the neural network after training corresponds to the minimum energy of the network and thus gives the reflectivity solution of the migration problem. Using synthetic examples, we determine that (1) Hopfield neural networks are fast and efficient and (2) they provide reflectivity images with mitigated migration artifacts and improved spatial resolution. Specifically, the presented approach minimizes the artifacts that arise from limited aperture, low subsurface illumination, coarse sampling, and gaps in the data.

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