Accurate forward modeling is essential for solving inverse problems in exploration seismology. Unfortunately, it is often not possible to afford being physically or numerically accurate. To overcome this conundrum, we make use of raw and processed data from nearby surveys. We have used these data, consisting of shot records or velocity models, to pretrain a neural network to correct for the effects of, for instance, the free surface or numerical dispersion, both of which can be considered as proxies for incomplete or inaccurate physics. Given this pretrained neural network, we apply transfer learning to fine-tune this pretrained neural network so it performs well on its task of mapping low-cost, but low-fidelity, solutions to high-fidelity solutions for the current survey. As long as we can limit ourselves during fine-tuning to using only a small fraction of high-fidelity data, we gain processing the current survey while using information from nearby surveys. We examined this principle by removing surface-related multiples and ghosts from shot records and the effects of numerical dispersion from migrated images and wave simulations.

A main challenge in seismic imaging is acquiring densely sampled data. Compressed Sensing has provided theoretical foundations upon which desired sampling rate can be achieved by applying a sparsity promoting algorithm on sub-sampled data. The key point in successful recovery is to deploy a randomized sampling scheme. In this paper, we propose a novel deep learning-based method for fast and accurate reconstruction of heavily under-sampled seismic data, regardless of type of sampling. A neural network learns to do reconstruction directly from data via an adversarial process. Once trained, the reconstruction can be done by just feeding the frequency slice with missing data into the neural network. This adaptive nonlinear model makes the algorithm extremely flexible, applicable to data with arbitrarily type of sampling. With the assumption that we have access to training data, the quality of reconstructed slice is superior even for extremely low sampling rate (as low as 10%) due to the data-driven nature of the method.

We propose a 'learned' iterative solver for the Helmholtz equation, by combining traditional Krylov-based solvers with machine learning. The method is, in principle, able to circumvent the shortcomings of classical iterative solvers, and has clear advantages over purely data-driven approaches. We demonstrate the effectiveness of this approach under a 1.5-D assumption, when adequate a priori information about the velocity distribution is known.

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