Mitigation of numerical dispersion in seismic data in spectral domain with neural networks

Seismic modeling has various engineering applications, including exploration seismology, seismic monitoring of greenhouse gas sequestration, and earthquake engineering. However, it is computationally demanding if conventional grid-based methods are used due to the mathematical restrictions on the grid size. This research presents an approach combining conventional grid-based seismic modeling with machine learning, where the solution is simulated using a coarse grid with high numerical error. Then, it is corrected by the numerical dispersion mitigation neural network (NDM-net). Previously, the NDM-net was applied to the simulated seismic data in the time domain, where either large datasets are treated, leading to increased training time and memory usage, or the patches are constructed, leading to accuracy reduction. This paper focuses on applying the NDM-net in the frequency domain, where only low frequencies of about 10% to 30% of spectra are used. It is possible due to the band-limited nature of the source’s impulse. Thus, the frequency domain NDM-net allows for preserving the original NDM-net’s high accuracy with reduced computational resources and time demand, improving the NDM-net performance and making it applicable to large-scale 3D problems. We illustrate the applicability of the suggested approach on three velocity models representing completely different geological environments where NDM-net allows to speed up seismic modeling by a factor of 2.5 to 4 in comparison to fine-grid modeling.