Application of machine learning for the extrapolation of seismic data

Low frequencies in seismic data are often challenging to acquire. Without low frequencies, though, a method like full-waveform inversion might fail due to cycle-skipping. This thesis aims to investigate the potential of neural networks for the task of low-frequency extrapolation to overcome aforementioned problem. Several steps are needed to achieve this goal: First, suitable data for training and testing the network must be found. Second, the data must be pre-processed to condition them for machine learning and efficient application. Third, a specific workflow for the task of low-frequency extrapolation must be designed. Finally, the trained network can be applied to data it has not seen before and compared to reference data. In this work, synthetic data are used for training and evaluation because in such a controlled experiment the target for the network is known. For this purpose, 30 random but geologically plausible subsurface models were generated based on a simplified geology around the Asse II salt mine, and used for finite-difference simulations of seismograms. The corresponding shot gathers were pre-processed by, among others, normalizing them and splitting them up into patches, and fed into a convolutional neural network (U-Net) to assess the network’s performance and its ability to reconstruct the data. ... mehrTwo different approaches were investigated for the task of low-frequency extrapolation. The first approach is based on using only low frequencies as the network’s target, while the second approach has the full bandwidth as target. The latter yielded superior results and was therefore chosen for subsequent applications. Further tests of the network design led to the introduction of ResNet blocks instead of simple convolutions in the U-Net layers, and the use of the mean-absolute-error instead of the mean-squared-error loss function. The final network designed in this way was then applied to the synthetic data originally reserved for testing. It turned out that the chosen method is able to successfully extrapolate low frequencies by more than half an octave (from about 8 to 5 Hz) given the experimental setup at hand. Although the results start to deteriorate in the low-frequency band for larger offsets, full-waveform inversion will overall benefit from the application of the presented machine learning approach.