De-migration-based supervised learning for interpolation and regularization of 3D offset classes

Regularization and interpolation of 3D offset classes prior to imaging are an important and challenging step in the marine seismic data processing flow. Here we describe how to perform this task using a deep neural network, and we explain how to overcome the challenge of creating a suitable training data set. The training data set is generated by de-migrating stacked pre-stack depth migration images. For each offset class volume, we de-migrate the pre-stack depth migrated stacked image into two configurations: (i) the original survey configuration consisting of the recorded source/receiver positions and (ii) an 'Ideal' survey configuration with constant offset and azimuth for each 3D offset class. The training creates a 3D convolutional encoder-decoder model that will regularize and interpolate seismic data. The convolutional encoder-decoder is trained on 3D sliding windows in each 3D offset cube to map from (i) to (ii), i.e. to map the original survey configuration with irregular and sparse sampling into the fully sampled regular offset cubes suitable for offset-based migration, such as Kirchhoff migration. Such migration algorithms rely on regular and sufficiently dense sampling to achieve constructive interference to image the structures and destructive interference to suppress migration noise. We test the new method on one synthetic and one field data example and show that it performs better than a standard regularization/interpolation method based on anti-leakage Fourier transform, especially for the smallest offset classes. On the synthetic data, we also demonstrate that the convolutional encoder-decoder method preserves the amplitude versus offset as well as the standard method.