Robust high frequency seismic bandwidth extension with a deep neural network trained using synthetic data

Geophysicists interpreting seismic reflection data aim for the highest resolution possible as this facilitates the interpretation and discrimination of subtle geological features. Various deterministic methods based on Wiener filtering exist to increase the temporal frequency bandwidth and compress the seismic wavelet in a process called spectral shaping. Auto-encoder neural networks with convolutional layers have been applied to this problem, with encouraging results, but the problem of generalization to unseen data remains. Most published works have used supervised learning with training data constructed from field seismic data or synthetic seismic data generated based on measured well logs or based on seismic wavefield modelling. This leads to satisfactory results on datasets similar to the training data but requires re-training of the networks for unseen data with different characteristics. In this work seek to improve the generalization, not by experimenting with network architecture (we use a conventional U-net with some small modifications), but by adopting a different approach to creating the training data for the supervised learning process. Although the network is important, at this stage of development we see more improvement in prediction results by altering the design of the training data than by architectural changes. The approach we take is to create synthetic training data consisting of simple geometric shapes convolved with a seismic wavelet. We created a very diverse training dataset consisting of 9000 seismic images with between 5 and 300 seismic events resembling seismic reflections that have geophysically motived perturbations in terms of shape and character. The 2D U-net we have trained can boost robustly and recursively the dominant frequency by 50%. We demonstrate this on unseen field data with different bandwidths and signal-to-noise ratios. Additionally, this 2D U-net can handle non-stationary wavelets and overlapping events of different bandwidth without creating excessive ringing. It is also robust in the presence of noise. The significance of this result is that it simplifies the effort of bandwidth extension and demonstrates the usefulness of auto-encoder neural network for geophysical data processing.