Nonhyperbolic normal moveout stretch correction with deep learning automation
Normal-moveout (NMO) correction is a fundamental step in seismic data processing. It consists of mapping seismic data from recorded traveltimes to corresponding zero-offset times. This process produces wavelet stretching as an undesired by-product. We have addressed the NMO stretching problem with two methods: (1) an exact stretch-free NMO correction that prevents the stretching of primary reflections and (2) an approximate post-NMO stretch correction. Our stretch-free NMO produces parallel moveout trajectories for primary reflections. Our post-NMO stretch correction calculates the moveout of stretched wavelets as a function of offset. Both methods are based on the generalized moveout approximation and are suitable for application in complex anisotropic or heterogeneous environments. We use new moveout equations, modify the original parameter functions to be a constant over the primary reflections, and then interpolate the seismogram amplitudes at the calculated traveltimes. For fast and automatic modification of the parameter functions, we use deep learning. We design a deep neural network (DNN) using convolutional layers and residual blocks. To train the DNN, we generate a set of 40,000 synthetic NMO-corrected common-midpoint gathers and the corresponding desired outputs of the DNN. The data set is generated using different velocity profiles, wavelets, and offset vectors, and it includes multiples, ground roll, and band-limited random noise. The simplicity of the DNN task - a 1D identification of primary reflections - improves the generalization in practice. We use the trained DNN and find successful applications of our stretch-correction method on synthetic and different real data sets.