Estimating normal moveout velocity using the recurrent neural network

Machine learning (ML) has recently gained immense popularity because of its successful application in complex problems. It develops an abstract relation between the input and output. We have evaluated the application of ML to the most basic seismic processing of normal moveout (NMO) correction. The arrival times of reflection events in a common midpoint (CMP) gather follow a hyperbolic trajectory; thus, they require a correction term to flatten the CMP gather before stacking. This correction term depends on an rms velocity, also referred to as the NMO velocity. In general, NMO velocity is estimated using the semblance measures and picking the peaks in the velocity panel. This process requires a lot of human intervention and computation time. We have developed a novel method using one of the tools based on an ML- approach and applied to the NMO velocity estimation problem. We use the recurrent neural network (RNN) to estimate the NMO velocity directly from the seismic data. The input to the network is a seismic gather and corresponding precalculated NMO velocity (as prelabeled data set) to flatten the gather. We first train the network to develop a relationship between the input gathers (before NMO correction) and the corresponding NMO velocities for a few CMPs as a supervised learning process. Adam optimization algorithm is used to train the RNN. The output from the network is then compared against the correct NMO velocity. The error between the two velocities is then used to update the weight of the neurons and to minimize the mean-squared error between the two velocities. After the network is trained, it can be used to calculate the NMO velocity for the rest of the seismic gathers. We evaluate our method on a noisy data set from Poland. We used only 10% of the CMPs to train the network, and then we used the trained network to predict NMO velocity for the remaining CMP locations. The stack section obtained by using RNN-generated NMO velocities is nearly identical to that obtained by the conventional semblance method.