A Sparse Spike Deconvolution Algorithm Based on a Recurrent Neural Network and the Iterative Shrinkage-Thresholding Algorithm

Conventional sparse spike deconvolution algorithms that are based on the iterative shrinkage-thresholding algorithm (ISTA) are widely used. The aim of this type of algorithm is to obtain accurate seismic wavelets. When this is not fulfilled, the processing stops being optimum. Using a recurrent neural network (RNN) as deep learning method and applying backpropagation to ISTA, we have developed an RNN-like ISTA as an alternative sparse spike deconvolution algorithm. The algorithm is tested with both synthetic and real seismic data. The algorithm first builds a training dataset from existing well-logs seismic data and then extracts wavelets from those seismic data for further processing. Based on the extracted wavelets, the new method uses ISTA to calculate the reflection coefficients. Next, inspired by the backpropagation through time (BPTT) algorithm, backward error correction is performed on the wavelets while using the errors between the calculated reflection coefficients and the reflection coefficients corresponding to the training dataset. Finally, after performing backward correction over multiple iterations, a set of acceptable seismic wavelets is obtained, which is then used to deduce the sequence of reflection coefficients of the real data. The new algorithm improves the accuracy of the deconvolution results by reducing the effect of wrong seismic wavelets that are given by conventional ISTA. In this study, we account for the mechanism and the derivation of the proposed algorithm, and verify its effectiveness through experimentation using theoretical and real data.