Parallel matrix factorization algorithm and its application to 5D seismic reconstruction and denoising

Tensors, also called multilinear arrays, have been receiving attention from the seismic processing community. Tensors permit us to generalize processing methodologies to multidimensional structures that depend on more than 2D. Recent studies on seismic data reconstruction via tensor completion have led to new and interesting results. For instance, fully sampled noise-free multidimensional seismic data can be represented by a low-rank tensor. Missing traces and random noise increase the rank of the tensor. Hence, multidimensional prestack seismic data denoising and reconstruction can be tackled with tools that have been studied in the field of tensor completion. We have investigated and applied the recently proposed parallel matrix factorization (PMF) method to solve the 5D seismic data reconstruction problem. We have evaluated the efficiency of the PMF method in comparison with our previously reported algorithms that used singular value decomposition to solve the tensor completion problem for prestack seismic data. We examined the performance of PMF with synthetic data sets and with a field data set from a heavy oil survey in the Western Canadian Sedimentary Basin.