Tensor factorization and its application to multidimensional seismic data recovery

Research in the area of data analytics and recommendation systems have lead to important efforts toward solving the problem of matrix completion. The latter entails estimating the missing elements of a matrix by assuming a low-rank matrix representation. The aforementioned problem can be extended to the recovery of the missing elements of a multilinear array or tensor. Prestack seismic data in midpoint-offset domain can be represented by a 5th order tensor. Therefore, tensor completion methods can be applied to the recovery of unrecorded traces. Furthermore, tensor completion methodologies can also be applied for multidimensional signal-tonoise-ratio enhancement. We discuss the implementation of the Parallel Matrix Factorization (PMF) algorithm, an SVDfree tensor completion method that we applied to 5D seismic data reconstruction. The Parallel Matrix Factorization (PMF) algorithm expands our first generation of 5D tensor completion codes based on High Order SVD and Nuclear norm minimization. We review the PMF method and explore its applicability to processing industrial data sets via tests with synthetic and field data.

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