Rank-constrained Multidimensional Reconstruction of Seismic Data

Abstract

Our ability to generate accurate images of the Earth interior relies on three steps: data acquisition, data preconditioning, and imaging/inversion. Imaging and inversion methods adopt mathematical physics principles associated with wave propagation phenomena to transform the seismic observations acquired on the surface of the Earth subsurface images. Preconditioning techniques aim to remove coherent and incoherent noise, equalize the energy of the source, and solve problems resulting from inadequate data acquisition. This thesis focuses on developing data preconditioning methods for multidimensional seismic volumes. I propose new data completion algorithms based on reduced-rank filtering for matrices and multilinear arrays (tensors). These techniques execute signal enhancement and data reconstruction simultaneously. My research explores unsolved questions of reduced-rank reconstruction methods, including alleviating irregular data sampling and reconstructing data contaminated with outliers. To provide solutions to these questions, I propose two new algorithms. The first algorithm, based on the Multichannel Singular Spectrum Analysis (MSSA) algorithm, is named Interpolated MSSA (I-MSSA). Unlike classical MSSA methods, I-MSSA can honour true spatial coordinates of an irregularly sampled dataset. The second algorithm reconstructs five-dimensional seismic volumes based on robust tensor completion principles. To do so, I explore robust loss functions that attenuate the influence of outliers in the reconstruction.