Multicomponent sensor arrays now are commonly used in seismic acquisition to record polarized waves. In this article, we use a three-mode model (polarization mode, distance mode, and temporal mode) to take into account the specific structure of signals that are recorded with these arrays, providing a data-structure-preserving processing. With the suggested model, we propose a multilinear decomposition named higher-order singular value decomposition and unimodal independent component analysis (HOSVD/unimodal ICA) to split the recorded three-mode data into two orthogonal subspaces: the signal and noise subspaces. This decomposition allows the separation and identification of polarized waves with infinite apparent horizontal propagation velocity. The HOSVD leads to a definition of a subspace method that is the counterpart of the well-known subspace method for matrices that is driven by singular value decomposition (SVD), a classic tool in monocomponent array processing.
The proposed three-mode subspace decomposition provides a multicomponent wave-separation algorithm. To enhance the separation result, when the signal-to-noise ratio is low or when orthogonality constraints are not well adapted to the recorded waves, a unimodal-ICA step is included on the temporal mode. Doing this replaces the classic orthogonality constraints between estimated waves with independence constraints that might allow better recovery of recorded seismic waves. A simulation on realistic two-component (2C) geophysical data shows qualitative and quantitative improvements for the wavefield-separation results. The relative-mean-square errors between the original and estimated signal subspaces are, respectively, 52% for SVD applied on each component separately, 27.4% for HOSVD-based technique applied to the whole three-mode dataset, and 7.3% for HOSVD/unimodal-ICA technique. The efficiency of the three-mode subspace decompositions also is shown on real three-component (3C) geophysical data. These results emphasize the potential of the HOSVD/unimodal-ICA subspace method for multicomponent seismic-wave separation.