GPR Energy Attribute Slices Based on Multivariate Variational Mode Decomposition and Teager–Kaiser Energy Operator

Abstract

The GPR signals appear nonlinear and nonstationary during propagation. To evaluate the nonstationarity, the empirical mode decomposition (EMD) and its modifications have been proposed to localize the variations of energy and frequency components over time. Among the EMD−based algorithms, the variational mode decomposition (VMD) is one of the representative methods. It eliminates the drawbacks of EMD, to some extent, but is still executed in one dimension. In this work, the multivariate variational mode decomposition (MVMD) algorithm is introduced for decomposing the GPR B-scans into several IMF-slices in two dimensions, which inherits the advantages of the VMD and considers the stratigraphic constraints. Then, by applying the Teager–Kaiser energy operator (TKEO) within each IMF-slice, a novel energy attribute is formed and termed as the “TKEO-slices”. The proposed TKEO-slices can localize the energy attribute of geophysical information of different scales with good stratigraphic continuity. The proposed scheme is evaluated by the synthetic benchmark, model data, and field data. Compared with the VMD−based scheme and the classic instantaneous amplitude, the proposed TKEO-slices show better resolution and lateral continuity