Processing Time-Domain Induced Polarization Data Using Variational Mode Decomposition

Time-domain induced polarization (TDIP) data are often perturbed by undesired electrical and electromagnetic (EM) responses, i.e., powerline harmonics and spikes, which along with the random noise from the instrument mask the measured induced polarization (IP) data. This limits access to the spectral content, which is vital for characterizing the electrical properties of rocks, soil, and minerals in the subsurface. Therefore, mitigating noise responses is key to gaining access to the spectral content. To this end, existing literature assumes prior noise models to deal with the harmonic, spike, and random noises whereby errors in the estimated model parameters can leave residuals, which are significant enough to question the reliability of the inversion results. To address this problem, we employ variational mode decomposition (VMD) that uses a data-driven approach to decompose a TDIP signal into its intrinsic oscillatory modes, i.e., amplitude-modulated frequency-modulated (AM-FM) sinusoids. The optimization-based decomposition framework in VMD dynamically adjusts filtering properties according to the nature of the input TDIP signal. Since IP decays and noise have different spectral properties, we employ a multistage VMD operation to gradually isolate the signal of interest from noise. Through simulations and field examples, we demonstrate that the proposed VMD-based approach enhances the reconstruction of the IP decay and hence improves its inversion and interpretation.