Research on linear inversion of SIP using the Debye decomposition method

Abstract

Spectral-induced polarization data can provide information regarding the polarization properties of underground media. The characteristic relaxation time of polarized media is related in part to the composition of rocks and minerals and porosity. Therefore, the spectral-induced polarization method is widely used to obtain underground lithology/structure, hydrogeology, and geochemical data. Because the Debye decomposition method can flexibly fit the spectrum shape, it is being increasingly used to analyze the relaxation time distribution of spectral-induced polarization (SIP) signals. In this study, the Debye decomposition method was used to directly invert the relaxation time distribution curve from SIP data to extract the characteristic relaxation time of the target. First, we discuss the Debye decomposition method in terms of its physical principle and show the relationship between the multi-Cole–Cole model and Debye decomposition through a numerical simulation. We then used the linear inversion method to invert the synthetic and measured data based on the Debye decomposition parameterization and verify the effectiveness of the inversion. Compared with the numerical simulations of several models, we proved that the parameters of the Cole–Cole model are strongly correlated. Additionally, the inversion results show that the linear inversion method is suitable for inverting the Debye decomposition and that expanding the range of the relaxation time in the Debye decomposition can effectively alleviate the influence of the truncation error on inversion.