Reconstruction quality of SIP parameters in multi-frequency complex resistivity imaging
Complex resistivity imaging provides information on the subsurface distribution of the electrical conduction and polarisation properties. Spectral induced polarisation (SIP) refers to the frequency dependence of these complex resistivity values. Measured SIP signatures are commonly analysed by performing a Cole–Cole model fit or a Debye decomposition, yielding in particular chargeability and relaxation time values. Given the close relation of these parameters with petrophysical properties of relevance in various hydrogeological and environmental applications, it is crucial to understand how well they can be reconstructed from multi-frequency complex resistivity imaging with subsequent Cole–Cole or Debye decomposition analysis. In this work, we investigate, in a series of numerical simulations, the reconstruction behaviour of the main spectral induced polarisation parameters across a two-dimensional complex resistivity imaging plane by considering a local anomalous polarisable body at different depths. The different anomaly positions correspond to different cumulated sensitivity (coverage) values, which we find to be a simple and computationally inexpensive proxy for resolution. Our results show that, for single-frequency measurements, the reconstruction quality of resistivity and phase decreases strongly with decreasing cumulated sensitivity. A similar behaviour is found for the recovery of Cole–Cole and Debye decomposition chargeabilities from multi-frequency imaging results, while the reconstruction of the Cole–Cole exponent shows non-uniform dependence over the examined sensitivity range. In contrast, the Cole–Cole and Debye decomposition relaxation times are relatively well recovered over a broad sensitivity range. Our results suggest that a quantitative interpretation of petrophysical properties derived from Cole– Cole or Debye decomposition relaxation times is possible in an imaging framework, while any parameter estimate derived from Cole–Cole or Debye decomposition chargeabilities must be used with caution. These findings are of great importance for a successful quantitative application of spectral induced polarisation imaging for improved subsurface characterisation, which is of interest particularly in the fields of hydrogeophysics and biogeophysics.