Debye decomposition of time-lapse spectral induced polarisation data

Spectral induced polarisation (SIP) measurements capture the low-frequency electrical properties of soils and rocks and provide a non-invasive means to access lithological, hydrogeological, and geochemical properties of the subsurface. The Debye decomposition (DD) approach is now increasingly being used to analyse SIP signatures in terms of relaxation time distributions due to its flexibility regarding the shape of the spectra. Imaging and time-lapse (monitoring) SIP measurements, capturing SIP variations in space and time, respectively, are now more and more conducted and lead to a drastic increase in the number of spectra considered, which prompts the need for robust and reliable DD tools to extract quantitative parameters from such data. We here present an implementation of the DD method for the analysis of a series of SIP data sets which are expected to only smoothly change in terms of spectral behaviour, such as encountered in many time-lapse applications where measurement geometry does not change. The routine is based on a non-linear least-squares inversion scheme with smoothness constraints on the spectral variation and in addition from one spectrum of the series to the next to deal with the inherent ill-posedness and non-uniqueness of the problem. By means of synthetic examples with typical SIP characteristics we elucidate the influence of the number and range of considered relaxation times on the inversion results. The source code of the presented routines is provided under an open source licence as a basis for further applications and developments.