Maximilian Weigand and Andreas Kemna (2015)
Debye decomposition of time-lapse spectral induced polarisation data
Computers & Geosciences, 86:34–45.
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.