Using the stretched exponential function for automatic processing of time-domain induced polarization data and further interpretation

SUMMARY Time-domain induced polarization (TDIP) data carry spectral information that can be used for petrophysical interpretation. At the same time, TDIP data can be collected in the field more efficiently than frequency-domain induced polarization (FDIP) data, thanks to the use of square-wave signals. However, TDIP field data are prone to noise, particularly strong near industrial installations and urban areas, above conductive media and in cases where little current is injected. The integral chargeability is a useful parameter to smoothen out the signal but it precludes any spectral interpretation. Debye decomposition (DD) is recognized as one of the best methods for spectral interpretation but the extracted parameters are particularly affected by data noise. More generally, processing TDIP data before further analysis, such as inversion or spectral analysis, is usually necessary for any quantitative interpretation. We propose here an automatic processing algorithm, based on the Kohlrausch–Williams–Watts (KWW) function, which is very close to the Havriliak-Negami model in frequency-domain, that fulfills this need. The processing is completed by an empirical handling of early-time electromagnetic coupling effects to improve the overall performance. The resulting procedure, tested and validated on three data sets that cover a large range of contexts, electrode configurations and acquisition settings, is available as open-source MATLAB scripts. The proposed approach is especially useful for further extracting spectral information from TDIP data through DD. Thanks to the theoretical framework offered by the KWW function, the behaviour of the integral chargeability could be investigated in a systematic manner, using both synthetic and field TDIP data. Recommendations could be formulated on how to make use of the spectral information, while keeping the automatic processing transparent and accessible to unexperienced users. This work advances the use of TDIP in the field of environmental geophysics.