We have derived a reasonably accurate expression for the apparent spectral induced polarization (SIP) response of an arbitrary number of polarizable objects. The expression set a logical ground to the recently popularized Debye decomposition technique and provided a physical basis to phenomenological induced polarization models, such as Cole-Cole and others. For data complying with the Cole-Cole type of relaxation, the most important SIP parameters are the frequency dependence and time constant because they carry information about the grain size distribution and the mean grain size in a polarizable object. We have determined a simple method to rapidly estimate these parameters from characteristic features of a measured phase curve, such as the location of its peak frequency and maximum value of its derivative on a log-log plot. We tested the approach on a synthetic 2D example and field data, representing a multifrequency vertical electrical sounding carried out over a known sedimentary section with three differently polarizable layers. In both cases, the proposed technique yielded reasonably good results.

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