We investigate the problem of determination of the volumetric ratio between the two components of a heterogeneous mixture with unknown internal structure. If both resistivity and permittivity of one component are known to be much higher than those of the other within a sufficiently wide frequency range, the volumetric ratio may be roughly estimated from measured electromagnetic response of the mixture by making use of the variational approach. Otherwise, such estimation requires the exact knowledge of the inherent electrical properties of the mixed materials and application of some universal mixing model, such as the weighted power mean formula.The high-frequency induced polarization measurements are strongly influenced by the presence of ice inclusions in an investigated rock formation, which is commonly used for mapping of frozen ground within the permafrost regions. We show that for sedimentary rocks with low clay content, it is also possible to roughly estimate the ice concentration from broadband induced polarization data by using the two-component, weighted power mean model, which is confirmed by a lab experiment on a frozen core sample with known ice content.

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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Application of the dispersion relations (DR) in magnetotellurics (MT) is an efficient tool of post-processing and quality assessment of broadband field data. The main limitation of the approach is that it requires the observed transfer functions to be causal and minimum-phase (MP), which is formally secured only for 1-D and some types of 2-D impedances. As a consequence, many MT practitioners involuntarily restrict the DR application to apparent resistivity curves acquired in relatively simple geological conditions. In the present research, we show how an inherently non-MP or non-causal transfer function could be recognized, and propose a universal technique, which makes it possible to correctly apply the DR virtually to any set of field MT data.