Ultra-broad-band electrical spectroscopy of soils and sediments—a combined permittivity and conductivity model

Abstract

We combined two completely different methods measuring the frequency-dependent electrical properties of moist porous materials in order to receive an extraordinary large frequency spectrum. In the low-frequency (LF) range, complex electrical resistivity between 1 mHz and 45 kHz was measured for three different soils and sandstone, using the spectral induced polarization (SIP) method with a four electrode cell. In the high-frequency (HF) radio to microwave range, complex dielectric permittivity was measured between 1MHz and 10 GHz for the same samples using dielectric spectroscopy by means of the coaxial transmission line technique. The combined data sets cover 13 orders of magnitude and were transferred into their equivalent expressions: the complex effective dielectric permittivity and the complex effective electrical conductivity.We applied the Kramers-Kronig relation in order to justify the validity of the data combination. A new phenomenological model that consists of both dielectric permittivity and electrical conductivity terms in a Debye- and Cole–Cole-type manner was fitted to the spectra. The combined permittivity and conductivity model accounts for the most common representations of the physical quantities with respect to the individual measuring method. A maximum number of four relaxation processes was identified in the analysed frequency range. Among these are the free water and different interfacial relaxation processes, the Maxwell-Wagner effect, the counterion relaxation in the electrical double layer and the direct-current electrical conductivity. There is evidence that free water relaxation does not affect the electrical response in the SIP range. Moreover, direct current conductivity contribution (bulk and interface) dominates the losses in the HF range. Interfacial relaxation processes with relaxations in the HF range are broadly distributed down to the LF range. The slowest observed process in the LF range has a minor contribution to the HF response.