On the use of the Cole–Cole equations in spectral induced polarization

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Abstract
Two different equations, both of which are often called ‘the Cole–Cole equation’, are widely used to fit experimental Spectral Induced Polarization data. The data are compared on the basis of fitting model parameters: the chargeability, the time constant and the exponent. The difference between the above two equations (the Cole–Cole equation proposed by the Cole brothers and Pelton's equation) is manifested in one of the fitting parameters, the time constant. The Cole–Cole time constant is an inverse of the peak angular frequency of the imaginary conductivity, while Pelton's time constant depends on the chargeability and exponent values. The difference between the time constant values corresponding to the above two equations grows with the increase of the chargeability value, and with the decrease of the Cole–Cole exponent value. This issue must be taken into consideration when comparing the experimental data sets for high polarizability media presented in terms of the Cole–Cole parameters.

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