Abstract
Clay minerals show a distinct induced-polarization phenomenon, which is one of the most important factors for predicting groundwater flow and contaminant transport. This paper presents a step-by-step process to estimate Cole-Cole parameters from spectral induced-polarization (IP) data measured on the surface of three-dimensional earth. First, the inversion of low-frequency resistivity survey data is made to identify the dc resistivity ${\rho}_dc$ of a volume having IP effects. The other parameters, chargeability m, time constant $\tau$, and frequency dependence c, are sought for the polarizable volume. Next, using multi-frequency data, c can be obtained as high or low asymptotes of the slope of log phase vs. log frequency. Further, for low m, intrinsic $\tau$ is approximated by apparent one, ${\tau}_a$, which is derived from the relation ${{\omega}{\tau}}_a$=1 at an angular frequency $\omega$, where the imaginary component of spectral IP data has an extreme value. Finally, to obtain intrinsic m a two-step linearized procedure has been derived. For a body of given $\tau$ and c, forward modeling with a progression of m values yields a plot of observed vs. intrinsic imaginary components for a frequency. Since this plot is essentially linear, to extract the intrinsic imaginary component is quite simple with an observed value. Using the plot of intrinsic imaginary component vs. m, intrinsic m is determined. We present a synthetic example to illustrate that the Cole-Cole parameters can be recovered from spectral IP data.