| Abstract: | Theoretical model study shows that when an earth model is composed of two (Cole-Cole) polarizable media, its normalized complex resistivity spectrum is approximately a multiplicative combination of the contributions of the two media. This also applies on inversion, but the two dispersions thus obtained are apparent rather than intrinsic dispersions. In models consisting of two media, either a multiplicative or an additive combination of Cole-Cole functions fits the complex apparent resistivity spectrum. On inversion each combination gives similar parameters except for the apparent chargeability of the component with the shorter time constant. However, this can be compensated simply. In this sense the two representations are almost equivalent. We show that the apparent spectrum due to a finite polarizable body is actually a true Cole-Cole dispersion, as is usually assumed in practice. The behavior of a complex apparent resistivity spectrum and its corresponding apparent Cole-Cole dispersion parameters is influenced by the variation of the dilution factor with frequency. Hence when estimating intrinsic parameters from the nomogram, based on constant (frequency-independent) dilution factors, particular care is required to correctly relate apparent parameters to intrinsic parameters. |
