Time-domain induced polarization – an analysis of Cole–Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion. Issue 3 (22nd August 2017) - Madsen, Line Meldgaard; Fiandaca, Gianluca; Auken, Esben; Christiansen, Anders Vest
Abstract: The application of time-domain induced polarization (TDIP) is increasing with advances in acquisition techniques, data processing and spectral inversion schemes. An inversion of TDIP data for the spectral Cole–Cole parameters is a non-linear problem, but by applying a 1-D Markov Chain Monte Carlo (MCMC) inversion algorithm, a full non-linear uncertainty analysis of the parameters and the parameter correlations can be accessed. This is essential to understand to what degree the spectral Cole–Cole parameters can be resolved from TDIP data. MCMC inversions of synthetic TDIP data, which show bell-shaped probability distributions with a single maximum, show that the Cole–Cole parameters can be resolved from TDIP data if an acquisition range above two decades in time is applied. Linear correlations between the Cole–Cole parameters are observed and by decreasing the acquisitions ranges, the correlations increase and become non-linear. It is further investigated how waveform and parameter values influence the resolution of the Cole–Cole parameters. A limiting factor is the value of the frequency exponent, C . As C decreases, the resolution of all the Cole–Cole parameters decreases and the results become increasingly non-linear. While the values of the time constant, τ, must be in the acquisition range to resolve the parameters well, the choice between a 50 per cent and a 100 per cent duty cycle for the current injection does not have an influence on the parameter resolution. The limits of resolution and linearity are also studied in a comparison between the MCMC and a linearized gradient-based inversion approach. The two methods are consistent for resolved models, but the linearized approach tends to underestimate the uncertainties for poorly resolved parameters due to the corresponding non-linear features. Finally, an MCMC inversion of 1-D field data verifies that spectral Cole–Cole parameters can also be resolved from TD field measurements.