Time-domain induced polarization - an analysis of Cole-Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion

Line Meldgaard Madsen, Gianluca Fiandaca, Esben Auken, Anders Vest Christiansen

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)

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, t, 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.

Original languageEnglish
Pages (from-to)1341-1353
Number of pages13
JournalGeophysical Journal International
Volume211
Issue number3
DOIs
Publication statusPublished - 1 Dec 2017
Externally publishedYes

Keywords

  • Electrical properties
  • Inverse theory
  • Probability distributions

Programme Area

  • Programme Area 2: Water Resources

Fingerprint

Dive into the research topics of 'Time-domain induced polarization - an analysis of Cole-Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion'. Together they form a unique fingerprint.

Cite this