Statistical Estimation of the Depth of Investigation of ERT and IP Surveys Based on a Modified DOI Index Method

Several techniques are available to estimate the depth of investigation (DOI) or to identify possible artifacts in resistivity and IP surveys. Commonly, the DOI is mainly estimated using an arbitrarily chosen cut-off value on a selected resolution indicator (resolution, sensitivity or DOI index). Small changes in threshold values may induce strong variations in the estimated DOI. To overcome this problem, we developed a new statistical method to estimate the DOI based on a modified DOI index approach. Three inversions are performed using three strongly different resistivity reference models. We found that the cumulative distribution function of the DOI index values is well fitted by the sum of two normal distributions. We then focused on the evaluation of the mean and standard deviation of the normal distribution linked to the statistically well-constrained cells. We introduced two reliability indexes RI2σ and RI3σ based on confidence intervals, respectively 2σ and 3σ. They are used as alpha transparency values when plotting resistivity and chargeability models to discriminate between well- and poorly-constrained cells. The efficiency of the proposed methodology is assessed on synthetic data. Based on synthetic benchmark analysis, we demonstrated that the selected well-constrained cells are well-reconstructed in size, shape and resistivity.