A modified DOI-based method to statistically estimate the depth of investigation of dc resistivity surveys

Several techniques are available to estimate the depth of investigation or to identify possible artifacts in dc resistivity surveys. Commonly, the depth of investigation (DOI) is mainly estimated by using an arbitrarily chosen cut-off value on a selected indicator (resolution, sensitivity or DOI index). Ranges of cut-off values are recommended in the literature for the different indicators. However, small changes in threshold values may induce strong variations in the estimated depths of investigation. To overcome this problem, we developed a new statistical method to estimate the DOI of dc resistivity surveys based on a modified DOI index approach. This method is composed of 5 successive steps. First, two inversions are performed by using different resistivity reference models for the inversion (0.1 and 10 times the arithmetic mean of the logarithm of the observed apparent resistivity values). Inversion models are extended to the edges of the survey line and to a depth range of three times the pseudodepth of investigation of the largest array spacing used. In step 2, we compute the histogram of a newly defined scaled DOI index. Step 3 consists of the fitting of the mixture of two Gaussian distributions (G1 and G2) to the cumulative distribution function of the scaled DOI index values. Based on this fitting, step 4 focuses on the computation of an interpretation index (II) defined for every cell j of the model as the relative probability density that the cell j belongs to G1, which describes the Gaussian distribution of the cells with a scaled DOI index close to 0.0. In step 5, a new inversion is performed by using a third resistivity reference model (the arithmetic mean of the logarithm of the observed apparent resistivity values). The final electrical resistivity image is produced by using II as alpha blending values allowing the visual discrimination between well-constrained areas and poorly-constrained cells. The efficiency of the proposed methodology is assessed on synthetic and field data. By using synthetic benchmark analysis, we demonstrate that the selected well-constrained cells are well-reconstructed in size and shape as well as in resistivity contrasts. Compared to the existing image appraisal tools, the proposed statistical method allows the identification of the statistically well-constrained cells of the model without using any arbitrary cut-off value. Using this statistical method in combination with the resolution, when interpreting dc resistivity surveys, provides the geophysicist valuable information to avoid over- or misinterpretation of ERT images. © 2014 Elsevier B.V.

Jaar van publicatie:2014