Model reliability for 3D electrical resistivity tomography: Application of the volume of investigation index to a time-lapse monitoring experiment

Abstract

Solution appraisal is difficult for large 3D, nonlinear inverse problems such as electrical resistivity tomography (ERT). We construct the volume of investigation index (VOI) as the sensitivity of the inversion result to a variable-reference model. This limited exploration of the model space provides an efficient and pragmatic method of appraisal for a particular data set and a 3D model domain. We present a synthetic example to demonstrate the applicability of the VOI as a tool for characterizing model reliability for 3D ERT and as a method of survey design. We show how the VOI provides a measure of model resolution and how insight gained from VOI analysis cannot be gained through similar examination of the average sensitivity distributions. In the context of ERT monitoring of an injection/withdrawal experiment, we utilize the VOI for judging the degree of reliability of hydrogeological interpretations that stem from features observed in the estimated electrical-conductivity models. We employ the VOI for the experimental data as a comparative measure of survey performance. For this experiment, the VOI shows that a larger, more artifact-free region of reliability is achieved using a circulating vertical dipole-dipole survey geometry, as opposed to a horizontal dipole-dipole survey geometry. The experimental VOI distributions exhibit dependence on the borehole infrastructure and the actual earth model.

2D Model Study of CO2Plumes in Saline Reservoirs by Borehole Resistivity Tomography

“…This similarity reflects the reliability of the applied techniques. A comparison with published results (e.g., [34]) shows that the vertical configurations reflect better resolution (of lower ROI values) than the lateral ones which confirms the results obtained here.…”

“…However, their filtered data sets after removing this noise can resolve well the subsurface targets of CO 2 plume, reservoir, and cap rock assuming enough coverage of more than one electrode spacing. These conclusions are in accordance with that of, for example, Oldenburg and Li [16] and Oldenborger et al [34] and opposed to that of Zhou and Greenhalgh [23]. In solute transport experiments, the former authors found that the vertical βvcs tomograms show more reliable subsurface structures than the horizontal β tomograms.…”

“…Higher iteration numbers were tested and resulted in artifacts as the algorithm tries to reduce the data misfit by modeling the noise as well. Different pairs of multiplication factors (0.1 and 10, 0.1 and 10, and 0.2 and 5) were applied here and yield similar results (see also [34,36]). …”

High-resolution Electrical Resistivity Tomography monitoring of a tracer test in a confined aquifer

“…The images indicate thin alternating resistive and conductive layers, possibly underlain by conductive bedrock at ~8 m bgl. Two of these three resistive layers do not appear to be continuous, although their disappearance with increasing distance from the borehole electrodes is probably due to the associated decrease in image resolution with increasing distance (Kemna et al, 2002, Oldenborger et al, 2007b. It is possible that the lack of quantitative agreement between the logs and the images below 6 m bgl is due to slippage in the core barrel.…”

Assessing the monitorability of CO2 saturation in subsurface saline aquifers

“…Optimal experimental and data processing designs may be used to improve these uncertainties. Optimal design theory is applied to both linear and nonlinear geophysical problems (Curtis, 2004a,b) such as seismic tomography (Curtis, 1999a,b;Maurer et al, 2009;Ajo-Franklin, 2009), amplitude variation with offset/angle survey and processing (van den Berg et al, 2003;Coles and Curtis, 2010;Guest and Curtis, 2009, 2011) earthquake or microcosmic location surveys (Curtis et al, 2004;Winterfors and Curtis, 2008) and electric and electromagnetic surveys (Maurer and Boerner, 1998;Maurer et al, 2000;Stummer et al, 2002aStummer et al, ,b, 2004Oldenborger et al, 2007). A review of the recent advances in survey design is given in Maurer et al (2010).…”