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Time-lapse resistivity surveys are commonly used to monitor temporal changes in the subsurface. In certain cases, it is known from other information that the resistivity will only decrease or increase with time. The 4-D resistivity smoothness-constrained inversion method reduces artifacts due to noise by including a temporal roughness filter constraint that ensures the temporal changes vary in a smooth manner. A least-squares optimization method is used to find a solution by attempting to locate the minimum of an objective function that consists of the data misfit and model (spatial and temporal) roughness. In some cases, the 4-D time-lapse inverse models show an increase in the resistivity with time in parts of the subsurface where it is only expected to decrease (or vice versa). We compare two methods, the barrier function and transformation methods, that attempt to minimize or eliminate these artifacts. We incorporate the barrier function constraint into the 4-D inverse method by using a modified difference matrix as a temporal roughness filter. The barrier function constraint includes an additional term that increases the objective function value greatly if the model values cross the allowed thresholds. This greatly minimizes the artifacts but does not completely eliminate them. It has the advantage that there are minimal changes in the objective function in regions of model space that are not close to the imposed thresholds. The method of transformations changes the model parameter such that the additional positivity or negativity constraints are implicitly included in the transformed model parameter. It has the advantage that it can completely eliminate the artifacts. However, it modifies the entire objective function which could be a disadvantage in some cases. We also explore a combination of the two methods, using the barrier function method to generate an initial model that minimizes the artifacts followed by the transformation method. This hybrid technique completely removes the residual artifacts left by the barrier method, and produces an inverse model which is closer to the true model for a synthetic data set. We also describe a post-inversion modification of the L-curve method to determine the optimum model that takes into account the non-linear nature of the inverse problem and the forward modelling method. The technique gave an estimate of the noise level for a field data set and produced a model which is consistent with independent hydrological measurements at the test site. • 4-D ERT inversion. • Asymmetric time constraints. • Barrier function methods. • Transformation methods. • Post-inversion L-curve analysis. [ABSTRACT FROM AUTHOR]

Abstract: There have been major improvements in instrumentation, field survey design and data inversion techniques for the geoelectrical method over the past 25years. Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. Continued developments in computer technology, as well as fast data inversion techniques and software, have made it possible to carry out the interpretation on commonly available microcomputers. Multi-dimensional geoelectrical surveys are now widely used in environmental, engineering, hydrological and mining applications. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Large areas on land and water can be surveyed rapidly with computerized dynamic towed resistivity acquisition systems. The use of existing metallic wells as long electrodes has improved the detection of targets in areas where they are masked by subsurface infrastructure. A number of PC controlled monitoring systems are also available to measure and detect temporal changes in the subsurface. There have been significant advancements in techniques to automatically generate optimized electrodes array configurations that have better resolution and depth of investigation than traditional arrays. Other areas of active development include the translation of electrical values into geological parameters such as clay and moisture content, new types of sensors, estimation of fluid or ground movement from time-lapse images and joint inversion techniques. In this paper, we investigate the recent developments in geoelectrical imaging and provide a brief look into the future of where the science may be heading. [Copyright &y& Elsevier]

Abstract: We describe the application of 3D electrical resistivity tomography (ERT) to the characterisation and reserve estimation of an economic fluvial sand and gravel deposit. Due to the smoothness constraints used to regularise the inversion, it can be difficult to accurately determine the geometry of sharp interfaces. We have therefore considered two approaches to interface detection that we have applied to the 3D ERT results in an attempt to provide an accurate and objective assessment of the bedrock surface elevation. The first is a gradient-based approach, in which the steepest gradient of the vertical resistivity profile is assumed to correspond to the elevation of the mineral/bedrock interface. The second method uses an intrusive sample point to identify the interface resistivity at a location within the model, from which an iso-resistivity surface is identified that is assumed to define the interface. Validation of these methods has been achieved through direct comparison with observed bedrock surface elevations that were measured using real-time-kinematic GPS subsequent to the 3D ERT survey when quarrying exposed the bedrock surface. The gradient-based edge detector severely underestimated the depth to bedrock in this case, whereas the interface resistivity method produced bedrock surface elevations that were in close agreement with the GPS-derived surface. The failure of the gradient-based method is attributed to insufficient model sensitivity in the region of the bedrock surface, whereas the success of the interface resistivity method is a consequence of the homogeneity of the mineral and bedrock, resulting in a consistent interface resistivity. These results highlight the need for some intrusive data for model validation and for edge detection approaches to be chosen on the basis of local geological conditions. [Copyright &y& Elsevier]