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New developments in mobile resistivity meter instrumentation have made it possible to survey large areas with dense data coverage. The mobile system usually has a limited number of electrodes attached to a cable that is pulled along behind an operator so that a large area can be covered within a short time. Such surveys can produce three‐dimensional datasets with hundreds of thousands of electrodes positions and data points. Similarly, the inverse model used to interpret the data can have several hundred thousand cells. It is impractical to model such large datasets within a reasonable time on microcomputers used by many small companies employing standard inversion techniques. We describe a model segmentation technique that subdivides the finite‐element mesh used to calculate the apparent resistivity and Jacobian matrix values into a number of smaller meshes. A fast technique that optimizes the calculation of the Jacobian matrix values for multi‐channel systems was also developed. A one‐dimensional wavelet transform method was then used to compress the storage of the Jacobian matrix, in turn reducing the computer time and memory required to solve the least‐squares optimization equation to determine the inverse model resistivity values. The new techniques reduce the calculation time and memory required by more than 80% while producing models that differ by less than 1% from that obtained using the standard inversion technique with a single mesh. We present results using a synthetic model and a field dataset that illustrates the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

ABSTRACT The use of optimized arrays generated using the 'Compare R' method for cross-borehole resistivity measurements is examined in this paper. We compare the performances of two array optimization algorithms, one that maximizes the model resolution and another that minimizes the point spread value. Although both algorithms give similar results, the model resolution maximization algorithm is several times faster. A study of the point spread function plots for a cross-borehole survey shows that the model resolution within the central zone surrounded by the borehole electrodes is much higher than near the bottom end of the boreholes. Tests with synthetic and experimental data show that the optimized arrays generated by the 'Compare R' method have significantly better resolution than a 'standard' measurement sequence used in previous surveys. The resolution of the optimized arrays is less if arrays with both current (or both potential) electrodes in the same borehole are excluded. However, they are still better than the 'standard' arrays. [ABSTRACT FROM AUTHOR]

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]