A comparison of smooth and blocky inversion methods in 2-D electrical imaging surveys

Abstract

Two-dimensional electrical imaging surveys are now widely used in engineering and environmental surveys to map moderately complex structures. In order to adequately resolve such structures with arbitrary resistivity distributions, the regularised least-squares optimisation method with a cell-based model is frequently used in the inversion of the electrical imaging data. The l2 norm or smoothness-constrained optimisation method that attempts to minimise the sum of squares of the spatial changes in the model resistivity is frequently used. The resulting inversion model has a smooth variation in the resistivity values. In cases where the true subsurface resistivity consists of several regions that are approximately homogenous internally and separated by sharp boundaries, the result obtained by the smooth inversion method is not optimal. It tends to smear out the boundaries and give resistivity values that are too low or too high. The l1 norm or blocky optimisation method can be used for such situations. This method attempts to minimise the sum of the absolute values of the spatial changes in the model resistivity. It tends to produce models that are piecewise constant. Results from tests with the smooth and blocky inversion methods with several synthetic and field data sets are given to highlight the strengths and weaknesses of both methods. The smooth inversion method gives better results for areas where the subsurface resistivity changes in a gradual manner, while the blocky inversion method gives significantly better results where there are sharp boundaries. While fast computers and software has made the task of interpreting data from electrical imaging surveys much easier, it still remains the responsibility of the interpreter to choose the appropriate tool for the task based on the available geological information.