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Calculating the electric potentials for 3-D resistivity inversion algorithms can be time consuming depending on the structure of the mesh. There have been generally two approaches to generating finite-element meshes. One approach uses a structured rectangular mesh with hexahedral elements on a rectangular model grid. The distribution of the model cells can be designed to follow known boundaries, and directional roughness constraints can be easily imposed. A 1-D wavelet transform that takes advantage of the regular arrangement of the model cells can also be used to reduce the computer time and memory required to solve the smoothness-constrained least-squares equation. However, the structured rectangular mesh uses an unnecessarily fine mesh in parts of the model that are far away from the electrodes where the potential changes gradually. A second approach uses an unstructured mesh with tetrahedral elements created automatically by a mesh generation program with finer elements nearer the electrodes and coarser elements in the more remote regions. This generates a mesh with a much smaller number of nodes. The disadvantage is that an irregular model grid is normally used.We examine an alternative approach that combines structured and unstructured meshes. We employ a regular model grid with a finer mesh near the surface and a coarser mesh in deeper regions using a combination of hexahedral and tetrahedral elements. The semi-structured mesh reduces the calculation time by more than three times compared to a structured mesh. An adaptive semi-structured mesh that also uses a coarser mesh for model cells near the surface if they are more than one unit electrode spacing from the nearest electrode was also developed for surveys with non-uniform data coverage. For the Bonsall Leys field survey, that used a capacitively coupled mobile system and collected a data set with nearly a million electrode positions, the adaptive mesh reduces the calculation time by about 80%. The calculation time can be further reduced by about 93% when it is combined with a mesh segmentation method.

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SUMMARYMost optimal survey design algorithms for resistivity imaging have not incorporated prior knowledge of the resistivity of the subsurface. The resulting surveys are optimal for a homogeneous earth, but little investigation has yet been carried out to test whether they are robust, i.e. that they remain optimal when applied to imaging heterogeneous subsurface resistivity distributions. This paper compares a generic survey, which is designed to maximise the estimated model resolution evenly across a homogeneous earth, with specific surveys similarly designed for a number of heterogeneous resistivity distributions. In terms of both the average estimated model resolution and the correlations between the inverted and true resistivity models, the generic and heterogeneous survey designs give near-identical results. This suggests that surveys designed using homogeneous earth approximations are robust in the presence of resistivity heterogeneities and are therefore generally applicable. Traditional dipole-dipole surveys with the same number of measurements do not give such good inverted images, and their degree of optimality (measured either by average resolution or image correlation) is less robust in the presence of heterogeneity.

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