The use of a semi‐structured finite‐element mesh in 3‐D resistivity inversion

Loke, M.H.; Wilkinson, P.B.; Kuras, O.; Meldrum, P.I.; Rucker, D.F.. 2022 The use of a semi‐structured finite‐element mesh in 3‐D resistivity inversion. Geophysical Prospecting, 70 (9). 1580-1601. 10.1111/1365-2478.13260

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Abstract/Summary

Calculating the electric potential 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 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 with 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, which 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.

Item Type:	Publication - Article
Digital Object Identifier (DOI):	10.1111/1365-2478.13260
ISSN:	0016-8025
Date made live:	22 Nov 2022 11:11 +0 (UTC)
URI:	https://nora.nerc.ac.uk/id/eprint/533596

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