Three-dimensional modelling and inversion of dc resistivity data incorporating topography - II. Inversion

Abstract

S U M M A R YWe present a novel technique for the determination of resistivity structures associated with arbitrary surface topography. The approach represents a triple-grid inversion technique that is based on unstructured tetrahedral meshes and finite-element forward calculation. The three grids are characterized as follows: A relatively coarse parameter grid defines the elements whose resistivities are to be determined. On the secondary field grid the forward calculations in each inversion step are carried out using a secondary potential (SP) approach. The primary fields are provided by a one-time simulation on the highly refined primary field grid at the beginning of the inversion process.We use a Gauss-Newton method with inexact line search to fit the data within error bounds. A global regularization scheme using special smoothness constraints is applied. The regularization parameter compromising data misfit and model roughness is determined by an L-curve method and finally evaluated by the discrepancy principle. To solve the inverse subproblem efficiently, a least-squares solver is presented.We apply our technique to synthetic data from a burial mound to demonstrate its effectiveness. A resolution-dependent parametrization helps to keep the inverse problem small to cope with memory limitations of today's standard PCs. Furthermore, the SP calculation reduces the computation time significantly. This is a crucial issue since the forward calculation is generally very time consuming. Thus, the approach can be applied to large-scale 3-D problems as encountered in practice, which is finally proved on field data.As a by-product of the primary potential calculation we obtain a quantification of the topography effect and the corresponding geometric factors. The latter are used for calculation of apparent resistivities to prevent the reconstruction process from topography induced artefacts.

A cylindrical electrical resistivity tomography array for three-dimensional monitoring of hydrate formation and dissociation

“…In short, BERT uses a triple-grid inversion technique that is based on unstructured finite element meshes for forward calculation and parameter identification. 16 By using triangles (2D) and tetrahedrons (3D), BERT can follow arbitrary geometries. BERT is already well described and further details can be found, e.g., in Günther et al 16 …”

“…16 By using triangles (2D) and tetrahedrons (3D), BERT can follow arbitrary geometries. BERT is already well described and further details can be found, e.g., in Günther et al 16 …”

3D Inversion of Large-scale Time Domain Electromagnetic Data

“…This work extends our previous work on time domain electromagnetics inversion using a single regular mesh to OcTree meshes. The underlying regular structure of OcTree meshes greatly simplifies mesh handling and algorithmic development, compared to the finite element method on unstructured tetrahedral meshes (Günther, Rücker and Spitzer, 2006;Schwarzbach et al, 2011). A similar approach has been published by Cox and Zhdanov (2008).…”

Non-destructive monitoring of early stages of white rot by Trametes versicolor in Fraxinus excelsior

“…In the following years ERT was applied to find discoloured wood (Weihs, 2001) and decay in trees Rust et al, 2007). New reconstruction algorithms (Günther et al, 2006) have improved the result further by using the exact shape of the measuring level.…”

“…A low frequency current (8.3 Hz) was applied to measure apparent electric resistivities in dipole-dipole configuration (Reynolds, 1997). The software DC2dTree (Günther et al, 2006) was used for tomographic inversion. The colours in the tomogram represent the 2-dimensional distribution of electric resistivity in Ω m where blue shows the lowest and red the highest electric resistivities measured.…”