Three-dimensional modelling and inversion of dc resistivity data incorporating topography - I. Modelling

Abstract

SUMMARY We present techniques for the efficient numerical computation of the electrical potential with finite element methods in 3‐D and arbitrary topography. The crucial innovation is, firstly, the incorporation of unstructured tetrahedral meshes, which allow for efficient local mesh refinement and most flexible description of arbitrary model geometry. Secondly, by implementation of quadratic shape functions we achieve considerably more accurate results. Exploiting a secondary potential (SP) approach, meshes are downsized significantly in comparison with highly refined meshes for total potential calculation. However, the latter is necessary for the determination of the required primary potential in arbitrary model domains. To start with, we concentrate on the simulation of homogeneous models with different geometries at the surface and subsurface to quantify their influence. This results in a so‐called geometry effect, which is not only a side effect but may be responsible for serious misinterpretations. Moreover, it represents the basis for treating heterogeneous conductivity models with the SP approach, which is especially promising for the inverse problem. We address how the resulting system of equations is solved most efficiently using modern multifrontal direct solvers in conjunction with reordering strategies or rather traditional pre‐conditioned conjugate gradient methods depending on the size of the problem. Furthermore, we present a reciprocity approach to estimate modelling errors and investigate to which degree the model discretization has to be refined to yield sufficiently accurate results.

Electric resistivity and seismic refraction tomography: a challenging joint underwater survey at Äspö Hard Rock Laboratory

“…We used the open-source ERT software package BERT (Boundless Electrical Resistivity Tomography) for ERT inversion (Günther et al, 2006b) using irregular triangle meshes to accurately take into account both the surface and submarine topography (Rücker et al, 2006). Furthermore, we used the underlying framework pyGIMLi (Python Geophysical Inversion and Modelling Library; http://www.…”

Coupled hydrogeophysical parameter estimation using a sequential Bayesian approach

“…Model grids were created for the hydrological simulation with 1000 equally sized hexagonal cells that were further subdivided into 6000 tetrahedral cells. The parameter mesh for the ERT model was of equal size, but internally an irregular grid with tetrahedral cells was used (see Ruecker et al, 2006).…”

“…For this 3-D simulation, the hydrological model PARSWMS (Hardelauf et al, 2007) was coupled to the ERT forward code by Ruecker et al (2006). The state vector was initialized uniformly for each particle with 1331 pressure head values (one for each grid node) and a variable k S .…”

“…Ulrich and Slater (2004) determined saturation exponents ranging from 1.0 to 2.7 for unconsolidated sands. We use an ERT forward code by Ruecker et al (2006) for 3-D modelling domains and the CRMOD code (Kemna et al, 2000) for 2-D modelling domains. Both ERT forward models were coupled to hydrological models following the approach and considerations presented in Huisman et al (2010).…”

Seismic Waves - Research and Analysis

“…The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods Rücker et al, 2006), diffusive methods (Cognon, 1971;Druskin & Knizhnerman, 1988;Goldman & Stover, 1983;Hohmann, 1988;Kuo & Cho, 1980;Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968;Bolt & Smith, 1976;Dablain, 1986;Kelly et al, 1976;Levander, 1988;Marfurt, 1984;Virieux, 1986). Seismic waves belong to the last category.…”