On: “The interpretation of direct current resistivity measurements” by D. W. Oldenburg (GEOPHYSICS, April 1978, p. 610–625)

Oldenburg made an excellent example of the application of linearized inverse theory to invert dc resistivity sounding data to fit a continuous vertical variation of resistivity. In the Introduction he mentioned that the Frechet kernels for resistivity are the same as the depth investigation characteristic function (DIC) used by Roy and Apparao (1971). In the second part of the paper, he showed that it is so for a uniformly conducting half space. He mentioned that the electrostatic analog which was used (by Roy and Apparao) becomes quite complex when a layered medium is introduced, and that the extension to a continuous ρ(z) would be a difficult task (p. 623).

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THE INTERPRETATION OF DIRECT CURRENT RESISTIVITY MEASUREMENTS

Geophysics ◽

10.1190/1.1440840 ◽

1978 ◽

Vol 43 (3) ◽

pp. 610-625 ◽

Cited By ~ 32

Author(s):

D. W. Oldenburg

Keyword(s):

Continuous Function ◽

Direct Current ◽

Inverse Theory ◽

Iterative Technique ◽

Electrode Arrays ◽

Resistivity Measurements ◽

The Earth ◽

Resistivity Model ◽

Surface Observations ◽

Layered Half Space

The linearized inverse theory of Backus and Gilbert has been used to invert potential difference measurements obtained from direct current resistivity soundings. The resistivity is assumed to be a continuous function of depth, hence many of the difficulties encountered when assuming that the earth is a layered half‐space are avoided. An iterative technique is used to construct a resistivity model whose calculated responses agree with the observations, and the model is then appraised to find those features which are uniquely determined by the surface observations. Also, the existence of the Fréchet kernels allows direct comparisons of the resolution provided by various electrode geometries and thus the design of electrode arrays to enhance resolution becomes more feasible.

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Direct current (DC) resistivity measurements in long-term groundwater monitoring programmes

Environmental Geology ◽

10.1007/s00254-001-0447-1 ◽

2002 ◽

Vol 41 (6) ◽

pp. 662-671 ◽

Cited By ~ 13

Author(s):

J. Aaltonen, B. Olofsson

Keyword(s):

Direct Current ◽

Groundwater Monitoring ◽

Dc Resistivity ◽

Resistivity Measurements

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An algorithm for computation of resistivity soundings over inhomogeneous layers

Geophysics ◽

10.1190/1.1441990 ◽

1985 ◽

Vol 50 (7) ◽

pp. 1166-1172 ◽

Cited By ~ 2

Author(s):

S. P. Dasgupta

Keyword(s):

Half Space ◽

Kernel Function ◽

Transition Layer ◽

Recurrence Relations ◽

The Other ◽

Dc Resistivity ◽

Resistivity Sounding ◽

Transition Layers ◽

Homogeneous Form ◽

Layered Half Space

Calculation of dc resistivity sounding curves for a multilayer earth with transition layers has been treated by several authors since Mallick and Roy (1968). However, derivation of the kernel function for such problems has remained difficult for more than three‐layer models for want of a proper algorithm. The problem was first solved by Pekeris (1942) in the case of uniformly resistive layers. Other forms of recurrence relations for the kernel function of a half‐space containing such homogeneous layers were forwarded by Flathe (1955), Kunetz (1966), and Koefoed (1968). Patella (1977) considered the kernel function for a half‐space which contained a series of alternate layers, one having a linearly varying conductivity with depth while the other was homogeneously conductive. Koefoed (1979a) considered the case of a half‐space containing a transition layer situated anywhere among a series of homogeneous layers and possessing a resistivity that changed linearly with depth. In this article a very general form of algorithm is developed for generating the kernel function for a layered half‐space containing any number of transition layers having an arbitrary resistivity distribution [Formula: see text] in such ith layer. This new general form is very similar to the homogeneous form derived by Pekeris (1942).

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QUADRIPOLE‐QUADRIPOLE ARRAYS FOR DIRECT CURRENT RESISTIVITY MEASUREMENTS—MODEL STUDIES

Geophysics ◽

10.1190/1.1440609 ◽

1976 ◽

Vol 41 (1) ◽

pp. 79-95 ◽

Cited By ~ 6

Author(s):

Dariu Doicin

Keyword(s):

Half Space ◽

Electric Fields ◽

Direct Current ◽

Apparent Resistivity ◽

Cross Product ◽

Resistivity Measurements ◽

Model Studies ◽

True Resistivity ◽

Vertical Contact ◽

Source Dipole

For a quadripole‐quadripole array, in which current is sequentially injected into the ground by two perpendicular dipoles, an apparent resistivity can be defined in terms of the vectorial cross product of the two electric fields measured at the receiver site. Transform equations are derived (for horizontally layered media) which relate this apparent resistivity to the apparent resistivities obtained with conventional dipole‐dipole and Schlumberger arrangements. To evaluate the method, two mathematical models are used. The first model is a half‐space with an “alpha conductivity center,” and the second model is a half‐space with a vertical contact. For an idealized quadripole‐quadripole array, simple expressions are found for the apparent resistivity, which is shown to be independent of the orientation of the current quadripole. Theoretical anomalies calculated for the quadripole‐quadripole array are compared with those obtained for a dipole‐quadripole array. It is shown that whereas the apparent resistivity map for the dipole‐quadripole array varies greatly with the azimuth of the source dipole, the results obtained with the quadripole‐quadripole array consistently display a remarkable resemblance to the assumed distribution of true resistivity. This is especially true when the current quadripole is placed at a large distance from the surveyed area.

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Use of Direct Current Resistivity Measurements to Assess AISI 304 Austenitic Stainless Steel Sensitization

Materials Research ◽

10.1590/1516-1439.308714 ◽

2015 ◽

Vol 18 (2) ◽

pp. 341-346 ◽

Cited By ~ 2

Author(s):

Ramaiany Carneiro Mesquita ◽

José Manoel Rivas Mecury ◽

Auro Atsumi Tanaka ◽

Regina Célia de Sousa

Keyword(s):

Stainless Steel ◽

Austenitic Stainless Steel ◽

Direct Current ◽

Aisi 304 ◽

Resistivity Measurements ◽

304 Austenitic Stainless Steel

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Dispersion of Love waves in prestressed double-layered medium over a gravitating half-space

Arabian Journal of Geosciences ◽

10.1007/s12517-020-05354-2 ◽

2020 ◽

Vol 13 (13) ◽

Author(s):

Bishwanath Prasad ◽

Santimoy Kundu ◽

Prakash Chandra Pal ◽

Parvez Alam

Keyword(s):

Half Space ◽

Layered Medium ◽

Love Waves

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Using Direct Current Resistivity Sounding and Geostatistics to Aid in Hydrogeological Studies in the Choshuichi Alluvial Fan, Taiwan

Ground Water ◽

10.1111/j.1745-6584.2002.tb02501.x ◽

2002 ◽

Vol 40 (2) ◽

pp. 165-173 ◽

Cited By ~ 10

Author(s):

Chieh-Hou Yang ◽

Wei-Feng Lee

Keyword(s):

Direct Current ◽

Alluvial Fan ◽

Resistivity Sounding ◽

Hydrogeological Studies

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Pixels and their neighbors: Finite volume

The Leading Edge ◽

10.1190/tle35080703.1 ◽

2016 ◽

Vol 35 (8) ◽

pp. 703-706 ◽

Cited By ~ 4

Author(s):

Rowan Cockett ◽

Lindsey J. Heagy ◽

Douglas W. Oldenburg

Keyword(s):

Finite Element ◽

Finite Difference ◽

Finite Volume Method ◽

Finite Volume ◽

Direct Current ◽

Numerical Results ◽

Dc Resistivity ◽

Matrix Representations ◽

Volume Method

We take you on the journey from continuous equations to their discrete matrix representations using the finite-volume method for the direct current (DC) resistivity problem. These techniques are widely applicable across geophysical simulation types and have their parallels in finite element and finite difference. We show derivations visually, as you would on a whiteboard, and have provided an accompanying notebook at http://github.com/seg to explore the numerical results using SimPEG ( Cockett et al., 2015 ).

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