Analysis of direct current flowing inside a linear increasing conductivity half-space

2010 ◽  
Author(s):  
Ovidiu Centea ◽  
Iosif Vasile Nemoianu ◽  
Emil Cazacu ◽  
Veronica Paltanea ◽  
Gheorghe Paltanea
Keyword(s):  
Half Space ◽  
Direct Current

Depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space in direct current methods

Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 768-780 ◽  
Author(s):  
B. B. Bhattacharya ◽  
M. K. Sen
Keyword(s):  
Half Space ◽  
Direct Current ◽  
Inverse Relationship ◽  
Electrode Arrays ◽  
Definition Of ◽  
Depth Of Investigation

The definition of depth of investigation as suggested by Evjen (1938) [subsequently used by Roy and Apparao (1971) also for the study of depth of investigation of electrode arrays in direct current methods for homogeneous isotropic earth] has been used to study the depth of investigation of various collinear electrode arrays for a homogeneous anisotropic half‐space. It has been shown that some simple transformations are to be applied to the expressions of normalized depth of investigation characteristic (NDIC) of the same arrays over homogeneous isotropic earth to obtain normalized depth of investigation characteristic of various arrays placed over homogeneous anisotropic earth. The novelty of anisotropy is that the depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space bears an inverse relationship with the coefficient of anisotropy and also depends upon array length and dip of the plane of stratification. The effect of the coefficient of anisotropy is most pronounced for horizontally stratified anisotropic earth and is independent of it for vertically stratified anisotropic earth—entirely consistent with the concept of the “;paradox of anisotropy.” The depth of investigation of all the collinear arrays for inclined stratification lies somewhere between the values obtained for horizontal and vertical stratifications.

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

Geophysics ◽  
1982 ◽  
Vol 47 (2) ◽  
pp. 264-265 ◽  
Author(s):  
D. Guptasarma
Keyword(s):  
Characteristic Function ◽  
Half Space ◽  
Direct Current ◽  
Layered Medium ◽  
Inverse Theory ◽  
Dc Resistivity ◽  
Vertical Variation ◽  
Resistivity Sounding ◽  
Resistivity Measurements

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).

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

Geophysics ◽  
1976 ◽  
Vol 41 (1) ◽  
pp. 79-95 ◽  
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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