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.

Depth of investigation of collinear symmetrical four‐electrode arrays

Geophysics ◽  
1989 ◽  
Vol 54 (8) ◽  
pp. 1031-1037 ◽  
Author(s):  
R. D. Barker
Keyword(s):  
Characteristic Curve ◽  
Electrode Array ◽  
Electrode Arrays ◽  
Definition Of ◽  
Depth Of Investigation

A study of collinear symmetrical four‐electrode arrays and their tripotential variations indicates the existence of an electrode array for which all the tripotential arrangements have the same depth of investigation. Examination of computer‐generated sounding curves confirms this result only when depth of investigation is defined as the median of the depth of investigation characteristic curve. The results lend support to this being the most practically useful definition of depth of investigation.

A MODIFIED PSEUDOSECTION FOR RESISTIVITY AND IP

Geophysics ◽  
1977 ◽  
Vol 42 (5) ◽  
pp. 1020-1036 ◽  
Author(s):  
L. S. Edwards
Keyword(s):  
Relative Depth ◽  
Electrode Arrays ◽  
Anomalous Body ◽  
Vertical Scale ◽  
Depth Scale ◽  
Effective Depth ◽  
Definition Of ◽  
Empirical Coefficients ◽  
Theoretical Results ◽  
Depth Of Investigation

Dipole‐dipole induced‐polarization measurements are commonly presented as pseudosections, but results using different dipole lengths cannot be combined into a single pseudosection. By considering the theoretical results for simple earth models, a unique set of relative depth coefficients is empirically derived, such that measurements with different array parameters will “mesh” smoothly into a combined pseudosection. Application of these coefficients to a number of theoretical and field cases shows that they give reasonable results when applied to more complicated models. The empirical coefficients are compared with Roy’s theory of “depth of investigation characteristic,” and support that theory, if a modified definition of “effective depth” is accepted. This leads to an absolute depth scale for the modified pseudosection. It is shown that rough estimates of the depth to the top of an anomalous body can be made directly on the pseudosection, at true vertical scale. This definition of effective depth is applied to other electrode arrays. It is shown, by examples, that the resulting pseudosections give consistent estimates of depth to top, within the characteristic anomaly patterns of each array. The effective depths for various arrays are compared; the results agree with the traditional applications of each array.

On: “Depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space in direct current methods,” by B. B. Bhattacharya and M. K. Sen (May 1981 GEOPHYSICS, 46, p. 768–780).

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1936-1941
Author(s):  
A. Apparao ◽  
G. S. Srinivas
Keyword(s):  
Half Space ◽  
Basic Equation ◽  
Homogeneous Medium ◽  
Current Strength ◽  
Senior Author ◽  
Electrode Arrays ◽  
The Subject ◽  
Geoelectrical Methods ◽  
Electrode Systems ◽  
Depth Of Investigation

Bhattacharya and Sen (1981) are the first to study the depths of investigation of various collinear electrode arrays for a homogeneous anisotropic half‐space. In their study they substituted the aniosotropic medium by an appropriate homogeneous medium of resistivity [Formula: see text]. However, they committed a serious error at assuming their basic equation‐13 as the “expression of potential at a point (X, y, Z) due to a point source of current strength I placed over a semi‐infinite homogeneous isotropic medium of resistivity [Formula: see text]”. The error is that X and Z in equation (13) are not independent coordinates. As a consequence, all their expressions for NDICs for different electrode arrays become incorrect. Consequently, their results and conclusions also become invalid. The mistake was detected only recently by the senior author of this paper (A. Apparao) in the course of his writing a book on ‘Developments in geoelectrical methods’. Since the subject of anisotropy is very interesting, there arises an urgent need to derive the correct expressions of the depth investigation characteristics for different electrode arrays. We present in this paper the expressions for normalized depth investigation characteristics (NDIC) for homogeneous and anisotropic half spaces for different electrode systems, including dipolar systems.

THE INTERPRETATION OF DIRECT CURRENT RESISTIVITY MEASUREMENTS

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 610-625 ◽  
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.

Estimating depth of investigation in dc resistivity and IP surveys

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 403-416 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li
Keyword(s):  
Electrode Array ◽  
Physical Property ◽  
Model Space ◽  
Visual Assessment ◽  
Order Estimate ◽  
Dc Resistivity ◽  
Electrode Arrays ◽  
The Earth ◽  
Surface Data ◽  
Depth Of Investigation

In this paper, the term “depth of investigation” refers generically to the depth below which surface data are insensitive to the value of the physical property of the earth. Estimates of this depth for dc resistivity and induced polarization (IP) surveys are essential when interpreting models obtained from any inversion because structure beneath that depth should not be interpreted geologically. We advocate carrying out a limited exploration of model space to generate a few models that have minimum structure and that differ substantially from the final model used for interpretation. Visual assessment of these models often provides answers about existence of deeper structures. Differences between the models can be quantified into a depth of investigation (DOI) index that can be displayed with the model used for interpretation. An explicit algorithm for evaluating the DOI is presented. The DOI curves are somewhat dependent upon the parameters used to generate the different models, but the results are robust enough to provide the user with a first‐order estimate of a depth region below which the earth structure is no longer constrained by the data. This prevents overinterpretation of the inversion results. The DOI analysis reaffirms the generally accepted conclusions that different electrode array geometries have different depths of penetration. However, the differences between the inverted models for different electrode arrays are far less than differences in the pseudosection images. Field data from the Century deposit are inverted and presented with their DOI index.

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

On: “Depth of Investigation in Direct Current Methods,” by A. Roy and A. Apparao (GEOPHYSICS, October 1971, p. 943–959)

Geophysics ◽  
1972 ◽  
Vol 37 (4) ◽  
pp. 703-704 ◽  
Author(s):  
O. Koefoed
Keyword(s):  
Direct Current ◽  
Electrical Current ◽  
Potential Difference ◽  
Interesting Paper ◽  
Depth Of Investigation

In this very interesting paper, the authors ascribe the potential difference that is measured in resistivity methods to electrical‐current polarization of the subsurface. This description enables them to compare the relative contributions of different portions of the subsurface to the measured potential difference.

scholarly journals Review of top notch electrode arrays for geoelectrical resistivity surveys

2020 ◽  
pp. 147-155
Author(s):  
Henry Ekene Ohaegbuchu ◽  
F. C. Anyadiegwu ◽  
P. O. Odoh ◽  
F. C. Orji
Keyword(s):  
Signal To Noise Ratio ◽  
Electrode Arrays ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Geoelectrical Resistivity ◽  
Depth Of Investigation ◽  
Horizontal Layers

The different arrangements of electrodes used in geoelectrical resistivity surveys and measurements are referred to as electrode arrays. In this review, we have revisited most of the widely used electrode arrays as well as the uncommon ones, which are nonetheless, useful in certain situations. This review has provided detailed information about eleven (11) of the top notch electrode arrays employable in our regular resistivity surveys, making it clear that in practice, the arrays that are most commonly used for 2-D imaging surveys are the Wenner, Dipole-Dipole, Wenner-Schlumberger, Pole-Pole and the Pole-Dipole arrays. They have their strengths and weaknesses. They are typically described by their signal-to-noise ratio. Their depth of investigation, ability for lateral location of the target and their mapping abilities of horizontal layers or steeply dipping structures among other factors determine which array to adopt.

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