THE INTERPRETATION OF DIRECT CURRENT RESISTIVITY MEASUREMENTS

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 610-625 ◽  
Author(s):  
D. W. Oldenburg

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.

Geophysics ◽  
1983 ◽  
Vol 48 (5) ◽  
pp. 636-638 ◽  
Author(s):  
M. El‐Raey

A variety of methods have been developed to solve the general problem of determining underground resistivity from surface measurements using two current electrodes and two collinear potential electrodes (Ghosh, 1971; Parker, 1971; Inman et al, 1973; Inman, 1975; Koefoed, 1979). Nevertheless, problems associated with measurement errors, nonlinearities, and nonuniqueness have not been completely resolved. Recently, a method of interpretation of direct current resistivity measurements, using a linearized Backus and Gilbert technique was advanced by Oldenburg (1978). In this method, the resistivity is assumed to be a continuous function of depth, and an iterative technique is used to construct a resistivity model whose calculated responses agree with observations within a prescribed error. The nonuniqueness of the problem was resolved by determining only averages of resistivity at depth. However, even in this method the nonlinearity of the problem prohibits definitive statements about advantages and disadvantages of any particular electrode configuration until a large variety of resistivity structures have been considered. The main problems are (1) a nonlinear resistivity profile, (2) a nonlinear current penetration, (3) a nonlinear dependence of measurable potential on resistivity, and (4) a nonlinear depth investigation characteristic.


Geophysics ◽  
1982 ◽  
Vol 47 (2) ◽  
pp. 264-265 ◽  
Author(s):  
D. Guptasarma

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).


2015 ◽  
Vol 18 (2) ◽  
pp. 341-346 ◽  
Author(s):  
Ramaiany Carneiro Mesquita ◽  
José Manoel Rivas Mecury ◽  
Auro Atsumi Tanaka ◽  
Regina Célia de Sousa

2021 ◽  
Author(s):  
Sabyasachi Dash ◽  
◽  
Zoya Heidari ◽  

Conventional resistivity models often overestimate water saturation in organic-rich mudrocks and require extensive calibration efforts. Conventional resistivity-porosity-saturation models assume brine in the formation as the only conductive component contributing to resistivity measurements. Enhanced resistivity models for shaly-sand analysis include clay concentration and clay-bound water as contributors to electrical conductivity. These shaly-sand models, however, consider the existing clay in the rock as dispersed, laminated, or structural, which does not reliably describe the distribution of clay network in organic-rich mudrocks. They also do not incorporate other conductive minerals and organic matter, which can significantly impact the resistivity measurements and lead to uncertainty in water saturation assessment. We recently introduced a method that quantitatively assimilates the type and spatial distribution of all conductive components to improve reserves evaluation in organic-rich mudrocks using electrical resistivity measurements. This paper aims to verify the reliability of the introduced method for the assessment of water/hydrocarbon saturation in the Wolfcamp formation of the Permian Basin. Our recently introduced resistivity model uses pore combination modeling to incorporate conductive (clay, pyrite, kerogen, brine) and non-conductive (grains, hydrocarbon) components in estimating effective resistivity. The inputs to the model are volumetric concentrations of minerals, the conductivity of rock components, and porosity obtained from laboratory measurements or interpretation of well logs. Geometric model parameters are also critical inputs to the model. To simultaneously estimate the geometric model parameters and water saturation, we develop two inversion algorithms (a) to estimate the geometric model parameters as inputs to the new resistivity model and (b) to estimate the water saturation. Rock type, pore structure, and spatial distribution of rock components affect geometric model parameters. Therefore, dividing the formation into reliable petrophysical zones is an essential step in this method. The geometric model parameters are determined for each rock type by minimizing the difference between the measured resistivity and the resistivity, estimated from Pore Combination Modeling. We applied the new rock physics model to two wells drilled in the Permian Basin. The depth interval of interest was located in the Wolfcamp formation. The rock-class-based inversion showed variation in geometric model parameters, which improved the assessment of water saturation. Results demonstrated that the new method improved water saturation estimates by 32.1% and 36.2% compared to Waxman-Smits and Archie's models, respectively, in the Wolfcamp formation. The most considerable improvement was observed in the Middle and Lower Wolfcamp formation, where the average clay concentration was relatively higher than the other zones. Results demonstrated that the proposed method was shown to improve the estimates of hydrocarbon reserves in the Permian Basin by 33%. The hydrocarbon reserves were underestimated by an average of 70000 bbl/acre when water saturation was quantified using Archie's model in the Permian Basin. It should be highlighted that the new method did not require any calibration effort to obtain model parameters for estimating water saturation. This method minimizes the need for extensive calibration efforts for the assessment of hydrocarbon/water saturation in organic-rich mudrocks. By minimizing the need for extensive calibration work, we can reduce the number of core samples acquired. This is the unique contribution of this rock-physics-based workflow.


Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 403-416 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li

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.


Geophysics ◽  
1974 ◽  
Vol 39 (1) ◽  
pp. 93-94 ◽  
Author(s):  
B. N. Satpathy

It is generally accepted that the resistivity of the top layer largely influences the apparent resistivity measured through conventional surface electrode arrays. Thus, intuitively it would be assumed that the overlaying of a conductive layer would give an apparent resistivity which is less than the value obtained without the conducting cover and an opposite result would be obtained by introducing a resistive top layer. Though this belief is valid for many geoelectric sections, it is here shown that for a two‐layer section with [Formula: see text], if the top portion of the first layer is replaced with a layer of higher or lower resistivity, the apparent resistivity value changes in an opposite manner after a critical value of the electrode separation: the apparent resistivity for large separations is decreased due to the introduction of the resistive top layer. It is intended in this note to elucidate this paradox through a suitable example.


1977 ◽  
Vol 15 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Avihu Ginzburg ◽  
Amos Levanon

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. E11-E24 ◽  
Author(s):  
Anand Singh ◽  
Shashi Prakash Sharma ◽  
İrfan Akca ◽  
Vikas Chand Baranwal

We evaluate the use of a fuzzy c-means clustering procedure to improve an inverted 2D resistivity model within the iterative error minimization procedure. The algorithm is coded in MATLAB language for the Lp-norm inversion of 2D direct current resistivity data and is referred to as fuzzy constrained inversion (FCI). Two additional input parameters are required to be provided by the interpreter: (1) the number of geologic units in the model (i.e., the number of clusters) and (2) the mean resistivity values of each geologic unit (i.e., cluster center values of the geologic units). The efficacy of our approach is evaluated by tests carried on the synthetic and field electrical resistivity tomography (ERT) data. Inversion results from the FCI algorithm are presented for conventional L1- and L2-norm minimization techniques. FCI indicates improvement over conventional inversion approaches in differentiating the geologic units if a proper number of the geologic units is provided to the algorithm. Inappropriate clustering information will affect the resulting resistivity models, particularly conductive geologic units existing in the model. We also determine that FCI is only effective when the observed ERT data can recognize the particular geologic units.


Geophysics ◽  
1968 ◽  
Vol 33 (5) ◽  
pp. 838-842 ◽  
Author(s):  
René Bodmer ◽  
Stanley H. Ward

Among the different four‐electrode arrays used in resistivity sounding and profiling, the dipole‐dipole array can provide, in some instances, advantages over the more conventional Schlumberger and Wenner configurations. Interpretation of data from Wenner and Schlumberger methods has been described by Compagnie Générale de Géophysique (1955), Mooney and Wetzel (1956), Zohdy (1964), and many others. The primary reason for using a dipole‐dipole array has been to minimize inductive coupling between the transmitting and receiving dipoles when performing frequency‐domain, induced‐polarization surveys (e.g., Marshall and Madden, 1959). This inductive coupling, as effected by the presence of the earth, produces spurious frequency‐dependent voltages in the measuring circuit. Such spurious voltages are small and only of importance when one wishes to calculate the percentage change in resistivity between two frequencies; they are usually much less than the 5 to 10 percent accuracy sought in most resistivity surveys. For this reason, and because the dipole‐dipole array leads to small measured potentials, it is seldom used in single‐frequency resistivity sounding or profiling. However, we shall demonstrate in this paper the manner in which the dipole‐dipole array may be used effectively for simultaneous sounding and profiling.


Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 768-780 ◽  
Author(s):  
B. B. Bhattacharya ◽  
M. K. Sen

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.


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