A NEW METHOD FOR DIFFERENTIAL RESISTIVITY SOUNDING

Geophysics ◽  
1969 ◽  
Vol 34 (6) ◽  
pp. 924-943 ◽  
Author(s):  
Adel A. R. Zohdy
Keyword(s):  
Apparent Resistivity ◽  
New Method ◽  
Resolving Power ◽  
Symmetric System ◽  
Electrode Spacing ◽  
Electrode Arrays ◽  
Resistivity Sounding ◽  
Probing Depth ◽  
Earth Models ◽  
Homogeneous Media

A new method designated TDS (transverse differential sounding) is proposed for obtaining high resolution direct current resistivity soundings in the field. The measured apparent resistivity is designated TDR (transverse differential resistivity) and is defined by [Formula: see text], where [Formula: see text] and L are the Schlumberger apparent resistivity and electrode spacing, respectively. A collinear symmetric system (B′AMNBA′) consisting of two pairs of current electrodes and one pair of potential electrodes is used for measuring the value of [Formula: see text] directly in the field. For the interpretation of TDS curves obtained in the field, theoretical sets of master curves are computed either directly from the formal expression for [Formula: see text] in terms of Stefanesco’s kernel function and Bessel functions or by transformation of Schlumberger (VES) and/or dipole‐dipole sounding curves. Conversely, TDS and VES curves computed for the same horizontally stratified earth models and for corresponding electrode spacings are easily transformed, by means of simple relations, into radial, perpendicular, and parallel dipole‐dipole, or LDS (longitudinal differential sounding) curves. It is mathematically established that TDS curves, for horizontally stratified laterally homogeneous media, are identical to sounding curves obtained with a parallel dipole‐dipole array at an azimuth angle of 60 degrees, and that negative values of apparent resistivity [Formula: see text] are measured for certain geoelectric sections. Examples of theoretical TDS and LDS curves for two‐, three‐, and four‐layer earth models compared with corresponding VES curves illustrate the higher resolving power and greater probing depth of differential soundings. The field procedures and electric current requirements described for TDS and other types of soundings show that seven apparent resistivity values, corresponding to four electrode arrays, can be measured at each electrode setup.

What is the depth of investigation of a resistivity measurement?

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. W1-W10 ◽  
Author(s):  
Enrique Gómez-Treviño ◽  
Francisco J. Esparza
Keyword(s):  
Apparent Resistivity ◽  
Resistivity Measurement ◽  
Weighted Average ◽  
Sensitivity Function ◽  
Resistivity Sounding ◽  
Practical Applications ◽  
Resistivity Profile ◽  
Definition Of ◽  
Homogeneous Media ◽  
Depth Of Investigation

Ever since the first computation of resistivity sounding curves, there has been the impression that somehow they are averages of the vertical resistivity profile. This prompted the idea to represent apparent resistivity as an integral over depth and to define depth of investigation using the integrands of the integrals as elementary contributions. However, elementary contributions for a boundary value problem cannot be uniquely defined and are not physically meaningful. Many practical applications that have been derived from this approach might be at stake regarding their theoretical basis. On the other hand, a sensitivity function has a definite physical meaning and it is uniquely defined, but it offers a different picture for a layered earth. The concept of elementary contributions must then be abandoned as not real, as some respected scholars have suggested, or it must be put on solid ground if we are going to continue using it. Our claim is that any definition of elementary contributions must comply with the concept of sensitivity; otherwise, it must be discarded not because it might be proved wrong, but because we cannot have multiple functions pretending to represent the depth of investigation of a resistivity measurement. We determined that both concepts can be unified and reconciled into a single formulation. That is, one and the same function of depth can be interpreted as an elementary contribution or as the local sensitivity. To further support the effectiveness of the concept, we applied it beyond its traditional application to homogeneous media. We developed an approximate formula for computing apparent resistivity as a weighted average of the vertical resistivity profile. The formula works in the way of a toy model; it is an approximation, but it provides immediate insights into how a vertical resistivity profile relates to its sounding curve.

Computation of apparent resistivities using an exponential approximation of kernel functions

Geophysics ◽  
1986 ◽  
Vol 51 (8) ◽  
pp. 1594-1602 ◽  
Author(s):  
Sri Niwas ◽  
M. Israil
Keyword(s):  
Integral Equation ◽  
Apparent Resistivity ◽  
Electrode Array ◽  
Kernel Functions ◽  
Exponential Approximation ◽  
Electrode Arrays ◽  
Layered Earth ◽  
Earth Models ◽  
Electrical Prospecting ◽  
Mathematical Computation

We present a fresh approach to the mathematical computation of apparent resistivities in electrical prospecting. The method is based on an exponential approximation of the kernel function which reduces the integral equation for the potential over a layered earth to a simple algebraic equation. The coefficients in the approximation are obtained using a least‐squares inversion technique. A single, unified matrix equation allows computation of apparent resistivity values for arbitrary four‐electrode arrays over a layered earth. The unified G function automatically reduces to that of a symmetrical four‐electrode array and dipole array function with the proper interelectrode separation. Computations for some two‐, three‐, and four‐layer earth models (Schlumberger configuration), along with a few Wenner and radial dipole apparent resistivity values, demonstrate the versatility of this unified equation.

Magnetotelluric static shift: Estimation and removal using the cokriging method

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. F25-F34 ◽  
Author(s):  
Benoit Tournerie ◽  
Michel Chouteau ◽  
Denis Marcotte
Keyword(s):  
Apparent Resistivity ◽  
A Priori ◽  
Shift Factor ◽  
Static Shift ◽  
Geostatistical Model ◽  
Data Set ◽  
Resistivity Sounding ◽  
The Difference ◽  
Cross Variogram

We present and test a new method to correct for the static shift affecting magnetotelluric (MT) apparent resistivity sounding curves. We use geostatistical analysis of apparent resistivity and phase data for selected periods. For each period, we first estimate and model the experimental variograms and cross variogram between phase and apparent resistivity. We then use the geostatistical model to estimate, by cokriging, the corrected apparent resistivities using the measured phases and apparent resistivities. The static shift factor is obtained as the difference between the logarithm of the corrected and measured apparent resistivities. We retain as final static shift estimates the ones for the period displaying the best correlation with the estimates at all periods. We present a 3D synthetic case study showing that the static shift is retrieved quite precisely when the static shift factors are uniformly distributed around zero. If the static shift distribution has a nonzero mean, we obtained best results when an apparent resistivity data subset can be identified a priori as unaffected by static shift and cokriging is done using only this subset. The method has been successfully tested on the synthetic COPROD-2S2 2D MT data set and on a 3D-survey data set from Las Cañadas Caldera (Tenerife, Canary Islands) severely affected by static shift.

scholarly journals Numerical Modeling of the Effects of Electrode Spacing and Multilayered Concrete Resistivity on the Apparent Resistivity Measured Using Wenner Method

2020 ◽  
Author(s):  
Karthick Thiyagarajan ◽  
Parikshit Acharya ◽  
Lasitha Piyathilaka ◽  
sarath kodagoda
Keyword(s):  
Contact Area ◽  
Apparent Resistivity ◽  
Resistivity Measurement ◽  
Gaussian Process Regression ◽  
Electrode Spacing ◽  
Electrical Resistivity Measurement ◽  
Resistivity Measurements ◽  
Electrode Contact ◽  
Concrete Resistivity ◽  
Moisture Conditions

Smart Sensing technologies can play an important role in the conditional assessment of concrete sewer pipe linings. In the long-term, the permeation of acids can deteriorate the pipe linings. Currently, there are no proven sensors available to non-invasively estimate the depth of acid permeation in real-time. The electrical resistivity measurement on the surface of the linings can indicate the sub-surface acid moisture conditions. In this study, we consider acid permeated linings as a two resistivity layer concrete sample, where the top resistivity layer is assumed to be acid permeated and the bottom resistivity layer indicates normal moisture conditions. Firstly, we modeled the sensor based on the four-probe Wenner method. The measurements of the developed model were compared with the previous studies for validation. Then, the sensor model was utilized to study the effects of electrode contact area, electrode spacing distance and two resistivity layered concrete on the apparent resistivity measurements. All the simulations were carried out by varying the thickness of top resistivity layer concrete. The simulation study indicated that the electrode contact area has very minimal effects on apparent resistivity measurements. Also, an increase in apparent resistivity measurements was observed when there is an increase in the distance of the electrode spacing. Further, a machine learning approach using Gaussian process regression modeling was formulated to estimate the depth of acid permeated layer

scholarly journals Breaks in Resistivity Sounding Curves as Indicators of Hard Rock Aquifers

1983 ◽  
Vol 14 (1) ◽  
pp. 33-40 ◽  
Author(s):  
P. N. Ballukraya ◽  
R. Sakthivadivel ◽  
R. Baratan
Keyword(s):  
Empirical Study ◽  
Deep Water ◽  
Apparent Resistivity ◽  
Hard Rock ◽  
Fracture Zones ◽  
Resistivity Sounding ◽  
Resistivity Method ◽  
Hard Rock Aquifers

In a previous paper (Nordic Hydrology, Vol. 12, 1981), the authors have discussed the inadequacies in the technique of resistivity method for location of sites for constructing deep water walls in hard rock areas. It was pointed out that the water bearing fracture zones in the bed rock could not be identified by merely considering geoelectrical parameters such as layer resistivity. An empirical study based on the correlation of minor irregularities or deviations – “BREAKS” – in the normally smooth sounding curves with the actual driller's logs reveals that under normal geo-electric conditions these water bearing zones (hard rock aquifers) are indicated in the curve by a perceptible lowering of apparent resistivity and hence could be used as a guide for locating well sites. As such breaks may also be caused by other conditions such as lateral inhomogeneities, certain methods for distinguishing them are discussed.

The inverse problem of resistivity sounding

Geophysics ◽  
1984 ◽  
Vol 49 (12) ◽  
pp. 2143-2158 ◽  
Author(s):  
Robert L. Parker
Keyword(s):  
Inverse Problem ◽  
Apparent Resistivity ◽  
Single Point ◽  
Quadratic Program ◽  
Data Set ◽  
Regularization Technique ◽  
Resistivity Sounding ◽  
Best Fitting ◽  
Electrical Data ◽  
Fitting Model

The electric potential due to a single point electrode at the surface of a layered conducting medium is calculated by means of a linear combination of the potentials associated with a set of two‐layer systems. This new representation is called the bilayer expansion for the Green’s function. It enables the forward problem of resistivity sounding to be solved very efficiently, even for complicated profiles. Also, the bilayer expansion facilitates the solution of the resistivity inverse problem: the coefficients in the expansion are linearly related to apparent resistivity as it is measured and they are readily mapped into parameters for a model. Specifically, I consider models comprising uniformly conducting layers of equal thickness; for a given finite data set a quadratic program can be used to find the best‐fitting model in this class for any specified thickness. As the thickness is reduced, models of this kind can approximate arbitrary profiles with unlimited accuracy. If there is a model that satisfies the data well, there are other models equally good or better whose variation takes place in an infinitesimally thin zone near the surface, below which there is a perfectly conducting region. This extraordinary class of solutions underscores the serious ambiguity in the interpretation of apparent resistivity data. It is evident that strong constraints from outside the electrical data set must be applied if reliable solutions are to be discovered. Previous work seems to have given a somewhat overly optimistic impression of the resolving abilities of this kind of data. I consider briefly a regularization technique designed to maximize the smoothness of models found with the bilayer inversion.

scholarly journals Evaluation of groundwater supply potential from hydraulic parameters estimated from vertical electrical sounding (VES) in Ikeduru, south east Nigeria

2019 ◽  
Vol 7 (1) ◽  
pp. 67
Author(s):  
Nwosu Jacinta Chiemela ◽  
Leonard I Nwosu ◽  
Godwin O Chukwu
Keyword(s):  
Apparent Resistivity ◽  
Groundwater Exploration ◽  
Hydraulic Parameters ◽  
Protective Capacity ◽  
Resistivity Sounding ◽  
Groundwater Supply ◽  
Electrical Sounding ◽  
Supply Potential ◽  
Soil Corrosivity ◽  
Very High

A Vertical Electrical resistivity Sounding (VES) survey was carried out, to study the groundwater supply potential, protective capacity and soil corrosivity of aquifers in Ikeduru Local Government Area of Imo state, Nigeria. A total of ten (10) geoelectric soundings were acquired. Schlumberger electrode configuration was used in acquiring the data. Six to seven geoelectric layers were delineated from the interpreted results, the Aquifers were delineated between the fifth and sixth geoelectric layers, having an apparent resistivity above 1000Ωm, with the highest thick of 69.0m at a depth of 144.0m. Longitudinal Conductance, Hydraulic Conductivity, Transmissivity and Product Conductance range are as followings for the aquifers; 1.720 – 127.000 x 10-3Ω-1, 15.90 – 188.79m/day, 1093.3 – 1097.1m2/day and 2.590 – 252.50 x 10-3 respectively. Inferring from our hydraulic parameters, all the aquiferous zones have very high designation, wwithdrawal of great regional importance of groundwater supply potential and practically noncorrosive, soil corrosivity. 40% percentage of the aquiferous units have very good protective capacity, while for excellent and good protective capacity of the study are is 30%. All the VES points are said to be a very viable potential for safe source for groundwater exploration.  

scholarly journals Electrical resistivity measurements on Ice Stream B, Antarctica

1994 ◽  
Vol 20 ◽  
pp. 129-136
Author(s):  
S. Shabtaie ◽  
C.R. Bentley
Keyword(s):  
Electrical Resistivity ◽  
Theoretical Models ◽  
Electrode Spacing ◽  
High Resistivity ◽  
Resistivity Sounding ◽  
Basal Ice ◽  
A Value ◽  
Ice Stream ◽  
Ice Stream B ◽  
The Antarctic

Electrical resistivity sounding using the four-electrode Schlumberger array was carried out at station UpB on Ice Stream B to an electrode spacing of 3 km. Measured apparent resistivities were compared with theoretical models based on known relations between resistivity, density and temperature. Densities were measured in a pit and two coreholes; temperatures were measured in the upper 200 m of the ice stream and have been calculated for greater depth from an ice-stream temperature model. The resistivity, after correction for density and temperature, increases with depth down to 650-700 m. Below that is a marked decrease over the next 100m or so that we correlate with the Holocene-Wisconsin transition zone. Still deeper there is an orders-of-magnitude increase to a value, in the basal ice, of 30 MΩ m or more. This extremely high resistivity is similar to that reported for temperate glaciers and deep in the Antarctic ice sheet elsewhere. We attribute it to the destruction, by extensive metamorphism, of impurity-conduction paths at two-grain boundaries

A New Method for Starch Gel Electrophoresis of Human Hemoglobins, with Special Reference to the Determination of Hemoglobin A2

1958 ◽  
Vol 4 (6) ◽  
pp. 484-495 ◽  
Author(s):  
C A J Goldberg
Keyword(s):  
Special Reference ◽  
Gel Electrophoresis ◽  
New Method ◽  
Resolving Power ◽  
Buffer System ◽  
Starch Gel Electrophoresis ◽  
Healthy Individuals ◽  
Starch Gel ◽  
Hemoglobin A2

Abstract A method for starch gel electrophoresis of hemoglobins is presented in which a modified Lintner starch is used for the preparation of the gel. A discontinuous buffer system of tris-EDTA-borate/barbital is used as the electrolyte medium because of its superior resolving power. Hemoglobin A2 values, obtained with this method, of healthy individuals, patients with thalassemia, and those with various anemias of nonthalassemic origin are presented.

DEEP ELECTRICAL PROSPECTING—A DISCUSSION

Geophysics ◽  
1948 ◽  
Vol 13 (1) ◽  
pp. 92-97
Author(s):  
Sulhi Yüngül
Keyword(s):  
Apparent Resistivity ◽  
The Other ◽  
New Method ◽  
Depth Of Penetration ◽  
Method Of Calculation ◽  
Comprehensive Knowledge ◽  
Electrical Sounding ◽  
The Subject ◽  
Electrical Prospecting

In two papers published in Geophysics, one in the October, 1944, issue and the other in October, 1946, a system and method of calculation, called “Resistolog” method, was presented. The object of the Resistolog method is to eliminate the effects of superficial inhomogeneities which are the most troublesome obstacles in interpreting electrical sounding results in exploring deep, horizontal discontinuities. The following is a discussion of the papers mentioned above, mainly of the subject of (1) the apparent‐resistivity formula derived for use with the Resistolog configuration, (2) determination of inflectional points on apparent resistivity curves, (3) depth of penetration, and (4) distortion caused by the “far electrode.” A new method to determine inflectional points is also given. This paper includes a comprehensive knowledge about the forementioned papers and the reader may not have to refer to them.

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