APPARENT RESISTIVITY FOR DIPPING BEDS

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 123-139 ◽  
Author(s):  
Katsuro Maeda
Keyword(s):  
Differential Equation ◽  
Reflection Coefficient ◽  
Point Source ◽  
Electric Current ◽  
Potential Field ◽  
Apparent Resistivity ◽  
Computing Methods ◽  
Image Theory ◽  
The Earth ◽  
Dip Angle

The potential field of a point source of electric current, located on the surface of the earth above a dipping bed, is determined exactly by solving the appropriate differential equation. It is concluded that image theory is useful only in the two cases in which the reflection coefficient is plus one and the angle of dip is [Formula: see text] and in which the reflection coefficient is minus one and the dip angle is [Formula: see text] m being an integer. Computing methods are also developed for the cases in which the image theory is not applicable. Some numerical tables necessary for computation and several apparent resistivity curves are presented.

POTENTIAL AND APPARENT RESISTIVITY OVER DIPPING BEDS

Geophysics ◽  
1956 ◽  
Vol 21 (3) ◽  
pp. 780-793 ◽  
Author(s):  
Jerome Chastenet De Gery ◽  
Geza Kunetz
Keyword(s):  
Point Source ◽  
Current Density ◽  
Potential Field ◽  
Apparent Resistivity ◽  
Exact Expression ◽  
Electrode Configuration ◽  
Vertical Profiles ◽  
The Earth ◽  
Electrode Separation

The potential field due to a point source of current, located on the surface of the earth near a dipping bed, is given in an exact expression and modified expressions are developed for computations. These expressions lead to graphs of the potential field and to apparent resistivity vertical profiles which are presented. The Schlumberger electrode configuration is used. This configuration consists of two current electrodes and two potential electrodes, the latter placed close enough together that the current density between them can be considered to be uniform. With this configuration oriented perpendicular to the strike of the dipping bed, the apparent resistivity is paradoxical in that it approaches either zero or infinity as the electrode separation increases without limit.

ELECTRIC EARTH TRANSIENTS IN GEOPHYSICAL PROSPECTING

Geophysics ◽  
1936 ◽  
Vol 1 (2) ◽  
pp. 271-277 ◽  
Author(s):  
Louis Statham
Keyword(s):  
Electric Current ◽  
Salt Dome ◽  
Geophysical Prospecting ◽  
The Earth ◽  
Electrical Methods ◽  
The Times

A suddenly applied electric current is passed through the earth by means of spaced electrodes. The form of the potential transient as it appears outside the current electrodes is studied. The potential transient is extremely rapid and refined methods of recording are necessary. Means for measuring the relative times of the transient potentials received from different points are discussed. A survey taken over a known deep salt dome is shown; anomalous times of the transients are found to exist over the dome. No correlation is seen between the times of the transients and the resistivity as found by ordinary electrical methods.

scholarly journals Application of hybrid boundary element method: Example of semishperical ground inhomogeneity

2014 ◽  
Vol 11 (4) ◽  
pp. 617-628
Author(s):  
Nenad Cvetkovic ◽  
Sasa Ilic ◽  
Dragan Vuckovic ◽  
Dejan Jovanovic ◽  
Dejan Krstic
Keyword(s):  
Boundary Element Method ◽  
Point Source ◽  
Numerical Method ◽  
Boundary Element ◽  
Program Package ◽  
Image Theory ◽  
Field Analysis ◽  
Grounding System ◽  
Em Field ◽  
Element Method

One new, so-called hybrid boundary element method (HBEM) is presented in this paper. It is a recently proposed numerical method for stationary and quasi-stationary EM field analysis. The method application is illustrated on the example of solving the problem of modelling hemispherical ground inhomogeneity influence on grounding system. The applied procedure also includes using of quasi-stationary image-theory. The obtained results are compared with those ones based on using the Green?s function for the point source inside semi-spherical inhomogeneities as well as with the results obtained by applying COMSOL program package.

scholarly journals Experimental Reflection Evaluation for Attitude Monitoring of Space Orbiting Systems with NRL Arch Method

2021 ◽  
Vol 11 (18) ◽  
pp. 8632
Author(s):  
Andrea Delfini ◽  
Roberto Pastore ◽  
Fabrizio Piergentili ◽  
Fabio Santoni ◽  
Mario Marchetti
Keyword(s):  
Reflection Coefficient ◽  
Space Debris ◽  
Reflection Method ◽  
Reliable System ◽  
The Earth ◽  
Static Reflection ◽  
Wide Range ◽  
Space Age ◽  
Orbiting Systems ◽  
Tracking Objects

The increasing number of satellites orbiting around Earth has led to an uncontrolled increase in objects within the orbital environment. Since the beginning of the space age on 4 October 1957 (launch of Sputnik I), there have been more than 4900 space launches, leading to over 18,000 satellites and ground-trackable objects currently orbiting the Earth. For each satellite launched, several other objects are also sent into orbit, including rocket upper stages, instrument covers, and so on. Having a reliable system for tracking objects and satellites and monitoring their attitude is at present a mandatory challenge in order to prevent dangerous collisions and an increase in space debris. In this paper, the evaluation of the reflection coefficient of different shaped objects has been carried out by means of the bi-static reflection method, also known as NRL arch measurement, in order to evaluate their visibility and attitude in a wide range of frequencies (12–18 GHz). The test campaign aims to correlate the experimental measures with the hypothetical reflection properties of orbiting systems.

ELECTRIC POTENTIAL NEAR A SPHERICAL BODY IN A CONDUCTING HALF‐SPACE

Geophysics ◽  
1971 ◽  
Vol 36 (4) ◽  
pp. 763-767 ◽  
Author(s):  
David B. Large
Keyword(s):  
Point Source ◽  
Electric Current ◽  
Half Space ◽  
Electric Potential ◽  
Spherical Body ◽  
Classical Potential

An extensive summary of classical potential solutions has been given recently by Van Nostrand and Cook (1966). This note presents a solution for the potential due to a point source of electric current placed on the earth’s surface in the vicinity of a buried spherical body of arbitrary resistivity. The analysis follows the procedure suggested by Van Nostrand and Cook and is similar to that used recently by Merkel (1969, 1971).

On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1874-1874
Author(s):  
David A. Chapin
Keyword(s):  
Point Source ◽  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
New Method ◽  
Potential Fields ◽  
Potential Field Data ◽  
Source Method ◽  
Equivalent Point ◽  
Breakthrough Technology

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.

The time-dependent electric current from a flame

1984 ◽  
Vol 393 (1805) ◽  
pp. 297-308 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Electric Current ◽  
Diffusion Flame ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ionization Detector ◽  
Flame Ionization ◽  
Dependent Potential ◽  
Ionization Detectors

An earlier static treatment of the electric current from the diffusion flame in a flame ionization detector has been extended to include time-dependent currents. The nonlinear differential equation describing the electric field in the space outside the flame has been solved analytically for a class of problems in which a time-dependent potential difference is switched on after a static current has been established. Both one- and two-dimensional geometrical configurations are considered. The results could be useful in suggesting new experiments on flame ionization detectors.

The Analytical Solution of Single Pipe Piles under Axially and Laterally Free Loads

2011 ◽  
Vol 383-390 ◽  
pp. 1701-1707
Author(s):  
Zhe Wang ◽  
Si Fa Xu ◽  
Guo Cai Wang ◽  
Yong Zhang
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Lateral Deformation ◽  
Lateral Loads ◽  
Axial Loads ◽  
Influence Curves ◽  
The Earth ◽  
Inclined Loads ◽  
Single Pipe ◽  
Foundation Type

The analytical solution of a single pipe piles under axially and laterally loads is presented, when the laterally loads is optional free load. As piles foundations are becoming a preferred foundation type, piles usually work under simultaneous axial and lateral loads in engineering. To analyze the function of free loads to pipe piles under inclined loads conditions, in the basis of ‘m’ method, deformation differential equation of elastic piles under inclined loads is established first in the paper with analytical method. Differential equation has two parts in according to the piles in the earth or in the air, and lateral deformation, obliquity, moment; shearing force of the piles can be gotten respectively by soluting equations. In the end of the paper, influences of several parameters is analyzed of the top axial loads, the top lateral loads and the free loads, and their influence curves are given.

Attenuation of seismograms obtained by the Cagniard‐Pekeris method

Geophysics ◽  
1983 ◽  
Vol 48 (9) ◽  
pp. 1204-1211 ◽  
Author(s):  
P. G. Kelamis ◽  
E. R. Kanasewich ◽  
F. Abramovici
Keyword(s):  
Reflection Coefficient ◽  
Point Source ◽  
Frequency Domain ◽  
Elastic Medium ◽  
Half Space ◽  
Ad Hoc ◽  
Synthetic Seismograms ◽  
Weathered Layer ◽  
Attenuation And Dispersion

Attenuation and dispersion are included in synthetic seismograms obtained by a Cagniard‐Pekeris formulation for the problem of a point source in a layer over a half‐space. The solution is decompose into generalized rays, and the effects of attenuation and dispersion are incorporated in an ad hoc manner in the frequency domain. The effects of the viscoelastic interfaces are taken into account by corrections to the reflection coefficient for an elastic medium. The results are illustrated with synthetics for a model simulating a weathered layer over a halt‐space. Both the SH and P‐SV cases are treated.

THE USE OF CUMULATIVE RESISTANCE IN EARTH-RESISTIVITY SURVEYS

1945 ◽  
Vol 23a (4) ◽  
pp. 57-72 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Apparent Resistivity ◽  
Middle Layer ◽  
The Other ◽  
Electrode Spacing ◽  
Line Graphs ◽  
Earth Resistivity ◽  
The Earth ◽  
Straight Line ◽  
The Individual

When the soil is assumed to consist of two layers—the upper of resistivity ρ1 and the lower of resistivity ρ2—and cumulative resistances are calculated by adding or integrating the earth-resistivity functions for intervals that are a fraction of the thickness of the upper layer, a practically linear relation is obtained between the cumulative resistance and the electrode spacing until the distance between the electrodes is equal to the thickness of the upper material. Should one of the materials be at least twice as conducting as the other, the extent of the deviation from the linear law enables the determination of the depth of the upper stratum and of the ratio between the resistivities of the two layers. When three layers are present and the middle layer is at least twice as thick as the top stratum, the thicknesses may be deduced from the two departures of the cumulative resistances from the linear law. Since these conclusions are based on the theory of the individual apparent resistivity of stratified ground at various electrode spacings, they have the same range of application as the earth-resistivity curves, but the occurrence of straight line graphs facilitates the plotting and the interpretation of results based on a necessarily limited number of measurements.

Sign in / Sign up

Export Citation Format

Share Document