Distortion in resistivity logging at shallow depth

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1058-1069 ◽  
Author(s):  
Tien‐Chang Lee ◽  
Brian N. Damiata
Keyword(s):  
Point Source ◽  
Line Source ◽  
Apparent Resistivity ◽  
Homogeneous Medium ◽  
Radial Distance ◽  
Ground Surface ◽  
Current Electrode ◽  
Potential Electrode ◽  
Resistivity Logging ◽  
Source Array

Owing to the proximity of an insulating ground surface, normal resistivity logging at shallow depths (less than 30 m) can yield an apparent resistivity that exceeds 200% of the formation resistivity for a homogeneous medium. The distortion is more acute for long‐normal than for short‐normal logging. Three examples from a landfill site in southern California are presented to show such distortion. The patterns of distortion are similar for logging devices consisting of either two point‐source electrodes or one point‐source and one finite length, line‐source electrode. The former electrode array is a generally accepted approximation of the latter. However, the simulated apparent resistivity for the line‐source array is greater than that for the point‐source array at any given depth. A resistivity contrast between the formation and the borehole fluid can shift the magnitude of the background apparent resistivity but does not significantly alter the pattern of distortion. The magnitude of the distortion can be reduced by placing the reference‐ground potential electrode at a radial distance that is about equal to the spacing between the downhole upper potential electrode and the upper current electrode. It can also be removed by including the radial distance in an array‐dependent geometric factor that accounts for the resistivity of the borehole fluid and the proximity of the logging device to the ground surface.

APPARENT RESISTIVITY CURVES FOR AN INFINITE LINE SOURCE PARALLEL TO AN INCLINED CONTACT

Geophysics ◽  
1975 ◽  
Vol 40 (4) ◽  
pp. 689-693 ◽  
Author(s):  
Sri Niwas ◽  
S. K. Upadhyay
Keyword(s):  
Point Source ◽  
Line Source ◽  
Apparent Resistivity ◽  
Master Curves ◽  
Harmonic Method ◽  
Resistivity Data ◽  
Infinite Line

Investigations of apparent resistivity due to a point source over an inclined contact have been reported by Aldredge (1937), Unz (1953), Maeda (1955), and Chastenet de Gery and Kunetz (1956). In these investigations either the image or the harmonic method has been utilized. In this note, we propose to solve the same problem as follows: (1) Transform point‐source potential data into line‐source apparent resistivity data. (2) Interpret transformed apparent resistivities by the master curves provided.

Depth of investigation studies for gradient arrays over homogeneous isotropic half‐space

Geophysics ◽  
1982 ◽  
Vol 47 (8) ◽  
pp. 1198-1203 ◽  
Author(s):  
B. B. Bhattacharya ◽  
Indrajit Dutta
Keyword(s):  
Point Source ◽  
Unit Length ◽  
Radial Distance ◽  
Current Electrode ◽  
Point Electrode ◽  
Maximum Value ◽  
Finite Line ◽  
Infinite Line ◽  
Electrode Systems ◽  
Depth Of Investigation

The depth of investigation of gradient arrays using point, finite, and infinite line sources over homogeneous isotropic ground has been studied. The depth of investigation depends for all cases on the radial distance of the plotting point (i.e., the midpoint of the line joining the potential probes) and separation between the current electrodes. For point electrode systems, it also depends upon azimuth of the plotting point, whereas for finite line electrode systems, it depends upon the azimuth and the length of the line electrode. The depth of investigation at the center of the array is maximum (0.145 L) for infinite line electrodes, decreases to 0.135 L for finite line electrodes of length L, and becomes least (0.125 L) for the point source, where L is the separation between the current electrodes. The depth of investigation for finite line electrodes of unit length L is practically independent of the y‐coordinate which is mathematically the case for infinite line electrode systems. The depth of investigation is least toward the current electrode and increases as one moves away from the current electrode; it ultimately reaches the maximum value of 0.135 L at the center of the system. The depth of investigation for point electrode systems is also minimum near the current electrode and increases with the increase of azimuth for any radial distance.

Effects of geologic noise on cross‐borehole electrical surveys

Geophysics ◽  
1986 ◽  
Vol 51 (10) ◽  
pp. 1978-1991 ◽  
Author(s):  
J. X. Zhao ◽  
L. Rijo ◽  
S. H. Ward
Keyword(s):  
Surface Topography ◽  
Apparent Resistivity ◽  
Field Studies ◽  
Current Electrode ◽  
Potential Electrode ◽  
Subsurface Current ◽  
Vertical Contact ◽  
Element Algorithm ◽  
Source Electrode ◽  
Layered Half Space

Using a finite‐element algorithm which allows for subsurface current and potential electrodes in dc resistivity, we have analyzed the detection of a thin, 2-D, conductive inhomogeneity in the presence of several sources of geologic noise. The pole‐pole array with the current electrode fixed in one borehole and the potential electrode movable in adjacent boreholes is the main array of concern. The sources of noise are surface topography, buried topography, random geologic noise, quasi‐random geologic noise (nontarget inhomogeneities), layering, and a vertical contact. For several positions of a downhole source electrode, normalized apparent resistivities have been computed. These resistivities have been contoured in section view as appropriate to cross‐borehole investigations. For the models studied here, surface topography, buried topography, random and quasi‐random geologic noise do not obscure the anomaly due to the thin conductive inhomogeneity. In a vertically or horizontally layered earth, the anomaly due to the inhomogeneity is almost totally obscured. Normalization of the apparent resistivity by the variable apparent resistivity of a layered half‐space can help alleviate the problem. However, it may not be possible to apply such normalization in field studies. Other arrays such as the cross‐borehole dipole‐dipole array, with the dipoles moved simultaneously, may then be required.

scholarly journals Method of Integral Equations for the Problem of Electrical Tomography in a Medium with Ground Surface Relief

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Tolkyn Mirgalikyzy ◽  
Balgaisha Mukanova ◽  
Igor Modin
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Surface Relief ◽  
Apparent Resistivity ◽  
Homogeneous Medium ◽  
Ground Surface ◽  
Surface Shape ◽  
Electrical Tomography ◽  
Secondary Current ◽  
Method Of Integral Equations

The direct task of the subsurface exploration of a homogeneous medium with surface relief by the resistivity method is analyzed. To calculate the resistivity field for such a medium, the method of integral equations was successfully applied for the first time. The corresponding integral equation for the density of secondary current sources on the surface of the medium was established. The method of computational grid construction, adapted to the characteristics of the surface relief, was developed for the numerical solution of the integral equation. This method enables the calculation of the resistivity field of a point source on a surface that is not smooth and allows for steep ledges. Numerical examples of the calculation of resistivity fields and apparent resistivity are shown. The anomalies of apparent resistivity arising from the deviation of the surface shape from a flat medium were quantitatively established as model examples. Calculations of apparent resistivity for the direct current sounding method were carried out using modifications of the electrical tomography approach.

scholarly journals Semi-analytical solutions of seismo-electromagnetic signals arising from the motional induction in 3-D multi-layered media: part II—numerical investigations

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Hengxin Ren ◽  
Ling Zeng ◽  
Yao-Chong Sun ◽  
Ken’ichi Yamazaki ◽  
Qinghua Huang ◽  
...  
Keyword(s):  
Point Source ◽  
Numerical Computation ◽  
Wave Velocity ◽  
Excellent Agreement ◽  
Seismic Waves ◽  
Averaging Method ◽  
Ground Surface ◽  
Induction Effect ◽  
Motional Induction ◽  
Electromagnetic Signals

AbstractIn this paper, numerical computations are carried out to investigate the seismo-electromagnetic signals arising from the motional induction effect due to an earthquake source embedded in 3-D multi-layered media. First, our numerical computation approach that combines discrete wavenumber method, peak-trough averaging method, and point source stacking method is introduced in detail. The peak-trough averaging method helps overcome the slow convergence problem, which occurs when the source–receiver depth difference is small, allowing us to consider any focus depth. The point source stacking method is used to deal with a finite fault. Later, an excellent agreement between our method and the curvilinear grid finite-difference method for the seismic wave solutions is found, which to a certain degree verifies the validity of our method. Thereafter, numerical computation results of an air–solid two-layer model show that both a receiver below and another one above the ground surface will record electromagnetic (EM) signals showing up at the same time as seismic waves, that is, the so-called coseismic EM signals. These results suggest that the in-air coseismic magnetic signals reported previously, which were recorded by induction coils hung on trees, can be explained by the motional induction effect or maybe other seismo-electromagnetic coupling mechanisms. Further investigations of wave-field snapshots and theoretical analysis suggest that the seismic-to-EM conversion caused by the motional induction effect will give birth to evanescent EM waves when seismic waves arrive at an interface with an incident angle greater than the critical angle θc = arcsin(Vsei/Vem), where Vsei and Vem are seismic wave velocity and EM wave velocity, respectively. The computed EM signals in air are found to have an excellent agreement with the theoretically predicted amplitude decay characteristic for a single frequency and single wavenumber. The evanescent EM waves originating from a subsurface interface of conductivity contrast will contribute to the coseismic EM signals. Thus, the conductivity at depth will affect the coseismic EM signals recorded nearby the ground surface. Finally, a fault rupture spreading to the ground surface, an unexamined case in previous numerical computations of seismo-electromagnetic signals, is considered. The computation results once again indicate the motional induction effect can contribute to the coseismic EM signals.

Determination of Dynamic Dispersion Coefficient for Solid Particles Flowing in a Fracture With Consideration of Gravity Effect

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Yanan Ding ◽  
Xiaoyan Meng ◽  
Daoyong Yang
Keyword(s):  
Particle Size ◽  
Point Source ◽  
Line Source ◽  
Dispersion Coefficient ◽  
Solid Particles ◽  
Gravity Effect ◽  
Dispersion Coefficients ◽  
Source Condition ◽  
Advection Diffusion Equation ◽  
Gravity Settling

Abstract A robust and pragmatic method has been developed and validated to analytically determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture, in which gravity settling has been considered due to its significant impact on particle flowing behavior. More specifically, a two-dimensional (2D) advection–diffusion equation together with the initial and boundary conditions has been formulated to describe the flow behavior of finite-sized particles on the basis of coupling the Poiseuille flow with vertical settling. Meanwhile, three types of instantaneous source conditions (i.e., point source, uniform line source, and volumetric line source) have been considered. Explicit expressions, which can directly and time-efficiently calculate dynamic dispersion coefficient, have been derived through the moment analysis and the Green’s function method. By performing the simulation based on the random walk particle tracking (RWPT) algorithm, the newly developed model has been verified to determine particle dispersion coefficients agreeing well with those obtained from the RWPT simulations. It is found that the point source is the most sensitive to gravity effect among different source conditions, while the volumetric line source is affected more than the uniform line source. For particle size larger than its critical value, an increased particle size leads to a decreased asymptotical dispersion coefficient for all the source conditions due to the significant gravity effect, while gravity positively affects the dispersion coefficient at early times for the point source condition. In addition, average flow velocity positively affects the dispersion coefficient for all the source conditions, while the associated gravity effect is influenced only at early times for the point source condition.

scholarly journals Modelling the thermal radiation from kitchen hob fires

2020 ◽  
Vol 38 (4) ◽  
pp. 377-394
Author(s):  
Michael Spearpoint ◽  
Charlie Hopkin ◽  
Danny Hopkin
Keyword(s):  
Heat Flux ◽  
Point Source ◽  
Radial Distance ◽  
Source Model ◽  
View Factor ◽  
Calculation Methods ◽  
Fire Dynamics ◽  
Potential Threat ◽  
Computational Tools

Kitchen hob fires present a potential threat to occupants escaping from dwellings and calculations may be needed to assess the hazard. Determination of the thermal heat flux from flames to a target can be achieved through the use of hand calculation methods or computational tools. This article compares point source, parallel plane and cylindrical view factor hand calculations and computational simulations using B-RISK and Fire Dynamics Simulator of thermal heat flux with kitchen hob fire experiments presented in the literature. Knowing the level of accuracy of each method provides useful information to designers. Although the point source model is influenced by whether the radial distance is measured perpendicular to the heat flux target or is offset relative to the centre of the flame, the article concludes that it provides an adequate approach for the calculation of thermal heat flux in the case of kitchen hob fires.

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