scholarly journals The Behaviour of the Apparent Resistivity Phase Spectrum in the Case of a Polarizable Prism in an Unpolarizable Half-Space

1984 ◽  
Vol 15 (3) ◽  
pp. 191-191
Author(s):  
H. Soininen
Keyword(s):  
Half Space ◽  
Apparent Resistivity ◽  
Phase Spectrum

The behavior of the apparent resistivity phase spectrum in the case of two polarizable media

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 810-819 ◽  
Author(s):  
Heikki Soininen
Keyword(s):  
Frequency Dependence ◽  
Half Space ◽  
Time Constant ◽  
Apparent Resistivity ◽  
Dispersion Model ◽  
Phase Spectrum ◽  
The Body ◽  
Spectral Parameters ◽  
The Difference ◽  
True Time

I employed numerical modeling to examine the formation of the apparent resistivity phase spectrum first of a polarizable prism situated in a polarizable half‐space, and second of two polarizable prisms joined in an unpolarizable half‐space. The calculations were done using the integral equation technique. The frequency dependence of the resistivity of the polarizable medium is depicted by means of the Cole‐Cole dispersion model. The effect of a weakly polarizable half‐space may be handled by simply adding the phase angle of the half‐space to the apparent phase due to the body. The apparent spectral parameters can be inverted by fitting the sum of two Cole‐Cole dispersion model phase spectra to the apparent phase spectrum. Of the parameters describing the prism, the apparent chargeability is smaller than the chargeability of the original petrophysical spectrum because of geometric attenuation. The apparent frequency dependence, on the other hand, is very close to the value of the original frequency dependence. The apparent time constant is commonly also near the true time constant of the petrophysical spectrum. The values of the apparent spectral parameters of the polarizable half‐space are all close to their petrophysical or true values. The apparent spectrum of two polarizable prisms builds up in a complex fashion. Nevertheless, by measuring the spectra at a number of points along a profile crossing over two formations differing in time constant, the various components can be discriminated from the apparent spectrum even if the difference in time constant is small. As the conductivity contrast decreases, the share of the spectrum of the formation in the apparent spectrum increases. Similarly, the formation with the smaller time constant is in a more advantageous position than the body with the greater time constant.

The behavior of the apparent resistivity phase spectrum in the case of a polarizable prism in an unpolarizable half‐space

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1534-1540 ◽  
Author(s):  
Heikki Soininen
Keyword(s):  
Frequency Dependence ◽  
Half Space ◽  
Time Constant ◽  
Apparent Resistivity ◽  
Dispersion Model ◽  
Three Dimensional ◽  
Phase Spectrum ◽  
True Time ◽  
Polarizable Body ◽  
Lower Frequencies

In the application of the broadband induced polarization method, it is necessary to know how a petrophysical resistivity spectrum is transformed into an apparent spectrum measured in the field. Investigated in the present work was the forming of an apparent spectrum in the case of a polarizable three‐dimensional prism embedded in an unpolarizable half‐space for gradient and dipole‐dipole arrays. The computations were done numerically using the integral equation technique. The frequency dependence of the resistivity of the prism was depicted by means of the Cole‐Cole dispersion model. With this simple model geometry, the phase spectra of apparent resistivity resemble quite closely in functional form the original petrophysical phase spectrum of the Cole‐Cole dispersion model. The apparent spectra have shifted on the log‐log scale downward, owing to geometric attenuation, and toward lower frequencies. The apparent Cole‐Cole parameters have been inverted from the apparent spectra. The apparent chargeability is generally noticeably smaller, owing to the geometric attenuation, than the chargeability of the original petrophysical spectrum. The apparent frequency dependence, on the other hand, is very close to the value of the original frequency dependence. The shift of the apparent phase spectrum toward lower frequencies partly compensates for the decrease in the apparent time constant caused by attenuation of the spectrum. The apparent time constant is thus close to the true time constant of the petrophysical spectrum. It is therefore possible in principle to obtain by direct inversion from an apparent spectrum measured in the field a reasonable estimate of the frequency dependence and time constant of the true spectrum of a polarizable body.

Airborne resistivity and susceptibility mapping in magnetically polarizable areas

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 502-511 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Half Space ◽  
Magnetic Permeability ◽  
Apparent Resistivity ◽  
Dynamic Range ◽  
Single Frequency ◽  
Measured Signal ◽  
Apparent Permeability ◽  
Quadrature Component ◽  
New Methods ◽  
Quadrature Response

The apparent resistivity technique using half‐space models has been employed in helicopter‐borne resistivity mapping for twenty years. These resistivity algorithms yield the apparent resistivity from the measured in‐phase and quadrature response arising from the flow of electrical conduction currents for a given frequency. However, these algorithms, which assume free‐space magnetic permeability, do not yield a reliable value for the apparent resistivity in highly magnetic areas. This is because magnetic polarization also occurs, which modifies the electromagnetic (EM) response, causing the computed resistivity to be erroneously high. Conversely, the susceptibility of a magnetic half‐space can be computed from the measured EM response, assuming an absence of conduction currents. However, the presence of conduction currents will cause the computed susceptibility to be erroneously low. New methods for computing the apparent resistivity and apparent magnetic permeability have been developed for the magnetic conductive half‐space. The in‐phase and quadrature responses at the lowest frequency are first used to estimate the apparent magnetic permeability. The lowest frequency should be used to calculate the permeability because this minimizes the contribution to the measured signal from conduction currents. Knowing the apparent magnetic permeability then allows the apparent resistivity to be computed for all frequencies. The resistivity can be computed using different methods. Because the EM response of magnetic permeability is much greater for the in‐phase component than for the quadrature component, it may be better in highly magnetic environments to derive the resistivity using the quadrature component at two frequencies (the quad‐quad algorithm) rather than using the in‐phase and quadrature response at a single frequency (the in‐phase‐quad algorithm). However, the in‐phase‐quad algorithm has the advantage of dynamic range, and it gives credible resistivity results when the apparent permeability has been obtained correctly.

Magnetotelluric response on vertically inhomogeneous earth having conductivity varying exponentially with depth

Geophysics ◽  
1982 ◽  
Vol 47 (1) ◽  
pp. 89-99 ◽  
Author(s):  
D. Kao
Keyword(s):  
Half Space ◽  
Apparent Resistivity ◽  
Bessel Functions ◽  
Homogeneous Layer ◽  
Modified Bessel Functions ◽  
Layer Model ◽  
Transitional Layer ◽  
Number Of Layers ◽  
Inhomogeneous Models ◽  
Electric And Magnetic Fields

Magnetotelluric (MT) response is studied for a vertically inhomogeneous earth, where conductivity (or resistivity) varies exponentially with depth as [Formula: see text]. Horizontal electric and magnetic fields in such an inhomogeneous medium are given in terms of modified Bessel functions. Impedance and apparent resistivity are calculated for (1) an inhomogeneous half‐space having conductivity varying exponentially with depth, (2) an inhomogeneous half‐space overlain by a homogeneous layer, and (3) a three‐layer model with the second layer as an inhomogeneous or transitional layer. Results are presented graphically and are compared with those of homogeneous multilayer models. In the case of resistivity increasing exponentially with depth, the results of the above inhomogeneous models are equivalent to those of Cagniard two‐layer models, with [Formula: see text]. In the case of resistivity decreasing exponentially with depth, the homogeneous multilayer approximation depends upon the number of layers and the layer parameters chosen; |Z/ωμ| as a function of frequency is more useful than the apparent resistivity in determining the values of p and [Formula: see text].

Dielectric permittivity and resistivity mapping using high‐frequency, helicopter‐borne EM data

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 727-738 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Dielectric Permittivity ◽  
Half Space ◽  
High Frequency ◽  
Free Space ◽  
Apparent Resistivity ◽  
Phase Component ◽  
High Frequencies ◽  
Space Model ◽  
Homogeneous Half Space ◽  
Displacement Currents

The interpretation of helicopter‐borne electromagnetic (EM) data is commonly based on the transformation of the data to the apparent resistivity under the assumption that the dielectric permittivity is that of free space and so displacement currents may be ignored. While this is an acceptable approach for many applications, it may not yield a reliable value for the apparent resistivity in resistive areas at the high frequencies now available commercially for some helicopter EM systems. We analyze the feasibility of mapping spatial variations in the dielectric permittivity and resistivity using a high‐frequency helicopter‐borne EM system. The effect of the dielectric permittivity on the EM data is to decrease the in‐phase component and increase the quadrature component. This results in an unwarranted increase in the apparent resistivity (when permittivity is neglected) for the pseudolayer half‐space model, or a decrease in the apparent resistivity for the homogeneous half‐space model. To avoid this problem, we use the in‐phase and quadrature responses at the highest frequency to estimate the apparent dielectric permittivity because this maximizes the response of displacement currents. Having an estimate of the apparent dielectric permittivity then allows the apparent resistivity to be computed for all frequencies. A field example shows that the permittivity can be well resolved in a resistive environment when using high‐frequency helicopter EM data.

The differential parameter method for multifrequency airborne resistivity mapping

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 100-109 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Half Space ◽  
Apparent Resistivity ◽  
Skin Depth ◽  
Parameter Method ◽  
Apparent Depth ◽  
Analytic Method ◽  
Geologic Mapping ◽  
Depth Images ◽  
True Resistivity ◽  
Differential Parameter

Helicopter EM resistivity mapping began to be accepted as a means of geologic mapping in the late 1970s. The data were first displayed as plan maps and images. Some 10 years later, sectional resistivity displays became available using the same “pseudolayer” half‐space resistivity algorithm developed by Fraser and the new centroid depth algorithm developed by Sengpiel. Known as Sengpiel resistivity sections, these resistivity/depth images proved to be popular for the display of helicopter electromagnetic (EM) data in conductive environments. A limitation of the above resistivity and depth algorithms is that the resulting Sengpiel section may imply that the depth of exploration of the EM system is substantially less than is actually the case. For example, a target at depth may be expressed in the raw data, but its appearance on the Sengpiel section may be too shallow (which is a problem with the depth algorithm), or it may not even appear at all (which is a problem with the resistivity algorithm). An algorithm has been adapted from a ground EM analytic method that yields a parameter called the differential resistivity, which is plotted at the differential depth. The technique yields the true resistivity when the half‐space is homogeneous. It also tracks a dipping target with greater sensitivity and to greater depth than does the Sengpiel display method. The input parameters are the apparent resistivity and apparent depth from the pseudolayer half‐space algorithm and the skin depth for the various frequencies. The output parameters are differential resistivity and differential depth, which are computed from pairs of adjacent frequencies.

On: “Results of a controlled‐source audiofrequency magnetotelluric survey at the Puhimau thermal area, Kilauea Volcano, Hawaii” by L. C. Bartel and R. D. Jacobson (GEOPHYSICS, 52, 665–677, May 1987).

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 724-725 ◽  
Author(s):  
Hans‐Martin Maurer
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Apparent Resistivity ◽  
Near Field ◽  
Electrical Dipole ◽  
Controlled Source ◽  
Space Curves ◽  
Wave Approximation ◽  
The Given ◽  
Plane Wave Approximation

Bartel and Jacobson try to correct apparent resistivity values from CSAMT measurements, where the plane‐wave approximation is not valid. They want to convert CSAMT curves to passive MT curves (Cagniard curves), which can be interpreted by 2-D modeling. The measured CSAMT [Formula: see text] value is projected onto the [Formula: see text] axis in parallel with the half‐space curves of a horizontal electrical dipole in the given distance between receiver and transmitter. The example looks convincing, and it may be supposed to be a simple near‐field correction.

RESISTIVITY MAPPING WITH AN AIRBORNE MULTICOIL ELECTROMAGNETIC SYSTEM

Geophysics ◽  
1978 ◽  
Vol 43 (1) ◽  
pp. 144-172 ◽  
Author(s):  
Douglas C. Fraser
Keyword(s):  
Half Space ◽  
Apparent Resistivity ◽  
Electromagnetic System ◽  
Contour Maps ◽  
The Earth ◽  
Engineering Problems ◽  
Transmitter Coil ◽  
Survey System

Dighem is a helicopter‐borne 900 Hz multicoil electromagnetic survey system. The EM device consists of a 30-ft towed bird containing a transmitter coil in the front and three mutually orthogonal receiver coils in the rear. Resistivity contour maps can be prepared from the EM data using any of several half‐space models. In this paper, two such models are selected and field examples of apparent resistivity derived from them are shown. The multicoil system has encountered areas of widespread conductivity while surveying for metallic minerals. In such areas, EM anomalies can be generated by changes of less than 10 m in survey altitude. EM anomalies of apparent significance, therefore, can reflect decreases in survey altitude as well as increases in conductivity of the earth. Under such conditions, apparent resistivity contour maps can aid the interpretation of the airborne data. The advantage of the contour maps is that anomalies caused by altitude changes are substantially reduced, and the contours reflect mainly the conductive anomalies. Resistivity contour maps improve the interpreter's ability to differentiate between conductive trends in the bedrock and those patterns typical of conductive overburden. Airborne resistivity mapping can be applied to a number of engineering problems. The multicoil system has been used for permafrost delineation and gravel detection. To be useful, the geologic units being mapped should have a resistivity less than 1000 Ω-m (for the 900 Hz frequency) and a surface extent of several acres.

APPARENT RESISTIVITY OF A PERFECTLY CONDUCTING SPHERE BURIED IN A HALF‐SPACE

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 742-751 ◽  
Author(s):  
Shri Krishna Singh ◽  
Juan Manuel Espindola
Keyword(s):  
Computer Program ◽  
Half Space ◽  
Field Data ◽  
Apparent Resistivity ◽  
Total Field ◽  
Method Of Images ◽  
Conducting Sphere

Recently, the application of the method of images to obtain apparent resistivity of a perfectly conducting sphere buried in a half‐space has been criticized on the grounds that the number of images needed is too large. Instead, use of the method of graphs, in conjuction with the method of images, has been suggested. Although the number of images needed is large, they are easy to compute and many of them occupy the same position, thereby the amount of necessary computation is drastically reduced. A computer program based on the method of images is used to give normalized total‐field apparent resistivity contours for bipole‐dipole arrays. Such theoretical contours can be used to locate the epicenter of a conductive buried sphere by comparing them with field data.

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