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.

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.

scholarly journals Phaseless Gauss-Newton Inversion for Microwave Imaging

2020 ◽  
Author(s):  
Chaitanya Narendra ◽  
Puyan Mojabi
Keyword(s):  
Field Data ◽  
Prior Information ◽  
Structural Information ◽  
Microwave Imaging ◽  
The Other ◽  
Total Field ◽  
Field Phase ◽  
Full Data ◽  
L2 Norm ◽  
Phase Data

<p>A phaseless Gauss-Newton inversion (GNI) algorithm is developed for microwave imaging applications. In contrast to full-data microwave imaging inversion that uses complex (magnitude and phase) scattered field data, the proposed phaseless GNI algorithm inverts phaseless (magnitude-only) total field data. This phaseless Gauss-Newton inversion (PGNI) algorithm is augmented with three different forms of regularization, originally developed for complex GNI. First, we use the standard weighted L2 norm total variation multiplicative regularizer which is appropriate when there is no prior information about the object being imaged. We then use two other forms of regularization operators to incorporate prior information about the object being imaged into the PGNI algorithm. The first one, herein referred to as SL-PGNI, incorporates prior information about the expected relative complex permittivity values of the object of interest. The other, referred to as SP-PGNI, incorporates spatial priors (structural information) about the objects being imaged. The use of prior information aims to compensate for the lack of total field phase data. The PGNI, SL-PGNI, and SP-PGNI inversion algorithms are then tested against synthetic and experimental phaseless total field data.</p>

scholarly journals Electrical Resistivity Profiles and Temperatures in the Ross Ice Shelf

1976 ◽  
Vol 16 (74) ◽  
pp. 307-308
Author(s):  
C.R. Bentley
Keyword(s):  
Electrical Resistivity ◽  
Computer Program ◽  
Depth Profile ◽  
Apparent Resistivity ◽  
Ice Shelf ◽  
Resistivity Measurements ◽  
Ross Ice Shelf ◽  
Field Season ◽  
A Site ◽  
Temperature Depth

AbstractDuring the 1973-74 Antarctic field season, two electrical resistivity profiles were completed along directions perpendicular to each other at a site in the south-easternpart of the Ross Ice Shelf. These profiles differ from each other only at short electrode spacings (less than 10 m) indicating no measurable horizontal anisotropy below the uppermost firn zone. The shape of the apparent resistivity curves is similar to that found by Hochstein on the Ross Ice Shelf near Roosevelt Island, but is displaced toward lower resistivities despite the colder 10 m temperature (—29°C instead of —26°C) at the more southerly site. Some factor other than temperature must therefore be effective in determining the overall magnitude of the resistivities in the shelf, although the variation with depth can still be expected to be primarily a temperature phenomenon.A computer program has been written to calculate apparent resistivities based on Crary’s analysis of temperatures in an ice shelf. Results are not yet available; when completed they should indicate the sensitivity of the resistivity measurements to differences in the temperature- depth profile, and hence their usefulness in estimating bottom melt/freeze rates.

A comparison of methods for approximating the vertical gradient of one‐dimensional magnetic field data

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1725-1735 ◽  
Author(s):  
J. W. Paine
Keyword(s):  
Magnetic Field ◽  
Fourier Transform ◽  
Field Data ◽  
Total Error ◽  
Vertical Gradient ◽  
Magnetic Data ◽  
Total Field ◽  
One Dimensional ◽  
Convolution Filter ◽  
Principal Factors

The vertical gradient of a one‐dimensional magnetic field is known to be a useful aid in interpretation of magnetic data. When the vertical gradient is required but has not been measured, it is necessary to approximate the gradient using the available total‐field data. An approximation is possible because a relationship between the total field and the vertical gradient can be established using Fourier analysis. After reviewing the theoretical basis of this relationship, a number of methods for approximating the vertical gradient are derived. These methods fall into two broad categories: methods based on the discrete Fourier transform, and methods based on discrete convolution filters. There are a number of choices necessary in designing such methods, each of which will affect the accuracy of the computed values in differing, and sometimes conflicting, ways. A comparison of the spatial and spectral accuracy of the methods derived here shows that it is possible to construct a filter which maintains a reasonable balance between the various components of the total error. Further, the structure of this filter is such that it is also computationally more efficient than methods based on fast Fourier transform techniques. The spacing and width of the convolution filter are identified as the principal factors which influence the accuracy and efficiency of the method presented here, and recommendations are made on suitable choices for these parameters.

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