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.

Advanced inversion methods for airborne electromagnetic exploration

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1983-1992 ◽  
Author(s):  
Klaus‐Peter Sengpiel ◽  
Bernhard Siemon
Keyword(s):  
Half Space ◽  
Apparent Resistivity ◽  
Target Identification ◽  
Initial Step ◽  
Conducting Layer ◽  
Geologic Mapping ◽  
Enhanced Sensitivity ◽  
Airborne Electromagnetic ◽  
The Right ◽  
Layered Half Space

Airborne electromagnetic (AEM) surveys can contribute substantially to geologic mapping and target identification if good‐quality multifrequency data are produced, properly evaluated, and displayed. A set of multifrequency EM data is transformed into a set of apparent resistivity ([Formula: see text]) and centroid depth ([Formula: see text]) values, which then are plotted as a sounding curve. These [Formula: see text] curves commonly provide a smoothed picture of the vertical resistivity distribution at the sounding site. We have developed and checked methods to enhance the sensitivity of sounding curves to vertical resistivity changes by using new definitions for apparent resistivity and centroid depth. One of these new sounding curves with enhanced sensitivity to vertical resistivity contrasts is plotted from [Formula: see text] [Formula: see text] values derived from differentiation of the [Formula: see text] curve with respect to the frequency f. This approach is similar to the Niblett‐Bostick transform used in magnetotellurics. It not only enhances vertical changes in resistivity but also increases the depth of investigation. Sounding curves can be calculated directly from EM survey data and can be used to generate a resistivity‐depth parasection. Based on such a section, it can be decided whether a Marquardt‐type inversion of the AEM data into a 1-D layered half‐space model is adequate. Each sounding curve can be transformed into an initial step model of resistivity as required for the Marquardt inversion. We have inverted data from sedimentary sequences with good results. For data from a dipping conducting layer and a dipping plate, we have found that the results depend on the right choice of the starting model, in which the number of layers should be large rather than too small. Complex resistivity structures, however, often are represented better by using the sounding‐curve results than with the parameters of a layered half‐space.

QUADRIPOLE‐QUADRIPOLE ARRAYS FOR DIRECT CURRENT RESISTIVITY MEASUREMENTS—MODEL STUDIES

Geophysics ◽  
1976 ◽  
Vol 41 (1) ◽  
pp. 79-95 ◽  
Author(s):  
Dariu Doicin
Keyword(s):  
Half Space ◽  
Electric Fields ◽  
Direct Current ◽  
Apparent Resistivity ◽  
Cross Product ◽  
Resistivity Measurements ◽  
Model Studies ◽  
True Resistivity ◽  
Vertical Contact ◽  
Source Dipole

For a quadripole‐quadripole array, in which current is sequentially injected into the ground by two perpendicular dipoles, an apparent resistivity can be defined in terms of the vectorial cross product of the two electric fields measured at the receiver site. Transform equations are derived (for horizontally layered media) which relate this apparent resistivity to the apparent resistivities obtained with conventional dipole‐dipole and Schlumberger arrangements. To evaluate the method, two mathematical models are used. The first model is a half‐space with an “alpha conductivity center,” and the second model is a half‐space with a vertical contact. For an idealized quadripole‐quadripole array, simple expressions are found for the apparent resistivity, which is shown to be independent of the orientation of the current quadripole. Theoretical anomalies calculated for the quadripole‐quadripole array are compared with those obtained for a dipole‐quadripole array. It is shown that whereas the apparent resistivity map for the dipole‐quadripole array varies greatly with the azimuth of the source dipole, the results obtained with the quadripole‐quadripole array consistently display a remarkable resemblance to the assumed distribution of true resistivity. This is especially true when the current quadripole is placed at a large distance from the surveyed area.

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.

Removal of static shift in two dimensions by regularized inversion

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2102-2106 ◽  
Author(s):  
Catherine deGroot‐Hedlin
Keyword(s):  
Electric Fields ◽  
Apparent Resistivity ◽  
Skin Depth ◽  
Two Dimensions ◽  
Small Scale ◽  
Low Frequencies ◽  
Near Surface ◽  
Regularized Inversion ◽  
Conductivity Anomalies ◽  
Local Distortions

A common problem in magnetotelluric (MT) sounding is the presence of static shifts in the data, i.e., a vertical shifting of the log‐apparent‐resistivity versus period curves relative to regional values (Jones, 1988; Jiracek, 1990; Berdichevsky et al., 1989). These static shifts are due to the presence of small‐scale, shallow conductivity anomalies near the measurement site. Electric charge builds up on near‐surface anomalies that are small in comparison to the skin depth of the electromagnetic (EM) fields. The charge buildup produces a perturbation of the measured electric fields from their regional values that persists to arbitrarily low frequencies. Incorrect removal of these local distortions leads to incorrect interpretation of the deeper targets of investigation.

To: “The electromagnetic response of thin sheets buried in a uniformly conducting half‐space,” by R. Clark Robertson in January 1987 GEOPHYSICS, p. 108–117

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 583-583
Keyword(s):  
Electric Field ◽  
Half Space ◽  
Thin Sheet ◽  
Skin Depth ◽  
Modeling Technique ◽  
Electromagnetic Response ◽  
Thin Sheets ◽  
Incident Electric Field

On p. 112, the caption of Figure 4 should read “The (a) magnitude and (b) phase in radians of the x component of the horizontal electric field obtained for a square thin sheet of integrated conductivity 1 S, 8 skin depths on a side, buried at a depth of 0.1 skin depth when the incident electric field is x polarized. Each segment is 1 skin depth on a side.” On p. 114, the last sentence of the first paragraph in the Discussion should read “It is easy to see why the surface thin sheet is a popular modeling technique for magnetotelluric applications.”

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].

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.

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.

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