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.

The use of quad–quad resistivity in helicopter electromagnetic mapping

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 459-467 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Apparent Resistivity ◽  
Single Frequency ◽  
Magnetic Polarization ◽  
Phase Component ◽  
Misleading Information ◽  
High Frequencies ◽  
Quadrature Component ◽  
The Earth ◽  
The Impact ◽  
Dependent Choice

The apparent resistivity from a helicopter-borne frequency-domain electromagnetic (EM) system is typically obtained from the in-phase and quadrature responses arising from the flow of conduction currents in the earth. The most commonly used resistivity algorithms, derived from half-space models and using single-frequency data, do not account for magnetic polarization and consequently do not yield a reliable value for apparent resistivity in highly magnetic areas. This is because magnetic polarization modifies the EM response, causing the computed resistivity to be erroneously high. The impact of magnetic permeability on the EM response is much greater for the in-phase component than for the quadrature component. If magnetic polarization is to be ignored, the calculation of the apparent resistivity using the quadrature component at two frequencies (the quad–quad algorithm) is less subject to error from magnetic polarization than if the in-phase and quadrature responses at a single frequency are used (the in-phase–quad algorithm). The quad–quad algorithm, however, can display undesirable behavior for large induction numbers, i.e., when conductivities and frequencies are large. Determining which algorithm is optimum is a data-dependent choice, which, of course, is area dependent. We have studied the behavior of the quad–quad (apparent) resistivity and its comparison to in-phase–quad resistivity to determine the conditions under which the use of quad–quad resistivity is appropriate. For a two-layer earth, the behavior of the quad–quad resistivity depends mainly upon the ratio of the lower frequency fL to the upper-layer resistivity ρ1. If this ratio is low, the quad–quad resistivity will behave well. In areas yielding a high value of the ratio fL/ρ1, the quad–quad resistivity may lie outside of the range of the true resistivities of the earth and therefore provide misleading information. Our studies therefore suggest that the quad–quad resistivity algorithm should be avoided in areas where the ratio is large, i.e., when using high frequencies in conductive areas. The term large is relative. For a two-layer case, for example, the use of quad–quad resistivity is only recommended for magnetic areas where fL/ρ1 < 500 Hz/ohm-m, when conductive cover exists, and where fL/ρ1 < 50 Hz/ohm-m when a conductive basement underlies resistive cover. In spite of these limitations, quad–quad resistivity is often preferable to in-phase–quad resistivity in highly magnetic areas.

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].

Detecting metal objects in magnetic environments using a broadband electromagnetic method

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1877-1887 ◽  
Author(s):  
Haoping Huang ◽  
I. J. Won
Keyword(s):  
Magnetic Permeability ◽  
Field Studies ◽  
Unexploded Ordnance ◽  
Apparent Conductivity ◽  
Physical Experiments ◽  
Detection And Identification ◽  
Em Method ◽  
Magnetic Basement ◽  
Quadrature Response ◽  
Layered Half Space

We analyze the use of the broadband electromagnetic (EM) method in detecting metallic objects, such as unexploded ordnance (UXO), buried in magnetic environments. Magnetic rocks close to the sensor often contribute a larger in‐phase response than does the target at depth, making target detection and identification difficult. On the other hand, magnetic rocks contribute little quadrature response, which gives rise to the concept of using quadrature response and apparent conductivity to detect metallic objects in highly magnetic environments. To test this concept, we employed numeric models, physical experiments, and field studies. A layered half‐space simulated conductive overburden and magnetic basement. Sphere models are used for isolated magnetic rocks and metal targets. The responses of the layered earth, magnetic rocks, and metal objects were added to obtain the approximate total response. We then inverted the EM data into apparent magnetic permeability and conductivity. The EM response at the lowest frequency was used initially to estimate apparent magnetic permeability, which let us calculate the apparent conductivity using the EM data at all frequencies. The simulations and field examples show that broadband EM sensors can detect small metal targets in magnetic environments, mainly by the quadrature component of the responses and the apparent conductivity.

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.

Influence of permeability on wave-tilt of EM waves

1982 ◽  
Vol 19 (6) ◽  
pp. 1323-1325 ◽  
Author(s):  
Ramesh P. Singh ◽  
Tarkeshwar Lal
Keyword(s):  
Half Space ◽  
Magnetic Permeability ◽  
Pronounced Effect ◽  
Earth Model ◽  
Theoretical Studies ◽  
Computational Results ◽  
Frequency Range ◽  
Magnetic Wave ◽  
Homogeneous Half Space ◽  
Wave Tilt

Theoretical studies on the influence of magnetic permeability on the amplitude and phase of electric and magnetic wave-tilt have been carried out in the frequency range 102–106 Hz over a homogeneous half-space Earth model. Computational results show a pronounced effect of magnetic permeability on the amplitude of wave-tilt measurements.

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.

scholarly journals Neuronal avalanches in input and associative layers of auditory cortex

2019 ◽  
Author(s):  
Zac Bowen ◽  
Daniel E. Winkowski ◽  
Saurav Seshadri ◽  
Dietmar Plenz ◽  
Patrick O. Kanold
Keyword(s):  
Auditory Cortex ◽  
Information Transfer ◽  
Dynamic Range ◽  
Speech Sound ◽  
Power Laws ◽  
Single Frequency ◽  
Population Activity ◽  
Sound Levels ◽  
Neuronal Avalanches

AbstractThe primary auditory cortex processes acoustic sequences for the perception of behaviorally meaningful sounds such as speech. Sound information arrives at its input layer 4 from where activity propagates to associative layer 2/3. It is currently not known whether there is a particular organization of neuronal population activity that is stable across layers and sound levels during sound processing. We used in vivo 2-photon imaging of pyramidal neurons in cortical layers L4 and L2/3 of mouse A1 to characterize the populations of neurons that were active spontaneously, i.e. in the absence of a sound stimulus, and those recruited by single-frequency tonal stimuli at different sound levels. Single-frequency sounds recruited neurons of widely ranging frequency selectivity in both layers. We defined neural ensembles as neurons being active within or during successive temporal windows at the temporal resolution of our imaging. For both layers, neuronal ensembles were highly variable in size during spontaneous activity as well as during sound presentation. Ensemble sizes distributed according to power laws, the hallmark of neuronal avalanches, and were similar across sound levels. Avalanches activated by sound were composed of neurons with diverse tuning preference, yet with selectivity independent of avalanche size. Thus, spontaneous and evoked activity in both L4 and L2/3 of A1 are composed of neuronal avalanches with similar power law relationships. Our results demonstrate network principles linked to maximal dynamic range, optimal information transfer and matching complexity between L4 and L2/3 to shape population activity in auditory cortex.

scholarly journals A Two-parameter Family of Exponentially-fitted Obrechkoff Methods for Second-order Boundary Value Problems

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Ashiribo Wusu
Keyword(s):  
Parameter Family ◽  
Single Frequency ◽  
Frequency Method ◽  
New Methods ◽  
New Family ◽  
Obrechkoff Methods ◽  
Periodic Behaviour ◽  
Leading Term ◽  
Exponentially Fitted ◽  
Two Parameter

Generally, classical numerical methods may not be well suited for problems with oscillatory or periodic behaviour. To overcome this deficiency, they are modified using a technique called exponential fittings. The modification makes it possible to construct new methods suitable for the efficient integration of oscillatory or periodic problems from classical ones.In this work, a two--parameter family of exponentially--fitted Obrechkoff methods for approaching problems that exhibit oscillatory or periodic behaviour is constructed. The construction is based on a six-step flowchart described in [13]. Unlike the single--frequency method in [21], the constructed methods depend upon two frequencies which can be tuned to solve the problem at hand more accurately. The leading term of the local truncation error of the new family of method can also be easily obtained from the given general expression. The efficiency of the new methods is demonstrated on some numerical examples. This work is related to [20,21] and provides extension to the results obtained in [21]

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