Depth sounding by means of a coincident coil frequency‐domain electromagnetic system

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 49-55 ◽  
Author(s):  
Kenneth Duckworth ◽  
Edward S. Krebes
Keyword(s):  
Frequency Domain ◽  
Half Space ◽  
Free Space ◽  
Thin Sheet ◽  
Electromagnetic System ◽  
Homogeneous Half Space ◽  
Scale Modeling ◽  
Physical Scale ◽  
Depth Sounding ◽  
Theoretical Developments

The concept of electromagnetic depth sounding by means of a coincident‐coil frequency‐domain electromagnetic system is developed in theory and demonstrated by means of physical scale modeling. The concept is based on the use of distance from the target as the sounding variable. The theoretical developments are confined to soundings conducted in free‐space with respect to either a homogeneous half‐space or a thin sheet conductor in conditions that approach the resistive limit. The use of distance from the target as the sounding variable becomes practical when the sounding system is a single compact unit of the type that a coincident coil concept inherently provides. In this method of sounding, the distance from the target is determined by taking the ratios of the fields measured at a variety of distances from the target conductor. This permits not only the distance to the target to be determined but also the direction to that target as may be of interest in soundings conducted in mines.

The transient EM step response of a dipping plate in a conductive half‐space

Geophysics ◽  
1992 ◽  
Vol 57 (9) ◽  
pp. 1116-1126 ◽  
Author(s):  
James E. Hanneson
Keyword(s):  
Half Space ◽  
Free Space ◽  
Early Time ◽  
Step Response ◽  
Current Loop ◽  
Late Time ◽  
Electromagnetic System ◽  
University Of Toronto ◽  
Transient Electromagnetic ◽  
Induction Process

An algorithm for computing the transient electromagnetic (TEM) response of a dipping plate in a conductive half‐space has been developed. For a stationary [Formula: see text] current loop source, calculated profiles simulate the response of the University of Toronto electromagnetic system (UTEM) over a plate in a 1000 Ω ⋅ m half‐space. The objective is to add to knowledge of the galvanic process (causing poloidal plate currents) and the local induction process (causing toroidal currents) by studying host and plate currents with respect to surface profiles. Both processes can occur during TEM surveys. Plates are all [Formula: see text] thick with various depths, dips, and conductances. Calculated host and plate currents provide quantitative examples of several effects. For sufficiently conductive plates, the late time currents are toroidal as for a free‐space host. At earlier times, or at all times for poorly conducting plates, the plate currents are poloidal, and the transitions to toroidal currents, if they occur, are gradual. At very late times, poloidal currents again dominate any toroidal currents but this effect is rarely observed. Stripped, point‐normalized profiles, which reflect secondary fields caused by the anomalous plate currents, illustrate effects such as early time blanking (caused by noninstantaneous diffusion of fields into the target), mid‐time anomaly enhancement (caused by galvanic currents), and late time plate‐in‐free‐space asymptotic behavior.

Magnetite mapping with a multicoil airborne electromagnetic system

Geophysics ◽  
1981 ◽  
Vol 46 (11) ◽  
pp. 1579-1593 ◽  
Author(s):  
Douglas C. Fraser
Keyword(s):  
Half Space ◽  
Eddy Current ◽  
Weight Percent ◽  
Positive Sign ◽  
Mapping Technique ◽  
Current Response ◽  
Magnetic Polarization ◽  
Electromagnetic System ◽  
Homogeneous Half Space ◽  
Frequency Independent

The information content of data from an in‐phase quadrature electromagnetic (EM) system consists of a combination of conductive eddy current response and magnetic polarization response. The secondary field resulting from conductive eddy current flow is frequency‐dependent and consists of both in‐phase and quadrature components of positive sign. Conversely, the field resulting from magnetic polarization is commonly frequency‐independent and consists of only an in‐phase component of negative sign. A magnetite mapping technique was developed for the horizontal coplanar coils of a closely coupled multicoil airborne EM system. The technique yields contours of apparent weight percent magnetite when using a homogeneous half‐space model. The method can be complementary to magnetometer mapping in certain cases. Compared to magnetometry, it is far less sensitive but is more able to resolve closely spaced magnetite zones. The method is also independent of remanent magnetism and magnetic latitude. It is sensitive to .25 percent magnetite by weight when the sensor is at a height of 30 m above a magnetitic half‐space. It can individually resolve steeply dipping narrow magnetite‐rich bands which are separated by 60 m.

Integral equation solution for the transient electromagnetic response of a three‐dimensional body in a conductive half‐space

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 798-809 ◽  
Author(s):  
William A. SanFilipo ◽  
Gerald W. Hohmann
Keyword(s):  
Integral Equation ◽  
Frequency Domain ◽  
Half Space ◽  
Time Constant ◽  
Free Space ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Basis Functions ◽  
The Body ◽  
Spatial Discretization

The time‐domain integral equation for the three‐dimensional vector electric field is formulated as a convolution of the scattering current with the tensor Green’s function. The convolution integral is divided into a sum of integrals over successive time steps, so that a numerical scheme can be formulated with a time stepping approximation of the convolution of past values of the solution with the system impulse response. This, together with spatial discretization, leads to a matrix equation in which previous solution vectors are multiplied by a series of matrices and fed back into the system by adding to the primary field source vector. The spatial discretization, based on a modification of the usual pulse basis formulation in the frequency domain, includes an additional subset of divergence‐free basis functions generated by integrating the Green’s function around concentric closed rectangular paths. The inductive response of the body is more accurately modeled with these additional basis functions, and a meaningful solution can be obtained for a body in free space. The resulting algorithm produces good results even for large conductivity contrasts. Internal checks, including convergence with respect to spatial and temporal discretization, and reciprocity, demonstrate self‐consistency of the numerical scheme. Independent checks include (a) comparison with results computed for a prism in free space, (b) comparison with results computed for a thin plate, (c) comparison of our conductive half‐space algorithm with an asymptotic solution for a sphere, and (d) comparison with results from inverse Fourier transformation of values computed using a frequency‐domain integral equation algorithm. Qualitative features of the results show that the relative importance of current channeling and confined eddy currents induced in the body depends upon both conductivity contrast and geometry. If the free‐space time constant is less than the time window during which currents in the host have not yet propagated well beyond the body, current channeling dominates the response. In such cases, simple superposition of free‐space results and the background is a poor approximation. In cases where the host currents diffuse beyond the body in a time less than the free‐space time constant of the body, the total response is approximately the sum of the free‐space and background (half‐space) responses.

SIMULATION OF TIME‐DOMAIN, AIRBORNE, ELECTROMAGNETIC SYSTEM RESPONSE

Geophysics ◽  
1969 ◽  
Vol 34 (5) ◽  
pp. 739-752 ◽  
Author(s):  
A. Becker
Keyword(s):  
Frequency Domain ◽  
Response Function ◽  
Time Domain ◽  
Digital Simulation ◽  
Thin Sheet ◽  
Scale Model ◽  
System Response ◽  
Electromagnetic System ◽  
Frequency Domain Response ◽  
Conducting Sheet

The response of a time‐domain electromagnetic system over a thin conducting sheet may be simulated by purely electronic means and without recourse to scale model experiments. The simulation is based on the similarity between the frequency domain response function for a thin sheet and the transfer function of certain RC active networks. Since this type of experiment employs actual field equipment, the proposed technique also constitutes a valid means of data quality control. It is difficult to carry out an analog simulation for conductors which do not resemble a thin sheet. If, however, the frequency domain response function for the situation in question is known, the simulation may be carried out on a digital computer. The digital simulation process involves a numerical Fourier decomposition of the primary field waveform (as seen by the receiver), the calculation of the effect of the ground on each harmonic component, and the recombination of the secondary field harmonics to form the observed transient. The technique is illustrated with some calculations of theoretical responses for an EM system over a homogeneous ground and over a thin horizontal conducting sheet. The digital simulation technique is more useful than the analog.

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.

Time‐domain solution for horizontal coaxial dipoles on a half‐space

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1850-1852 ◽  
Author(s):  
David C. Bartel
Keyword(s):  
Frequency Domain ◽  
Half Space ◽  
Time Domain ◽  
Inverse Laplace Transform ◽  
Direct Solution ◽  
Current Waveform ◽  
Laplace Domain ◽  
Homogeneous Half Space ◽  
The Time Domain ◽  
The Magnetic Field

The practice of transforming frequency‐domain results into the time domain is fairly common in electromagnetics. For certain classes of problems, it is possible to obtain a direct solution in the time domain. A summary of these solutions is given in Hohmann and Ward (1986). Presented here is another problem which can be solved directly in the time domain—the magnetic field of horizontal coaxial dipoles on the surface of a homogeneous half‐space. Solutions are presented for both an impulse transmitter current and a step turnon in the transmitter current. The solution in the time domain is obtained by taking the inverse Laplace transform of the product of the frequency‐domain solution and the Laplace‐domain representation of the current waveform.

QUANTITATIVE INTERPRETATION OF INPUT AEM MEASUREMENTS

Geophysics ◽  
1973 ◽  
Vol 38 (6) ◽  
pp. 1145-1158 ◽  
Author(s):  
G. J. Palacky ◽  
G. F. West
Keyword(s):  
Decay Rate ◽  
Half Space ◽  
Half Plane ◽  
Quantitative Approach ◽  
Quantitative Interpretation ◽  
Electromagnetic System ◽  
Quantitative Models ◽  
Apparent Conductivity ◽  
Homogeneous Half Space ◽  
Airborne Electromagnetic

Recent improvements of the INPUT airborne electromagnetic system have made possible a more quantitative approach to interpretation. The necessary interpretational aids can be obtained in two ways: either by correlating the system and ground EM measurements, or by devising computational or analog quantitative models. Both approaches have been explored. In the former, the system decay rate can be correlated with the apparent conductivity‐thickness (σt) estimated by ground surveys. In the latter, four quantitative models were investigated, vertical half‐plane, vertical ribbon, dipping half‐plane, and homogeneous half‐space. Nomograms have been constructed which make it possible to determine σt, conductor depth, and dip for sheet‐like conductors, and conductivity for a homogeneous half‐space. Field examples show that this procedure can be used satisfactorily in the routine interpretation of records obtained by this system.

scholarly journals Airborne electromagnetic footprints in 1D earths

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. G63-G72 ◽  
Author(s):  
James E. Reid ◽  
Andreas Pfaffling ◽  
Julian Vrbancich
Keyword(s):  
Sea Ice ◽  
Frequency Domain ◽  
Half Space ◽  
Field Data ◽  
Inductive Limit ◽  
Thin Sheet ◽  
Ice Thickness ◽  
Sea Ice Thickness ◽  
Flight Height ◽  
Airborne Electromagnetic

Existing estimates of footprint size for airborne electromagnetic (AEM) systems have been based largely on the inductive limit of the response. We present calculations of frequency-domain, AEM-footprint sizes in infinite-horizontal, thin-sheet, and half-space models for the case of finite frequency and conductivity. In a half-space the original definition of the footprint is extended to be the side length of the cube with its top centered below the transmitter that contains the induced currents responsible for 90% of the secondary field measured at the receiver. For a horizontal, coplanar helicopter frequency-domain system, the in-phase footprint for induction numbers less than 0.4 (thin sheet) or less than 0.6 (half-space) increases from around 3.7 times the flight height at the inductive limit to more than 10 times the flight height. For a vertical-coaxial system the half-space footprint exceeds nine times the flight height for induction numbers less than 0.09. For all models, geometries, and frequencies, the quadrature footprint is approximately half to two-thirds that of the in-phase footprint. These footprint estimates are supported by 3D model calculations that suggest resistive targets must be separated by the footprint dimension for their individual anomalies to be resolved completely. Analysis of frequency-domain AEM field data acquired for antarctic sea-ice thickness measurements supports the existence of a smaller footprint for the quadrature component in comparison with the in-phase, but the effect is relatively weak. In-phase and quadrature footprints estimated by comparing AEM to drillhole data are considerably smaller than footprints from 1D and 3D calculations. However, we consider the footprints estimated directly from field data unreliable since they are based on a drillhole data set that did not adequately define the true, 3D, sea-ice thickness distribution around the AEM flight line.

Mapping of the resistivity, susceptibility, and permittivity of the earth using a helicopter‐borne electromagnetic system

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 148-157 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Dielectric Properties ◽  
Dielectric Permittivity ◽  
Half Space ◽  
Magnetic Permeability ◽  
Free Space ◽  
Electromagnetic System ◽  
Space Model ◽  
The Earth

Interpretation of helicopter‐borne electromagnetic (EM) data is commonly based on the mapping of resistivity (or conductivity) under the assumption that the magnetic permeability is that of free space and dielectric permittivity can be ignored. However, the data obtained from a multifrequency EM system may contain information about the magnetic permeability and dielectric permittivity as well as the conductivity. Our previous work has shown how helicopter EM data may be transformed to yield the resistivity and magnetic permeability or, alternatively, the resistivity and dielectric permittivity. A method has now been developed to recover the resistivity, magnetic permeability, and dielectric permittivity together from the transformation of helicopter EM data based on a half‐space model. A field example is presented from an area which exhibits both permeable and dielectric properties. This example shows that the mapping of resistivity, magnetic permeability, and dielectric permittivity together yields more credible results than if the permeability or permittivity is ignored.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

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