On: “A grounded vertical long‐wire source system for plane wave magnetotelluric analog modeling” by R. N. Edwards (GEOPHYSICS, October 1980, p. 1523–1529).

Geophysics ◽  
1981 ◽  
Vol 46 (6) ◽  
pp. 934-935 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Radial Distance ◽  
Skin Depth ◽  
Space Model ◽  
Homogeneous Half Space ◽  
The Earth ◽  
Analog Modeling ◽  
Vertical Wire ◽  
Electrical Skin

In an interesting analysis, Edwards shows that a vertical long wire source will produce electromagnetic (EM) fields that satisfy simple impedance relationships for a homogeneous half‐space model of the earth. The important restriction is that the radial distance to the observer be large compared with an electrical skin depth. Certainly the vertical wire structures provide a very convenient modeling scheme for the “average prospector” to interpret magnetotelluric (MT) data collected over confined inhomogeneities within the conductive host region.

Doubling the effective skin depth with a local source

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 732-738 ◽  
Author(s):  
James E. Reid ◽  
James C. Macnae
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Survey Design ◽  
Data Interpretation ◽  
Skin Depth ◽  
Local Source ◽  
Electromagnetic Sounding ◽  
Homogeneous Half Space ◽  
Electric And Magnetic Fields ◽  
Thick Overburden

The depth at which the amplitude of the frequency‐domain electromagnetic fields due to dipole and square loop sources over a homogeneous half‐space fall to 1/e of their value at the surface is compared to the conventional plane‐wave skin depth. The skin depth due to a local source depends on the transmitter frequency, half‐space conductivity, transmitter altitude, and transmitter‐receiver offset, and may range from a fraction of to more than twice the plane‐wave skin depth. Unlike the plane‐wave skin depth, the “local‐source skin depth” is different for electric and magnetic fields, and may be nonunique for some transmitter geometries and field components. For all transmitter geometries, however, the local‐source skin depth approaches the plane‐wave skin depth as the transmitter altitude and/or receiver offset increase. The concept of the local‐source skin depth has direct application to survey design and data interpretation. A theoretical example demonstrates that it is possible to predict, for a given survey geometry and frequency range, whether or not an electromagnetic sounding can detect a conductive basement below a thick overburden layer.

On Anomalous Propagation of Radio Waves in Earth Strata

Geophysics ◽  
1954 ◽  
Vol 19 (2) ◽  
pp. 342-343 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Skin Depth ◽  
Radio Waves ◽  
Conventional Theory ◽  
The Earth ◽  
Anomalous Propagation ◽  
Unusual Situation ◽  
Electrical Skin

Reports have been made from time to time on the possibility of radio transmission to great depths in the earth of the order of 1,000 feet or more. (Barrett, 1949 and 1952). From the standpoint of conventional theory this would appear to be a rather unusual situation. For example for a typical rock resistivity of IO4 ohm-cm and a frequency of 1,600 kc the classical electrical “skin depth” δ is equal to 4 metres or about 13 feet. This corresponds to attenuations of the order of one decibel per foot.

scholarly journals The critical reflection theorem

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 965-972 ◽  
Author(s):  
Jacob T. Fokkema ◽  
Anton Ziolkowski
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Critical Reflection ◽  
Lower Layer ◽  
Plane Waves ◽  
Source Spectrum ◽  
Demarcation Criterion ◽  
The Earth ◽  
Reflection Theorem ◽  
Uppermost Layer

In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

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.

A grounded vertical long wire source system for plane wave magnetotelluric analog modeling

Geophysics ◽  
1980 ◽  
Vol 45 (10) ◽  
pp. 1523-1529 ◽  
Author(s):  
R. N. Edwards
Keyword(s):  
Plane Wave ◽  
Current Source ◽  
Skin Depth ◽  
Uniform Field ◽  
Induced Current ◽  
Horizontal Magnetic Field ◽  
Helmholtz Coils ◽  
Analog Modeling ◽  
Conductivity Anomalies ◽  
External Connections

A typical electromagnetic (EM) analog modeling apparatus consists of an electrolytic tank with embedded graphite blocks, representing conductivity anomalies. A plane wave magnetotelluric (MT) source is generated by alternating currents in a set of parallel horizontal overhead wires. A uniform horizontal magnetic field is produced over the surface of the electrolyte. A similar uniform field may also be generated by grounded semiinfinite vertical wires. Four such wires, two carrying current upward and two downward, when arranged at the corners of a rectangle of defined dimensions, generate a more uniform field than a corresponding pair of Helmholtz coils. If the size of the rectangle is large compared with a skin depth in the electrolyte, Cagniard’s MT relationships are obeyed both on and beneath the electrolyte. The vertical current source has the advantage over the horizontal current source since it requires no ancillary external connections between the ends of the modeling tank to complete the induced current circuit.

Conductivity-depth imaging of helicopter-borne TEM data based on a pseudolayer half-space model

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. F115-F120 ◽  
Author(s):  
Haoping Huang ◽  
Jonathan Rudd
Keyword(s):  
Half Space ◽  
Mineral Exploration ◽  
Synthetic Data ◽  
Depth Imaging ◽  
Space Model ◽  
Depth Images ◽  
Homogeneous Half Space ◽  
Time Domain Electromagnetic ◽  
Speed Up ◽  
Effective Depth

Helicopter-borne time-domain electromagnetic (HTEM) systems with a concentric horizontal coil configuration have been used increasingly in mineral exploration. Conductivity-depth imaging (CDI) is a useful tool for mapping the distribution of geologic conductivity and for identifying conductive targets. A CDI algorithm for HTEM systems with a concentric coil configuration is developed based on the pseudolayer half-space model. Primary advantages of this model are immunity to altimeter errors and better resolution of conductive layers than other half-space models. Effective depth is derived empirically from the diffusion depth and apparent thickness of the pseudolayer. A table lookup procedure is established based on the analytic solution of a half-space model to speed up processing. This efficiency makes generation of real-time conductivity-depth images possible. Tests on synthetic data demonstrate that the pseudolayer conductivity-depth-imaging algorithm maps a wider range of conduc-tivities and does a better job of resolving highly conductive layers, compared with that of the homogeneous half-space model. Effective depths are close to true depths in many circumstances. Field examples show stable and geologically meaningful conductivity-depth images.

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.

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