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: “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.

Electrical and magnetometric fields in a layered earth containing buried electrodes

Geophysics ◽  
1990 ◽  
Vol 55 (12) ◽  
pp. 1605-1612 ◽  
Author(s):  
D. Veitch ◽  
M. W. Asten ◽  
E. H. van Leeuwen
Keyword(s):  
Half Space ◽  
Field Data ◽  
Massive Sulfide ◽  
Magnetic Field Measurement ◽  
Layered Earth ◽  
Homogeneous Half Space ◽  
Electric And Magnetic Fields ◽  
Borehole Logs ◽  
Two Layer Model ◽  
The Magnetic Field

The number of analytical magnetometric resistivity (MMR) results available for basic earth geometries is limited compared to that of electrical resistivity methods, which is unfortunate since MMR has advantages for certain classes of problems. This paper extends the list of MMR results by deriving the response for the homogeneous half‐space and the multilayered earth. Both are calculated for arbitrary source and receiver positions. We show how the result for the layered earth reduces to that of the half‐space when there is only one layer. Necessary procedures for successful numerical evaluation of results for the layered case are given. Sample borehole logs of electric and magnetic fields for an example of a two‐layer model illustrate an advantage of the magnetic‐field measurement; namely, that it is sensitive to the position of layer boundaries rather than to the position of transmitter electrodes. The algorithm is also applied to interpretation of MMR field data from two boreholes drilled near massive sulfide conductors. The magnetometric influence (or background) due to borehole geometry in an electrically layered earth may be computed and subtracted from the field data, after which it is possible to perform quantitative modeling of the residual MMR anomaly to define the location of ore‐related conductors.

Inversion of slingram electromagnetic induction data using a Born approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. E201-E212 ◽  
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Born Approximation ◽  
High Efficiency ◽  
Three Dimensions ◽  
Background Model ◽  
Desktop Computer ◽  
Near Surface ◽  
Homogeneous Half Space ◽  
Integral Equation Formulation ◽  
Forward Operator

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

Numerical seismograms obtained using ω-κ integrals, for a point P source in a vertically inhomogeneous anelastic model

1996 ◽  
Vol 86 (3) ◽  
pp. 750-760
Author(s):  
F. Abramovici ◽  
L. H. T. Le ◽  
E. R. Kanasewich
Keyword(s):  
Half Space ◽  
Homogeneous Layer ◽  
Variable Step Size ◽  
Step Size ◽  
Adaptive Process ◽  
Cpu Time ◽  
Homogeneous Half Space ◽  
Linear Layer ◽  
Variable Step ◽  
Viscoelastic Layers

Abstract This article presents some numerical experiments in using a computer program for calculating the displacements due to a P source in a vertically inhomogeneous structure, based on the Fourier-Bessel representation. The structure may contain homogeneous, inhomogeneous, elastic, or viscoelastic layers. The source may act in any type of sublayer or in the half-space. Synthetic results for the simple case of a homogeneous layer overlaying a homogeneous half-space compare favorably with computations based on the Cagniard method. Numerical seismograms for an elastic layer having velocities and density varying linearly with depth were computed by integrating numerically the governing differential systems and compared with results based on the Haskell model of splitting the linear layer in homogeneous sublayers. Even an adaptive process with a variable step size based on the Haskell model has a poorer performance on the accuracy-cpu time scale than numerical integration.

Surface-wave dispersion computations

1970 ◽  
Vol 60 (2) ◽  
pp. 321-344 ◽  
Author(s):  
Fred Schwab ◽  
Leon Knopoff
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Wave Dispersion ◽  
Reduction Technique ◽  
Surface Wave Dispersion ◽  
Single Precision ◽  
Homogeneous Half Space ◽  
Full Control ◽  
Significant Figures ◽  
Rayleigh Wave Dispersion

abstract Fundamental-mode Love- and Rayleigh-wave dispersion computations for multilayered, perfectly-elastic media were studied. The speed of these computations was improved, and the accuracy brought under full control. With sixteen decimal digits employed in these computations, fifteen significant-figure accuracy was found possible with Love waves and twelve to thirteen figure accuracy with Rayleigh waves. In order to ensure that the computed dispersion is correct to a specified accuracy, say σ significant figures, (σ + 1)/4 wavelengths of layered structure must be retained above a homogeneous half-space. To this accuracy, the homogeneous half-space is a sufficient model of the true layering it replaces. Using this result, it was possible to refine the usual layer-reduction technique so as to ensure retention of the specified accuracy while employing reduction. With this reduction technique in effect, and with σ specified below single-precision accuracy, the program can be run entirely in single precision; the specified accuracy is maintained without overflow or loss-of-precision problems being encountered during calculations.

Electromagnetic Induction in a Stratified Conducting Half-Space by an Arbitrary Periodic Source

1973 ◽  
Vol 51 (10) ◽  
pp. 1064-1074 ◽  
Author(s):  
D. M. Summers ◽  
J. T. Weaver
Keyword(s):  
Half Space ◽  
Recursion Formula ◽  
Electric And Magnetic Fields ◽  
Hertz Potential ◽  
Infinite Line ◽  
The Fourier Transform ◽  
The One ◽  
External Time ◽  
Entire Theory ◽  
Time Periodic

A general theory of induction in a horizontally stratified plane conductor by an external, time-periodic, magnetic source is presented. The analysis is a generalization to the case of an N-layered conductor of a previously published theory for induction in a uniform conducting half-space, in which the electromagnetic field was expressed in terms of electric and magnetic Hertz vectors oriented normally to the surface of the conductor. With the aid of this representation the entire theory is developed in terms of the one scalar component of the magnetic Hertz vector. Solutions for the electric and magnetic fields above and within the conductor are obtained in the form of double integrals whose integrands are related through a recursion formula to the Fourier transform of the magnetic Hertz potential of the source evaluated at the surface of the conductor. Special formulas applicable to 1- and 2-layer conductors are derived and the form of solution for some elementary sources is also discussed. As an illustration of the theory, numerical calculations are given for an infinite line current above a 10-layer conductor whose conductivity increases (i) linearly and (ii) exponentially with depth.

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