Response of a layered earth to the Crone pulse electromagnetic system

Geophysics ◽  
1982 ◽  
Vol 47 (1) ◽  
pp. 63-70 ◽  
Author(s):  
S. K. Verma ◽  
S. S. Rai
Keyword(s):  
Half Space ◽  
Single Channel ◽  
Time Derivative ◽  
Measuring System ◽  
Difference Approximation ◽  
Earth Model ◽  
Theoretical Formulation ◽  
Electromagnetic System ◽  
Layered Earth ◽  
Derivative Formula

The response of a layered earth to the Crone pulse electromagnetic (PEM) system, which measures the decay of the time derivative [Formula: see text] has been computed. The transient vertical magnetic field component [Formula: see text] due to a vertical magnetic dipole is obtained by applying a Fourier series summation approach and using digital linear filters to compute the response at individual frequencies. Oscillations in [Formula: see text] due to Gibb’s phenomena are suppressed with Lanczos weights, and the derivative [Formula: see text] is computed numerically by using a linear difference approximation over five points. Decay curves for various half‐spaces are found to cross each other at different values of time. Thus, a single channel response cannot be used to estimate the half‐space resistivity uniquely. This can be achieved, however, by making use of responses at two different channels. Conductivity‐aperture diagrams for half‐space models are plotted for both [Formula: see text] and [Formula: see text]. For [Formula: see text], all the channel amplitudes show well‐defined peaks in the range of 0.3 to 5 ω-m, whereas for [Formula: see text] these peaks lie in the range of 0.7 to 20 Ω-m. This supports the finding by earlier workers that for higher conductivities a total field measuring system responds better than a derivative measuring system. A theoretical formulation is presented to compute the Crone PEM response of an n‐layered earth model. After checking the accuracy of the program, some results are presented for models with different numbers of layers. However, detailed investigation is reported for two‐layered earth only. It is found that overburden parameters can be determined by utilizing responses at two different channels. Nomograms to determine these parameters are presented. There nomograms reveal that for the resistive basement case the best discrimination can be done for the overburden resistivities in the range of 3 to 10 Ω-m and for thicknesses in the range of 0.5 L to 1.5 L (L being the coil separation). For the conductive basement situation the corresponding values are 3 to 15 Ω-m and 0.25 L to 1 L.

Q‐factor approximation of electromagnetic fields for high‐frequency sounding in the 300 kHz to 30 MHz range over layered media

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1253-1258 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Electromagnetic Fields ◽  
High Frequency ◽  
Analytic Solution ◽  
Layered Media ◽  
New Method ◽  
Earth Model ◽  
Q Factor ◽  
Layered Earth

A new method for rapid approximation of electromagnetic (EM) fields for high‐frequency sounding (HFS) over a layered earth is presented in this paper. The essence of this method uses a Q‐factor correction for extending a closed‐form, half‐space analytic solution to a layered earth model. Use of the Q‐factor in this context was first studied by Wait (1953, 1962). Kraichman (1976) also discusses the problem of when the Q‐factor method can be used to provide a good approximation to an exact layered earth solution.

scholarly journals TEM Response of a Large Loop Source over the Multilayer Earth Models

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
A. K. Tiwari ◽  
S. P. Maurya ◽  
N. P. Singh
Keyword(s):  
Time Derivative ◽  
Earth Model ◽  
Computational Technique ◽  
Fourier Cosine ◽  
Layered Earth ◽  
Large Loop ◽  
Earth Models ◽  
Central Loop ◽  
And Inversion ◽  
Decay Form

The general expression of TEM response of large loop source over the layered earth models is not available in the literature for arbitrary source-receiver positions, except for the case of central loop and coincident loop configurations over the homogeneous earth model. In the present study, an attempt is made to present the TEM response of a large loop source over the layered earth model for arbitrary receiver positions. The frequency domain responses of large loop source over the layer earth model for arbitrary receiver positions are converted into the impulse (time derivative of magnetic field) TEM response using Fourier cosine or sine transform. These impulse TEM responses in turn are converted into voltage responses for arbitrary receiver positions, namely, central loop, arbitrary in-loop, and offset-loop TEM responses over the layered earth models. For checking the accuracy of the method, results are compared with the results obtained using analytical expression over a homogeneous earth model. The complete matching of both of the results suggests that the present computational technique is capable of computing TEM response of large loop source over the homogeneous earth model with high accuracy. Thereafter, the technique is applied for computation of TEM response of a large loop source over the layered earth (2-layer, 3-layer, and 4-layer) models for the central loop, in-loop, and offset-loop configurations and the results are presented in voltage decay form. The results depict their characteristic variations. These results would be useful for modeling and inversion of large loop TEM data over the layer earth models for all the possible configurations resulting from a large loop source.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

Stress relaxation in a semi-infinite viscoelastic earth model

1973 ◽  
Vol 63 (6-1) ◽  
pp. 2145-2154
Author(s):  
Martin Rosenman ◽  
Sarva Jit Singh
Keyword(s):  
Free Surface ◽  
Stress Relaxation ◽  
Half Space ◽  
Epicentral Distance ◽  
Strike Slip ◽  
Strike Slip Fault ◽  
Earth Model ◽  
Contour Maps ◽  
Surface Stresses ◽  
Stress Components

Abstract Expressions for quasi-static surface stresses resulting from a finite, rectangular, vertical, strike-slip fault in a Maxwellian viscoelastic half-space are derived. Variation of the stresses with time and epicentral distance is studied. Contour maps are obtained in some representative cases. It is found that all nonvanishing stress components at the free surface die exponentially with time. This is in contrast to the behavior of the displacements and strains which, in general, do not vanish for large times.

Approximation to Cutoffs of Higher Modes of Rayleigh Waves for a Layered Earth Model

2009 ◽  
Vol 166 (3) ◽  
pp. 339-351 ◽  
Author(s):  
Yixian Xu ◽  
Jianghai Xia ◽  
Richard D. Miller
Keyword(s):  
Rayleigh Waves ◽  
Earth Model ◽  
Higher Modes ◽  
Layered Earth

Amplitude and phase correction of helicopter EM data

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. F119-F126 ◽  
Author(s):  
Yusen Ley-Cooper ◽  
James Macnae
Keyword(s):  
Half Space ◽  
Low Frequency ◽  
Earth Model ◽  
Data Sets ◽  
High Frequencies ◽  
Electromagnetic Data ◽  
Historic Data ◽  
Case Data ◽  
Best Fit ◽  
Deep Sediments

We aim to develop a quantitative method for recalibration of historic helicopter electromagnetic data sets. Recent research has shown that frequency-domain helicopter electromagnetic data collected over a conductive half-space such as calm seawater can be used to correct system calibration errors. However, most historic surveys consist only of data collected over land, where the conductive half-space assumption is rarely justified. We estimate the required recalibration parameters by analyzing systematic misfits in the inversion of statistically chosen measures of historic data. Our method requires the identification, within the survey area, of a zone of conductive responses that are reasonably uniform. From this zone, a set of altitude-corrected median responses are estimated. These are inverted using geologically specifiedconstraints to obtain a best-fit layered earth model. Systematic inconsistencies between the median measured altitude and the inverted depth to surface are attributed to altitude error. Remaining frequency-dependent fitting errors are assumed to be the calibration errors. We tested the method with partial success on helicopter electromagnetic data sets collected over uniform deep sediments where seawater data were also available and two different inland surveys over multiple lithologies in one general area. At high frequencies, our method works reliably. Recalibration of low-frequency data is not possible if the area used as a reference consists of moderate or poor conductors. In this case, data amplitudes are small and are greatly affected by imperfect drift and magnetic susceptibility corrections. Historic helicopter electromagnetic data may require amplitude rescaling up to 20%–30%, with phase shifts of up to 3°.

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