Electromagnetic fields of dipoles in stratified media

Stoyer, C. H.

doi:10.1109/tap.1977.1141618

Cited by 37 publications

(25 citation statements)

References 8 publications

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“…Two 120m deep wells are separated by lOOm and both penetrate the layer. The vertical magnetic field calculations for the layered model were made, for source and receiver intervals of 10m, with a 1 -D solution written by Lee (1 988) which is based on a method originally published by Stoyer (1977). To simulate the layer with the cylindrically symmetric model, a 20m thick slab was extended out to a radius of L. Different frequencies, conductivities and slab radii (L) have been employed and the errors between the two solutions computed.…”

Section: Comparison To 1-d Horizontally Layered Modelsmentioning

confidence: 99%

“…Wannemaker, et al, 1984, Newman andHohman, 1988). To formulate the 1-D background model for the 2-D cylindrical geometry being considered here, the impedance concept originally introduced by Wait (1970) for plane waves and later modified for dipoles by Stoyer (1977) and loops by Wait and Hill (1980) will be employed. Because the derivation is fairly lengthy, it is given in Appendix B and only the results are presented here.…”

Section: Theoretical Formulation For a 1-d Layered Background Modelmentioning

confidence: 99%

“…The method employed here to derive the theoretical formulation for the 1-D layered model containing either a magnetic dipole or large loop source follows that of Stoyer (1977) and Wait and Hill (1980). The reader is referred to Figure 4.26 which shows the geometry of the problem.…”

Section: Appendix a Definition Of The Smoothing Matricesmentioning

confidence: 99%

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Iterative electromagnetic Born inversion applied to earth conductivity imaging

Alumbaugh¹

1993

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order Born approximation is applied to linearize the integral equations. From these simplified equations, sensitivity functions are derived which define the ability of the crosswell magnetic field measurements to detect small local changes in conductivity. Plots of the spatial variation in sensitivity indicate that vertical resolution is a function of the spatial sampling density in the vertical direction, while the horizontal resolution depends on the vertical separation between the source and receiver. Additional improvement in the horizontal resolution can be provided by making additional measurements with both the source and receiver in the same hole.Further sensitivity analysis is completed in terms of a dimensionless background induction number that is defined by oopl2 where o is the background conductivity and 1 is the source-receiver separation. Analysis of the crosswell sensitivity in terms of this parameter facilitates experimental system design for a given borehole separation and background conductivity, as well as the determination of the operating frequency which falls within an optimal range of oo@ 2.For oopl2 ~1 0 , the scattered fields are very small compared to the primary field, making measurements of the inhomogenous response very difficult in the presence of noise. In addition, a given source-receiver pair is sensitive to a large volume of strata outside of the interwell zone rather than just the region immediately between the probes. The latter property requires that a larger region be considered in the interpretation phase and that the proper 2-D or 3-D model geometry is employed. As the induction number is increased the nature of the sensitivity functions change. For oopl2 > 50 a given source-receiver pair is sensitive only to a "ray-path" shaped zone immediately between the two probes and the scattered fields are on the same order of magnitude as the primary fields. Unfortunately the attenuation at these large induction numbers prevents accurate measurement of the fields for large vertical probe separation due to the dynamic range limitations of the measurement system.The validity of using a 2-D cylindrical model to simulate a generally inhomogenous earth is investigated by comparing the 2-D Born series solution to other 1-D, 2-D and 3-D modeling algorithms. For ooyl2 < 50 the size of the region outside of the wells that is included in the model has a significant effect on the properties of the calculated EM fields with the different model geometries producing significantly different results. At larger induction numbers (owpl2 >50) a given source-receiver pair senses only the medium directly between the probes and the resulting fields are fairly independent of whether a 1-D, 2-D or 3-D model is employed. Unfortunately at these large induction numbers the Born series does not readily converge.To image the subsurface conductivity smcture between two wells, the 2-D cylindrical Born series approximation is incorporated into an iterative Born inversion scheme. The inversion problem is stabiliz...

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Section: Comparison To 1-d Horizontally Layered Modelsmentioning

confidence: 99%

Section: Theoretical Formulation For a 1-d Layered Background Modelmentioning

confidence: 99%

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Iterative electromagnetic Born inversion applied to earth conductivity imaging

Alumbaugh¹

1993

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“…G E i j and G B i j are Green tensors of total EM fields for a uniform half space derived by Stoyer (1977) and shown in Appendix. In this study, we solve the piezoelectric EM fields observed on the earth's surface before the elastic wave reaches the surface.…”

Section: Fundamental Equations and Solutionsmentioning

confidence: 99%

Electromagnetic signals related to incidence of a teleseismic body wave into a subsurface piezoelectric body

Ogawa

Utada

2014

Earth Planet Sp

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This paper presents a case study of Electromagnetic (EM) signals associated with earthquakes due to the piezoelectricity of crustal rocks. For a simple model of crustal structure with a subsurface piezoelectric body, a mathematical expression was obtained that describes the behavior of piezoelectric EM signals due to incidence of a teleseismic body wave. Using this expression, we evaluated expected EM signals with physical parameters reasonable for crustal rocks. Results of the frequency domain analysis suggested that the intensity of the signal decreases with decreasing frequency due to decreasing stress rate at lower frequencies, and decreases with increasing frequency due to EM attenuation in the conducting medium at higher frequencies. However, the latter (the skin effect) was shown to be negligible at the dominant frequency range of seismic waves so far as a shallower piezoelectric body is concerned. Numerical results also indicated a resonant feature of the piezoelectric EM signals corresponding to geometry of the subsurface piezoelectric body. However, numerical calculations suggested that such signals cannot be detected except for strong motions. If detected, on the other hand, their spatial and frequency characteristics will provide information on the geometry of the subsurface piezoelectric body.

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“…However, for a buried source problem, when the propagation has to be carried out beyond the source level, numerical difficulties accruing from the exponential remain. For example, we refer to the work of Stoyer (1977) in which the EM field computations due to the buried dipole electromagnetic sources is carried out with a recursive scheme in which occur exponential functions of the form and exp (-(u; where (u; and ar complex quantities under radical sign and is a positive quantity (the vertical distance). If the real part of is taken either as positive or negative (see Stoyer, 1977), numerical instability in computations (due to one of the two terms) arises due to limited computer accuracy.…”

Section: Introductionmentioning

confidence: 99%

A reformalism for computing frequency‐ and time‐domain EM responses of a buried, finite‐loop source in a layered earth

Da¹

1995

SEG Technical Program Expanded Abstracts 1995

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Electromagnetic fields of dipoles in stratified media

Cited by 37 publications

References 8 publications

Iterative electromagnetic Born inversion applied to earth conductivity imaging

Iterative electromagnetic Born inversion applied to earth conductivity imaging

Electromagnetic signals related to incidence of a teleseismic body wave into a subsurface piezoelectric body

A reformalism for computing frequency‐ and time‐domain EM responses of a buried, finite‐loop source in a layered earth

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