Scattering of monochromatic acoustic and electromagnetic plane waves by two quarter spaces

Sampaio, Edson E. S.; Fokkema, J.T.

doi:10.1029/91jb02291

Cited by 11 publications

(5 citation statements)

References 4 publications

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“…Everywhere the dielectric permittivities and magnetic permeabilities are assumed to be free‐space values. Sampaio and Fokkema (1992) determined an exact solution to this TE‐mode problem in the form of two series of functions for each field component in each medium. We employed the first non‐zero terms of their series to compute the electromagnetic‐field components and to compute, subsequently, the relevant geophysical quantities.…”

Section: Scattering Of the Electromagnetic‐field Componentsmentioning

confidence: 99%

“…In spite of their versatility the results obtained with these techniques must be cross‐checked with each other and with analytical results. Among the articles that discuss analytical solutions of two‐dimensional problems are those by d'Erceville and Kunetz (1962), Weaver (1963) and Sampaio and Fokkema (1992) for the vertical fault, by Geyer (1972) for the inclined fault, and by Rankin (1962), Sampaio (1976) and Batista and Sampaio (1999) for the vertical dike.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we set up a method to interpret vertical faults and dikes by curve fitting, when scattering a TE‐mode plane‐wave primary field, suitable for the polarization‐ellipsoid methods. The algebra and the relative accuracy involved in the calculation of the electric‐field component is essentially as described by Sampaio and Fokkema (1992) for the vertical fault, and by Batista and Sampaio (1999) for the vertical dike, and they will not be further discussed here. We employed the results of these two papers to calculate the parameters of the magnetic‐field ellipsoid.…”

Section: Introductionmentioning

confidence: 99%

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Electromagnetic profiling interpretation across vertical faults and dikes

Sampaio

Dias

2001

Geophysical Prospecting

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When a vertical fault or dike scatters a normally incident TE‐mode plane wave, the horizontal components of the electric and the magnetic fields vary along the direction perpendicular to the strike. This scattering is also responsible for the formation of a vertical component of the magnetic field, which also varies along the direction perpendicular to the strike. Analysis of the lateral variations of the field components permits the identification of the type of geological structure, either fault or dike, as well as an estimate of the position of the geological contacts and the electrical conductivity of each medium. Previous exact analytical solutions have shown that two Fourier cosine integrals can express each field component. A series of functions specified for each model represent the kernel of each integral. From the field components obtained from the first non‐zero term of each series, we calculated the following functions: the dip angle and the ellipticity of the vertical polarization ellipse in a plane perpendicular to the strike of the structure, and the azimuth and the ellipticity of the horizontal ellipse. We established master‐curves of these functions for the interpretation of vertical faults and dikes for the polarization ellipsoid, for instance VLF or audio‐frequency methods. This representation has as variable the induction number , and as parameters σ2/σ1 and , where a denotes the half‐thickness of the dike. The interpretation procedure using curve fitting is possible because the induction number is represented on a logarithmic scale. This procedure represents an important step before automatic interpretation is carried out. Two case histories using field data illustrate the effectiveness of the procedure and the type of quantitative interpretation obtained from it.

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Section: Scattering Of the Electromagnetic‐field Componentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electromagnetic profiling interpretation across vertical faults and dikes

Sampaio

Dias

2001

Geophysical Prospecting

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“…The exact one-dimensional surface impedance expression for homogeneous plane wave incidence above a horizontally stratified (vertically inhomogeneous) earth has been well documented. Exact and approximate solutions for the surface impedance anomaly above a horizontally inhomogeneous half space with isotropic conductivity have been previously investigated for both TE-and TM-type waves [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The issue of a sloping contact has been considered theoretically by Dmitriev and Zakharov [16] and Geyer [17], and numerically by Reddy and Rankin [18].…”

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confidence: 99%

The Equivalence of Inclined Uniaxial and Biaxial Electrical Anisotropy in Inhomogeneous Two-Dimensional Media for Homogeneous TM-Type Plane Wave Propagation Problems

Wilson¹,

Thiel²

2003

PIER

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For a homogeneous TM-type wave propagating in a two-dimensional half space with both vertical and horizontal inhomogeneities, where the TM-type wave is aligned with one of the elements of the conductivity tensor, it is shown using exact solutions to boundary value problems that the shearing term in the homogeneous Helmholtz equation for inclined uniaxial anisotropic media unequivocally vanishes and solutions need only be sought to the homogeneous Helmholtz equation for fundamental biaxial anisotropic media. This implies that those problems posed with an inclined uniaxial conductivity tensor can be identically stated with a fundamental biaxial conductivity tensor, provided that the conductivity values are the reciprocal of the diagonal terms from the Euler rotated resistivity tensor. The applications of this for numerical methods of solving arbitrary two-dimensional problems for a homogeneous TM-type wave is that they need only to approximate the homogeneous Helmholtz equation and neglect the corresponding shearing term.

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“…I• also can be used to check •he degree of precision of other •echniques. Sampaio and Fokkema [1992] developed a complete and exact solution to this problem in the frequency domain. In the present paper we adapt their solution to find the scattered field in the time domain caused by a normally incident plane wave, represented by a causal time function that decays exponentially with time of propagation from a height of reference above the fault.…”

mentioning

confidence: 99%