Scattering of electromagnetic plane waves by a buried vertical dike

Abstract

The complete and exact solution of the scattering of a TE mode frequency domain electromagnetic plane wave by a vertical dike under a conductive overburden has been established. An integral representation composed of one-sided Fourier transforms describes the scattered electric field components in each one of the five media: air, overburden, dike, and the country rocks on both sides of the dike. The determination of the terms of the series that represents the spectral components of the Fourier integrals requires the numerical inversion of a sparse matrix, and the method of successive approaches. The zero-order term of the series representation for the spectral components of the overburden, for given values of the electrical and geometrical parameters of the model, has been computed. This result allowed to determine an approximate value of the variation of the electric field on the top of the overburden in the direction perpendicular to the strike of the dike. The results demonstrate the efficiency of this forward electromagnetic modeling, and are fundamental for the interpretation of VLF and Magnetotelluric data.<br>Estabelecemos a solução exata e completa do espalhamento de uma onda plana eletromagnética no domínio da freqüência e no modo elétrico transverso por um dique vertical soterrado por uma camada condutora. Uma representação integral composta de transformadas unilaterais de Fourier descreve os componentes do campo elétrico espalhado em cada um dos cinco meios: ar, cobertura, dique e as rochas encaixantes de cada lado do dique. A determinação dos termos da série que representa os componentes espectrais das integrais de Fourier requer a inversão numérica de uma matriz esparsa e o método das aproximações sucessivas. Calculamos o termo de ordem zero da série para os componentes espectrais da camada de cobertura, para valores especificados dos parâmetros geométricos e elétricos do modelo. Este resultado permitiu determinar um valor aproximado da variação do campo elétrico no contato entre o ar e a camada de cobertura em uma direção perpendicular ao traço do dique. Os resultados demonstram a eficiência desta modelagem eletromagnética direta, e são fundamentais para a interpretação de levantamentos geofísicos com os métodos VLF e Magnetotelúrico

Feature Extraction of Structures in Sea Water Using Self-Organizing Maps and Electromagnetic Waves

“…On the Transverse Magnetic (TM) Mode of Propagation, the magnetic field component H y is transverse to the direction of propagation [2]. The other components of the wave, the electric fields E x and E y , are dependent to H y .…”

“…In recent years, Electromagnetic (EM) technology have been employed in various applications, from geophysical remote sensing [2], [4], to most advanced medical interventions [5]. The development in Electromagnetic Imaging, notably in Remote Sensing, Geophysics and Medicine, allowed the advance of knowledge of EM waves propagating media, either to find and assess petroleum reservoirs [3], or to identify cancer in early stages [6].…”

Electromagnetic profiling interpretation across vertical faults and dikes

“…Everywhere, the dielectric permittivities and magnetic permeabilities are assumed to be free‐space values. Batista and Sampaio (1999) 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.…”

“…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.…”

“…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.…”