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Electric dipole fields over a quarter space earth inhomogeneity and application to ice hazard detection
Author(s) -
Ryan J.,
Walsh J.
Publication year - 1985
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs020i006p01518
Subject(s) - electric field integral equation , electric field , mathematical analysis , partial differential equation , boundary value problem , poisson's equation , laplace's equation , physics , heaviside step function , optical field , field (mathematics) , mathematics , quantum mechanics , pure mathematics
An analysis of the fields generated by an electric dipole over a quarter space earth inhomogeneity is carried out. The results of this analysis have a particular application to the long‐range detection of ice hazards such as multiyear ice, pressure ridges and icebergs. Navigation through Arctic regions and exploration in ice‐infested waters are severely limited by the inability of conventional microwave marine radar to provide adequate detection capability. The analysis is based on a method of space and electric field decomposition in which Heaviside functions are used to decompose a three‐dimensional space into regions having different electrical properties. The region above z = 0 represents free space and the region below represents two semi‐infinite homogeneous media. Maxwell's equations are used to derive a partial differential equation for the electric field for the complete space. This partial differential field equation is decomposed into three field equations, one for each region, and a boundary equation. The boundary equation represents the conditions which the electric field must satisfy at each of the interfaces. In this manner, this technique provides its own boundary conditions. Selecting the appropriate spherical Green's function, the resultant convolution type integral equations are simplified by using the boundary equation to eliminate half of the unknowns and taking the two‐dimensional (spatial) Fourier transform. By assuming the refractive indices of the media below are large and taking the source field as the far field of a vertical electric dipole, the three field equations are reduced to a single algebraic equation. This equation is inverse Fourier transformed, and the resultant convolution integral equation is written in operator notation. The operator is formally inverted in the form of a Neumann series. By utilizing stationary phase integration and the Laplace transform, the series may be summed to give either the propagated field or the backscattered field.