A model to calculate em fields in tropospheric duct environments at frequencies through SHF

Marcus, Sherman W.

doi:10.1029/rs017i005p00895

Cited by 25 publications

(6 citation statements)

References 8 publications

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“…Refractive effects are included by varying the effective Earth radius, which corresponds to varying the constant gradient of refractivity that is assumed. The gradient given above corresponds to an effective Earth radius of (4/3)a e. Calculations are made using a waveguide mode propagation model [Marcus, 1982] as well as the parabolic equation method. The particular waveguide program used here was written at the Naval Ocean Systems Center and is described by Hithey et al [1985] and Baumgartner [1983].…”

Section: Comparisons Between Parabolic Equation/splitstep Results Andmentioning

confidence: 99%

Theoretical description of the parabolic approximation/Fourier split‐step method of representing electromagnetic propagation in the troposphere

Kuttler¹,

Dockery²

1991

Radio Science

258

176

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A theoretical foundation for the use of the parabolic wave equation/Fourier split‐step method for modeling electromagnetic tropospheric propagation is presented. New procedures are used to derive a scalar Helmholtz equation and to subsequently transform to a rectangular coordinate system without requiring approximations. The assumptions associated with reducing the resulting exact Helmholtz equation to the parabolic wave equation that is used for computations are then described. A similar discussion of the error sources associated with the Fourier split‐step solution technique is provided as well. These discussions provide an important indication of the applicability of the parabolic equation/split‐step method to electromagnetic tropospheric propagation problems. A rigorous method of incorporating an impedance boundary at the Earth's surface in the split‐step algorithm is also presented for the first time. Finally, a few example calculations which demonstrate agreement with other propagation models are provided.

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Section: Comparisons Between Parabolic Equation/splitstep Results Andmentioning

confidence: 99%

Theoretical description of the parabolic approximation/Fourier split‐step method of representing electromagnetic propagation in the troposphere

Kuttler¹,

Dockery²

1991

Radio Science

258

176

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“…Lsm is particularly significant for trapped modes in a surface duct. For propagation over smooth Earth these modes experience little or no attenuation in the propagation direction, which accounts for the field enhancement within the duct [Marcus and Stuart, 1981]. For trapped modes within a surface duct characterized by a bilinear refractivity profile [Marcus, 1987] Predictions of the field relative to free space, using the four lowest-order modes, are shown in Figure 4 for a 6.814-GHz radio wave propagating within the duct defined by the refractivity profile of Figure 1.…”

Section: A Methods For Considering Ground Roughness Inmentioning

confidence: 99%

“…Numerical methods for predicting field strengths at large distances from a radiating source in surface and elevated ducts have been documented [Marcus, 1982;Marcus and Stuart, 1981]. These methods are based on the waveguide mode theory of wave propagation [Budden, 1961] and assume horizontal homogeneity, which implies a smooth Earth.…”

Section: Introductionmentioning

confidence: 99%

Propagation in a surface duct over a two‐dimensional sinusoidal rough Earth

Marcus¹

1988

Radio Science

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A solution for the problem of horizontally polarized radio waves propagating in a surface duct situated over a perfectly conducting, sinusoidally shaped ground with small amplitudes is obtained. The solution contains the assumption that the source is a horizontal line source perpendicular to the roughness variation. It is found that the specular contribution may be derived using an equivalent matrix with an effective reflection coefficient that accounts for scattering both out of and into the specular direction. The accuracy of a method for obtaining the rough Earth waveguide eigenvalues as a perturbation of those for the smooth Earth case is analyzed. Numerical field results are compared using the different approaches, demonstrating an attenuation effect due to the roughness.

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“…This would be the case if a fine path loss mapping were required for a large portion of the environment, since the field at all the mesh points of the finite difference grid are determined directly as part of the implicit finite difference algorithm. The normal mode expansion, on the other hand, would generally require either (a) evaluation of determinants with highly transcendental elements at each field location (Marcus, 1982), or (b) extensive use of a mass storage device.…”

Section: "Imposed" Homogeneitymentioning

confidence: 99%

A generalized impedance method for application of the parabolic approximation to underwater acoustics

Marcus

1991

The Journal of the Acoustical Society of America

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The parabolic equation (PE) has become an important computational tool for approximating underwater acoustic path losses in inhomogeneous environments. The numerical solution of this equation is performed on a grid over the propagation medium which includes the water column, and has also included a homogeneous "false bottom" below the actual ocean bottom. This situation is viewed as one in which the propagation medium can be divided into a horizontally inhomogeneous upper layer and a horizontally homogeneous lower layer. The pressure field in the latter layer is found using standard techniques valid for homogeneous media, and in the former layer is found using an implicit finite difference scheme. These fields and their normal derivatives are matched along the interface between the layers. The result is referred to as a generalized impedance boundary condition (GIBC), which serves to eliminate the need for a false bottom. Predictions obtained using the standard parabolic equation and a completely homogeneous bottom medium indicate improved numerical efficiency, and excellent agreement with other methods. The improved efficiency can be potentially significant for three-dimensional propagation problems.

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A model to calculate em fields in tropospheric duct environments at frequencies through SHF

Cited by 25 publications

References 8 publications

Theoretical description of the parabolic approximation/Fourier split‐step method of representing electromagnetic propagation in the troposphere

Theoretical description of the parabolic approximation/Fourier split‐step method of representing electromagnetic propagation in the troposphere

Propagation in a surface duct over a two‐dimensional sinusoidal rough Earth

A generalized impedance method for application of the parabolic approximation to underwater acoustics

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