1996
DOI: 10.1029/96rs02630
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Signal intensity in the geometrical optics approximation for the magnetized ionosphere

Abstract: The paper discusses theoretical and numerical aspects of signal intensity calculations in the geometrical optics approximation for ionospheric HF wave propagation. We present an efficient method for calculating a flux tube of rays for a very general ionosphere. The method is new in the sense that it allows for the effects of electron collisions and the anisotropy produced by the Earth's magnetic field. The basic idea is to calculate the focusing of infinitesimally separated rays by integrating the differential… Show more

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Cited by 8 publications
(6 citation statements)
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“…All Rights Reserved. 2169-9380/14/10.1002/2013JA019247 1991; Västberg and Lundborg, 1996;Strangeways, 2000;Tsai et al, 2010]. In most cases the equations were recast in spherical coordinates (Haselgrove used the Cartesian coordinate system).…”
Section: Hf Ray Tracing Techniquesmentioning
confidence: 99%
See 1 more Smart Citation
“…All Rights Reserved. 2169-9380/14/10.1002/2013JA019247 1991; Västberg and Lundborg, 1996;Strangeways, 2000;Tsai et al, 2010]. In most cases the equations were recast in spherical coordinates (Haselgrove used the Cartesian coordinate system).…”
Section: Hf Ray Tracing Techniquesmentioning
confidence: 99%
“…The canonical equations for the raypath are not able to be solved analytically for a general ionosphere and so Haselgrove and Haselgrove [] and Haselgrove [] reformulated the equations, apropos finding a solution via numerical integration techniques. The canonical equations, now commonly known as Haselgrove's equations, have been used extensively over many years to study HF radio wave propagation [e.g., Croft , ; Surtees , ; Bennett , , ; Jones and Stephenson , ; Nickisch , ; Reilly , ; Västberg and Lundborg , ; Strangeways , ; Tsai et al , ]. In most cases the equations were recast in spherical coordinates (Haselgrove used the Cartesian coordinate system).…”
Section: Introductionmentioning
confidence: 99%
“…The main disadvantage is accuracy; large perturbations are subject to quantization error, and small perturbations to roundoff error. A second approach is the direct variational method in which the differential equations describing the control‐vector sensitivities are derived and integrated alongside the original raytracing equations (Nickisch, 1988; Sambridge & Kennett, 1990; Västberg & Lundborg, 1996). The computational cost of the method is related to the number of control parameters which should therefore not be very large.…”
Section: Methodsmentioning
confidence: 99%
“…The third factor is the cross‐sectional area of the flux tube at the receive site. Estimating this area is referred to as focusing (e.g., Budden, 1991; Nickisch, 1988; Västberg & Lundborg, 1996). Consider a radiative flux tube at the transmitter with a differential solid angle dnormalΩ=sin(ηt)dηtdξt where dξt and dηt are variations in the azimuth and zenith angle of the transmit ray bearing, respectively.…”
Section: Methodsmentioning
confidence: 99%
“…The second column shows the ground range, the third column the phase path, the fourth column shows the spreading loss (calculated from quantities D + and D − ) and the final two columns show D + and D − , respectively. Included (in brackets) is the loss when evaluated by means of virtual ray deviation techniques [e.g., Nickisch , 1988; Vastberg and Lundborg , 1996]. It will be noted that the current technique produces results that are almost identical to those provided by the alternative techniques.…”
Section: Some Examplesmentioning
confidence: 99%