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Method for solving VLF mode equation root under conditions of actual stratum and ionized layer

An ionosphere and equation technology, applied in the field of electromagnetic calculations, can solve problems such as excessive dependence on initial values, failure to converge or converge to other zero points, etc.

Pending Publication Date: 2020-11-24
XIAN UNIV OF TECH
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Problems solved by technology

Compared with the numerical solution of differential equations, the Newton iterative method has a fast calculation speed, but due to the excessive dependence on the initial value, it may fail to converge or converge to other zero points in some cases

Method used

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  • Method for solving VLF mode equation root under conditions of actual stratum and ionized layer
  • Method for solving VLF mode equation root under conditions of actual stratum and ionized layer
  • Method for solving VLF mode equation root under conditions of actual stratum and ionized layer

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Embodiment

[0175] Carry out according to method step of the present invention, in the experiment, the parameter that ground is average seawater is: relative permittivity ε r =70, conductivity σ 1 =5S / m, the parameters of the ground being the average land are: relative permittivity ε r =22, conductivity σ 1 =3×10 -3 S / m; the parameters of the ionosphere are: ionosphere reference height H = 72km, gradient coefficient β = 0.3, distance H from the lower boundary of the ionosphere to the ground min = 0, the distance H between the upper boundary of the ionosphere and the ground max =120km, the number of stratified layers of the ionosphere m=200, the ionosphere incident angle θ'=80°; the radius of the earth a=6371.12km; the root of the modular equation under ideal conditions before Newton’s iterative correction needs to satisfy the preset Accuracy Eps1=1×10 -2 , the preset accuracy Eps2=1×10 that the root of the modular equation needs to satisfy in the ideal case and the actual formation a...

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Abstract

The invention discloses a method for solving a VLF modal equation root under the conditions of an actual stratum and an ionized layer. The method comprises the following steps: firstly, initializing parameters, and setting stratum parameters, ionized layer parameters, VLF electric wave parameters and preset precision required to be met by the modal equation root; solving a modal equation root under an ideal condition, namely under the condition that the stratum is completely conductive and the ionized layer is completely magnetic conductive; taking the modal equation root under the ideal condition as an initial value, and solving an approximate modal equation root under the actual stratum and ionized layer conditions by utilizing an improved Euler method with a large step length; further correcting the approximate mode equation root by using a Newton iteration method; and judging whether the corrected modal equation root meets preset precision or not, if the corrected modal equation root does not meet the preset precision, returning to the above, and if the corrected modal equation root meets the preset precision, outputting the corrected modal equation root and ending, so that theoutput result is the modal equation root under the actual stratum and ionospheric conditions. According to the method, the higher solving efficiency is achieved while the higher solving precision andreliability of the root of the modular equation are guaranteed.

Description

technical field [0001] The invention belongs to the technical field of electromagnetic calculation, and in particular relates to a method for solving roots of VLF modular equations under actual formation and ionosphere conditions. Background technique [0002] Very Low Frequency (VLF, Very Low Frequency) electromagnetic wave is a radio wave with a frequency in the range of 3-30 kHz, and its wavelength is 100-10 km. VLF waves have low propagation loss, stable amplitude and phase, and strong permeability. They are widely used in ultra-long-range navigation and timing, submarine communication, weather monitoring, ionospheric monitoring, and earthquake prediction. Since the wavelength of the VLF wave is comparable to the distance between the ground and the ionosphere, and both the ground and the ionosphere have good reflection characteristics, the VLF wave is reflected back and forth between the two reflecting walls and is guided by it to propagate forward ( called the ground-i...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/11
CPCG06F17/11
Inventor 蒲玉蓉韩雪妮张金生席晓莉
Owner XIAN UNIV OF TECH
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