Multiple-Mode Interference and Phase Standard Deviation of VLF Wave Propagation in an Anisotropic Earth–Ionosphere Waveguide

He, Tong; Zheng, Juan; Pan, Wei Yan; Li, Kai

doi:10.1109/tap.2018.2874491

Cited by 5 publications

(7 citation statements)

References 16 publications

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“…In Equation (8), ω p represents the electron cyclotron frequency. 31 ω T is the gyromagnetic frequency determined by the time-and location-varying geomagnetic field.…”

Section: Fem and Relative Permittivity Tensor For The Ionospherementioning

confidence: 99%

Finite Element Method study on VLF propagable modes coupling and interference in the anisotropic earth‐ionosphere waveguide

Liu,

Wang,

Zhang

et al. 2024

Int J Numerical Modelling

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In this paper, the coupled‐mode theory is incorporated into the improved frequency‐domain finite element method (FEM) to simulate very low frequency (VLF) propagable modes coupling and interference in the anisotropic Earth‐ionosphere waveguide. The matrix equation of the electric field is solved using parallel lower‐upper factorization technique to speed up the calculation. The method used to determine the propagation constants for different propagable modes is given. After the FEM is validated by comparing simulated results with the measured data, effects of variable geomagnetic information on the attenuation rate, relative phase velocity, mode coupling, and multiple‐mode interference of VLF electromagnetic wave in the anisotropic waveguide are investigated. This work provides an efficient way for improving the prediction accuracy of the VLF communication, positioning, navigation, and timing systems.

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“…In Equation (8), ω p represents the electron cyclotron frequency. 31 ω T is the gyromagnetic frequency determined by the time-and location-varying geomagnetic field.…”

Section: Fem and Relative Permittivity Tensor For The Ionospherementioning

confidence: 99%

Finite Element Method study on VLF propagable modes coupling and interference in the anisotropic earth‐ionosphere waveguide

Liu,

Wang,

Zhang

et al. 2024

Int J Numerical Modelling

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“…Very low frequency (VLF: 3-30 kHz) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] electromagnetic waves have been widely applied in the navigation, underwater communication, earthquake, and ionosphere detection, and so forth. The Omega and Alpha are common VLF ultra-long range navigation broadcasts that provide navigational aid for aviation, oceanic air, and marine shipping.…”

Section: Introductionmentioning

confidence: 99%

“…The analytical waveguide mode theory [11][12][13] is fast and often idealizes the ionosphere that exhibits gradual variations as an equivalent sharp boundary model. 5 Thus, the inter-layer reflections cannot be effectively demonstrated.…”

Section: Introductionmentioning

confidence: 99%

“…Direct measurements are difficult for large-scale efforts due to their high cost. Based on the exponential ionosphere profile [10][11][12][13][14][15] and International Reference Ionosphere (IRI) model, analytical and num erical methods are unable to accurately predict the VLF signal amplitude and phase in the waveguide. [24][25][26] Data for the time-and location-, instead of solar zenith angle-varying IRI electric density model may be insufficient or inaccurate for the lower ionosphere.…”

Section: Introductionmentioning

confidence: 99%

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Finite element method study on VLF propagation in the fine Earth‐ionosphere waveguide

Liu,

Baraya,

Zhang

et al. 2023

Int J Numerical Modelling

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A fast and highly efficient frequency‐domain finite element method (FEM) is developed to simulate propagation characteristics of very low frequency (VLF) waves in the fine Earth‐ionosphere waveguide structure containing the transition period between day and night. The FEM is accelerated by embedding the GPU‐based parallel LU factorization method. We present an approach for determining the waveguide structure with the VLF transmitter and receiver locations. After validating the method, effects of the time‐ and location‐varying electric density on the amplitude and phase of the VLF wave are investigated. The electric density of the International Reference Ionosphere (IRI) is revised by coupling with the solar zenith angle. Numerical results simulated using the revised IRI model show excellent agreement with the measured data for the VLF wave from Novosibirsk to Qingdao. This work provides a promising way to research VLF electromagnetic properties of the Earth‐ionosphere waveguide and improve the prediction accuracy of VLF navigation and communication.

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“…Chand & Kumar (2017) investigated the VLF modal interference distance and nighttime VLF reflection height for east-west propagation paths using amplitude minima at sunrise and sunset. He et al (2018) analyzed the multimode interference and phase standard deviation of VLF wave propagation in anisotropic ground ionospheric waveguides. Xin (2019) studied the propagating decay of the first fourth order mode at very low frequencies.…”

Section: Introductionmentioning

confidence: 99%

Observation and Analysis of VLF Nocturnal Multimode Interference Phenomenon based on Waveguide Mode Theory

Yang,

Niu,

Wang

et al. 2023

Res. Astron. Astrophys.

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Very low frequency (VLF) signals are propagated between the ground-ionosphere. Multimode interference will cause the phase to show oscillatory changes with distance while propagating at night, leading to abnormalities in the received VLF signal. This study uses the VLF signal received in Qingdao City, Shandong Province, from the Russian Alpha navigation system to explore the multimode interference problem of VLF signal propagation. The characteristics of the effect of multimode interference phenomena on the phase are analyzed according to the variation of the phase of the VLF signal. However, the phase of VLF signals will also be affected by the X-ray and energetic particles that are released during the eruption of solar flares, therefore the two phenomena are studied in this work. It is concluded that the X-ray will not affect the phase of VLF signals at night, but the energetic particles will affect the phase change, and the influence of energetic particles should be excluded in the study of multimode interference phenomena. Using VLF signals for navigation positioning in degraded or unavailable GPS conditions is of great practical significance for very low frequency navigation systems as it can avoid the influence of multimode interference and improve positioning accuracy.

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Multiple-Mode Interference and Phase Standard Deviation of VLF Wave Propagation in an Anisotropic Earth–Ionosphere Waveguide

Cited by 5 publications

References 16 publications

Finite Element Method study on VLF propagable modes coupling and interference in the anisotropic earth‐ionosphere waveguide

Finite Element Method study on VLF propagable modes coupling and interference in the anisotropic earth‐ionosphere waveguide

Finite element method study on VLF propagation in the fine Earth‐ionosphere waveguide

Observation and Analysis of VLF Nocturnal Multimode Interference Phenomenon based on Waveguide Mode Theory

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