<p>We present an autonomous model to simulate the daytime variation of sub-ionospheric Very Low Frequency (VLF) signal amplitude, beginning with the computation of the D-region electron density by numerically solving the electron continuity equation (ECE). From the resulting altitude-dependent electron density profile (<InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mi>e</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$N_{e}$</EquationSource> </InlineEquation>), we extract Wait’s ionospheric parameters (<InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msup> <mi>h</mi> <mo>′</mo> </msup> </math></EquationSource> <EquationSource Format="TEX">$h^{\prime }$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> <EquationSource Format="TEX">$\beta $</EquationSource> </InlineEquation>) using a log-linear fitting method. The study focuses on two VLF propagation paths (one short and one medium in length) in India, originating from the VTX / 18.2 kHz transmitter. The model effectively employs the Long Wave Propagation Capability (LWPC) framework to reproduce the daytime VLF signal amplitude profile. It accurately captures the daytime variations observed at the Bengaluru (BAN) station, where the ground wave component is dominant, as well as at Khukurdaha, WB (KHK). A quantitative comparison between the simulated (<InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mrow> <mi>s</mi> <mi>i</mi> <mi>m</mi> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$A_{sim}$</EquationSource> </InlineEquation>) and (<InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>s</mi> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$A_{obs}$</EquationSource> </InlineEquation>) observed amplitudes shows justified agreement, validating the physical consistency and possible predictive capability of the proposed approach.</p>

An autonomous approach to model daytime behavior of sub-ionospheric VLF signals over short and medium propagation paths in India

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发表日期：

2026年1月22日

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Sayak Chakraborty,
Tamal Basak,
Sourav Palit,
Sandip K. Chakrabarti

摘要

We present an autonomous model to simulate the daytime variation of sub-ionospheric Very Low Frequency (VLF) signal amplitude, beginning with the computation of the D-region electron density by numerically solving the electron continuity equation (ECE). From the resulting altitude-dependent electron density profile ( $N_{e}$ $N_{e}$ ), we extract Wait’s ionospheric parameters ( $h^{'}$ $h^{\prime }$ and $β$ $\beta $ ) using a log-linear fitting method. The study focuses on two VLF propagation paths (one short and one medium in length) in India, originating from the VTX / 18.2 kHz transmitter. The model effectively employs the Long Wave Propagation Capability (LWPC) framework to reproduce the daytime VLF signal amplitude profile. It accurately captures the daytime variations observed at the Bengaluru (BAN) station, where the ground wave component is dominant, as well as at Khukurdaha, WB (KHK). A quantitative comparison between the simulated ( $A_{s i m}$ $A_{sim}$ ) and ( $A_{o b s}$ $A_{obs}$ ) observed amplitudes shows justified agreement, validating the physical consistency and possible predictive capability of the proposed approach.