Theoretical Study & Modelling of the Intensity Distribution of VLF Signals

Tamal Basak[1], Sujay Pal[1], S K Chakrabarti[1,2]

1] S N Bose National Centre for Basic Sciences, India2] Indian Centre for Space Physics, India

The Stanford-Sharjah VLF Workshop22-24th Feb 2010

Sharjah, UAE

Wave-hop method of Subionospheric VLF propagation

Wave hop method is mainly based on EM ray theory .

Wave received at a receiver is composed of Ground wave & Sky wave.

In general the Sky wave reaches to receiver location after experiencing n-hops within Earth-ionosphere wave guide [Wakai et al, 2004].

Description of Model

This spatial amplitude distribution of VLF signal which is being emitted from a VLF transmitter, has been theoretically modelled for sunrise & sunset times.

The lower boundary of Ionosphere and earth surface have been considered as a good reflector of VLF electromagnetic wave, and wave-hop theory is applied for the wave propagation within Earth-Ionosphere wave guide.

The resultant signal strength at a given receiving location is the vector sum of the Ground & Sky wave components of signal.

Theoretical Details

A Wave-hop method is explained by electromagnetic ray theory.

Sky wave propagates by making multiple hops within the wave-guide.

Number of sky wave hops increases with distance from transmitter.

Sky wave path is calculated from geometry. Electric field of a n-hop experienced sky wave at a given receiving point is,

Esn=600.Pt1/2.cos(ѱ).Ri

n.Fi.Rgn-1.Ft.Fr / Ln

Net electric field at receiving point is,Etotal=Eg+Es1+Es2+Es3+... The phase is calculated as, ϕ = 2π.(Ln- d) / λ.

Interference of EM wave

Ground wave & all sky wave components interfere among themselves and give a final field strength.

Total electric field vector is calculated from the phasor diagram.

Phase delay of all the sky wave components are calculated relative to ground wave vector at receiving position.

(Yoshida et al,2008Yoshida et al 2008

VTX Transmitter

India

VTX transmitter

Kolkata

Pune

Delhi

Srinagar

Sunrise & sunset Terminators

Sunset terminator shifting ===>>

Sunrise terminator <<===shifting

March June Sep Dec

March June Sep Dec

Assumptions of the theoretical model

This spatial field distribution model has been done for short and medium path VLF propagation.

The ionospheric layers are assumed to be horizontally stratified. Its lower boundary is assumed to be a sharp VLF radio wave reflector.

Ionospheric reflection coefficients of daytime & nighttime are taken to be constant within the propagation path.

Irregular fluctuation of signal field strength at nighttime has been ignored here.

East west path propagation anomaly due to the geomagnetic field effect on charged particles are neglected for simplification.

Reflection height variation during daytime with solar flux

variation has been incorporated.Intensity variations of signal have been plotted after every

30min interval during morning and evening.

Model amplitude variation at Sunrise at 5:00am on a winter day

5:00am IST

5:30am IST

Pune

srinagar

VTX transmitter

Kolkata

Model amplitude variation at Sunrise at 5:30am on a winter day

Model amplitude variation at Sunrise at 6:00am on a winter day

Model amplitude variation at Sunrise at 6:30am on a winter day

Model amplitude variation at Sunrise at 7:00am on a winter day

6:00am IST

6:30am IST

Model amplitude variation at Sunrise at 7:30am on a winter day

7:00am IST

7:30am IST

Discussions

Regular constructive and destructive interference patterns can be observed.

The daytime signal is weaker in Kolkata in comparison to nighttime but the case is opposite for Pune.

Model amplitude variation at Sunset at 5:00pm on a winter day

5:00pm IST

5:30pm IST

VTX transmitter

Srinagar

Pune

Kolkata

Model amplitude variation at Sunset at 5:30pm on a winter day

Model amplitude variation at Sunset at 6:00pm on a winter day

Model amplitude variation at Sunset at 6:30pm on a winter day

6:00pm IST

6:30pm IST

Model amplitude variation at Sunset at 7:30pm on a winter day

As the terminator is shifting with time the distribution pattern is also differing as the model parameters are changing from daytime to nighttime.

7:30am IST

Final GoalsBy modifying the parameters of this model and

incorporating generalized forms for reflection coefficient,

geomagnetic field, ionosphere conductivity etc., actual

physics of spatial distribution of VLF signal of any

transmitter in the world can be obtained.Day-length measurement & annual variation of terminator

line will give the signal pattern at any instant of time.Many other phenomena like earthquake, GRB, solar flare

& their effects on this spatial distribution can also be

added in this model.

Conclusions

A simple form of the spatial distribution of VLF signal over

Indian subcontinent has been presented. It infers about

VLF wave spatial field strength distribution over Indian

subcontinent very well.Generalized form of it is very helpful to explain the

physical reasons behind the significant variations of

observational data obtained in VLF campaigns.

Thank You