1. 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, India 2] Indian Centre for Space Physics, India The Stanford-Sharjah VLF Workshop 22-24 th Feb 2010 Sharjah, UAE

2. 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].

3. 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.

4. 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, E sn =600.P t 1/2.cos( ѱ ).R i n.F i.R g n-1.F t.F r / L n Net electric field at receiving point is, E total =E g +E s1 +E s2 +E s3 +... The phase is calculated as, ϕ = 2π.(L n - d) / λ.

5. 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,2008 Yoshida et al 2008

6. VTX Transmitter India VTX transmitter Kolkata Pune Delhi Srinagar

7. Sunrise & sunset Terminators Sunset terminator shifting ===>>  Sunrise terminator <<===shifting March June Sep Dec

8. 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.

9. Model amplitude variation at Sunrise at 5:00am on a winter day 5:00am IST 5:30am IST Pune srinagar VTX transmitter Kolkata

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

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

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

13. Model amplitude variation at Sunrise at 7:00am on a winter day 6:00am IST 6:30am IST

14. Model amplitude variation at Sunrise at 7:30am on a winter day 7:00am IST 7:30am IST

15. 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.

16. Model amplitude variation at Sunset at 5:00pm on a winter day 5:00pm IST 5:30pm IST VTX transmitter Srinagar Pune Kolkata

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

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

19. Model amplitude variation at Sunset at 6:30pm on a winter day 6:00pm IST 6:30pm IST

20. 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

21. Final Goals By 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.

22. 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.

23. Thank You