1. Theoretical study of the diurnal behavior of VLF signal and comparison with VLF campaign data Sujay Pal [1], Sudipta Sasmal[2], and Sandip K. Chakrabarti[1,2] [1] S.N. Bose National Centre for Basic Sciences, Block JD, Sector – III, Kolkata 98 [2] Indian Centre for Space Physics, 43 Chalantika, Garia Station Rd, Kolkata 84 The Sharjah-Stanford AWESOME VLF Workshop Feb 22-24, 2010, Sharjah, UAE

2. Outline of my talk Introduction Diurnal behaviour of amplitudes and phases of VLF signals Motivation of the present work Theoretical background Our theoretical results of the variation of amplitudes and phases variation A comparison with observational results Conclusions

3. Introduction: Very Low Frequency (3-30 kHz) electromagnetic signal propagation through EIWG depends strongly upon the lower ionospheric ionization conditions. The ionization varies from time to time due to variation of incident radiation on the ionosphere and due to different photo- chemical reactions. It changes the effective reflection height and reflection coefficient of a VLF signal. The reflection takes place from the D-layer (60-90 km) during day-time and from the lower E-region during night-time. Accordingly, the amplitude and phase of a VLF signal shows a diurnal variation.

4. Typical diurnal behaviour of amplitude of VTX (18.2 kHz) signal AWESOME ICSP VTX-Kathmandu ~2300 km VTX-Kolkata ~1932 km VTX-Pune ~1209 km

5. Motivation of the present work Monitoring of VLF transmitter signals from different places of India is being continuously carried out by ICSP, Kolkata using AWESOME and ICSP made set up. Significant difference in the amplitude behaviour is found over different propagation paths. Understanding of these data requires a detailed theoretical knowledge. In this work, we have tried to simulate and understand the diurnal and seasonal behaviour of amplitudes and phases of VLF signals based on wave-hop theory, [Wakai et. al, 2004].

6. Theoretical Background The effective field strength received by a small loop antenna for a 1-hop sky-wave is, in where, P t = Transmitter power in kW, Ψ = launching elevation angle relative to horizontal, R i = Ionospheric reflection coefficient, F i = Ionspheric focusing factor, F t, F r are the transmitting and receiving antenna factors, L 1 is the total sky-wave path length of 1-hop wave. For 2-hop sky-wave

7. Assume R i1 ~ R i2, F i1 ~ F i2 and F i D g =1 Similarly, field strengths for higher-order hop can be obtained. The resultant field strength and resultant phase are calculated accordingly. Models of ionospheric reflection heights and reflection coefficients as functions of solar zenith angle help us to simulate the diurnal and seasonal behaviours of VLF signals over different propagation paths. We introduce two parameters h and dh such that h N =h+dh h= daytime effective reflection height h N =nighttime effective reflection height summer winter (ITU-R Recommendations)

8. Theoretical Results

9. Diurnal behavior of amplitude of VTX (18.2 kHz) at Kolkata in Summer

10. Diurnal behavior of amplitude of VTX (18.2 kHz) at Kolkata in Winter

11. Typical phase behaviour of VTX (18.2 kHz) signal

14. A comparison : VTX 18.2 kHZ

15. Conclusions We made an effort to understand theoretically the VLF signal propagation characteristics over the Indian subcontinent. It is seen that the variation of VLF reflection height is more sensitive than the variation of reflection coefficient. By choosing appropriate parameters for both variations, observational results can be reproduced. We are also modelling the variation of received signal during total or partial solar eclipses, Gamma- ray bursts and fluctuation of ionization due to Earthquakes. More works have to be done in near future.