## 3 Results
### Modelling and Simulation during LEP Event
Detailed methodology, related to utilisation of LWPC software and VLF signal propagation modelling for different cases, can be found in [14; 29; 56; 57]. Here, the procedure for modelling parameters \(\beta\) and \(H^{\prime}\) is only outlined. The basic parameters of the propagation medium, the sharpness of the upper boundary of the Earth-ionosphere waveguide \(\beta\) and the height of the signal's reflection \(H^{\prime}\) are related to the electron density \(N_{e}(z)\) within the waveguide. Each change in the electron density in the waveguide changes the propagation parameters, amplitude and phase delay of the VLF signal. According to the LWPM model, for regular night-time conditions in the ionosphere, the program code takes the parameter \(\beta\) as 0.40 km\({}^{-1}\) and the parameter \(H^{\prime}\) as 87 km. However, to model the values of the amplitude and phase delay of the VLF signal, in each individual case, it is necessary to independently determine the appropriate parameter pairs (\(\beta\), \(H^{\prime}\)) as input parameters, so that the simulated values of the amplitude and phase delay obtained as output by the computation, correspond to \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**VLF Signal**} & \multirow{2}{*}{**Time UT**} & \multicolumn{3}{c}{**Measured Values**} & \multicolumn{3}{c}{**LWPC Simulation**} \\ \cline{3-10}  & & **A (dB)** & \(\Delta A\) (dB)** & \(P\) (\({}^{\circ}\)) & \(\Delta P\) (\({}^{\circ}\)) & \(A\) (dB)** & \(\Delta A\) (dB) & \(P\) (\({}^{\circ}\)) & \(\Delta P\) (\({}^{\circ}\)) \\ \hline NAA/24.0 kHz & \multirow{2}{*}{20.16 s} & \multirow{2}{*}{55.42} & \multirow{2}{*}{0} & \multirow{2}{*}{157.08} & \multirow{2}{*}{0} & \multirow{2}{*}{55.63} & \multirow{2}{*}{0} & \multirow{2}{*}{173.18} & \multirow{2}{*}{0} \\ unperturbed values & & & & & & & & & \\ \hline NAA/24.0 kHz & \multirow{2}{*}{25.54 s} & \multirow{2}{*}{54.37} & \multirow{2}{*}{\(-1.05\)} & \multirow{2}{*}{170.03} & \multirow{2}{*}{12.95} & \multirow{2}{*}{54.62} & \multirow{2}{*}{\(-1.01\)} & \multirow{2}{*}{195.02} & \multirow{2}{*}{21.84} \\ perturbed values & & & & & & & & & \\ \hline GQD/22.1 kHz & \multirow{2}{*}{20.16 s} & \multirow{2}{*}{70.70} & \multirow{2}{*}{0} & \multirow{2}{*}{–178.05} & \multirow{2}{*}{0} & \multirow{2}{*}{70.40} & \multirow{2}{*}{0} & \multirow{2}{*}{\(-214.88\)} & \multirow{2}{*}{0} \\ unperturbed values & & & & & & & & & \\ \hline GQD/22.1 kHz & \multirow{2}{*}{25.54 s} & \multirow{2}{*}{68.96} & \multirow{2}{*}{\(-1.74\)} & \multirow{2}{*}{–169.05} & \multirow{2}{*}{9} & \multirow{2}{*}{68.65} & \multirow{2}{*}{\(-1.75\)} & \multirow{2}{*}{\(-209.22\)} & \multirow{2}{*}{5.66} \\ perturbed values & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured and estimated amplitude and phase delay values of NAA and GQD signals during the LEP event that occurred on 16 November 2004.  
the measured values of the amplitude and phase delay as close as possible, as the best fitting pair. The procedure itself consists of numerous trials, in which parameter pairs (\(\beta\), \(H^{\prime}\)) are manually defined as input parameters and the program gives calculated amplitude and phase delay as the output values. Program output is dependent on numerous factors (such as signal frequency, bearing angle, receiver and transmitter locations, observed date and time, solar zenith angle, geomagnetic dip and electro-conductivity of lower waveguide boundary) that are imbedded as background data in calculations. During night-time ionospheric VLF transmission, signal's amplitude is more stable than phase delay. During modelling, we focused on providing (\(\beta\), \(H^{\prime}\)) parameter pairs to obtain a really good agreement for relative amplitude change \(\Delta A\) (dB) for both analysed signals, while still obtaining a relatively good agreement for relative change in phase delay \(\Delta P\) (\({}^{\circ}\)).