# Equatorial Plasma Bubbles: A Review
## 2 Observations of EPBs and Associated Irregularities
### Ionospheric Scintillation Measurements
#### 2.3.1 Dependence of Scintillation Parameters on Irregularity Characteristics
In order to apply this technique, it is assumed that the space-time correlation function for intensity variations in the ground scintillation pattern is of the following form, considering the \(x\)-axis to be along the baseline of the receivers, which is in the magnetic east-west direction:  
\[C_{\rm f}(x,\ t)\ =\ F\Big{[}(x\ -\ V_{0}\ t)^{2}\ +\ V_{\rm C}^{2}\ t^{2}\Big{]} \tag{1}\]  
The parameter \(V_{\rm C}\) is referred to as the 'random' or 'characteristic' velocity in the literature [40]. For the computation of \(V_{0}\) and \(V_{\rm C}\) it is not necessary to know the functional form of \(F\), which is only required to be a monotonically decreasing function of its argument, with a maximum when the argument has a value 0: \(F(0)\ =\ 1\). It is seen from Equation (1) that for separation \(x_{0}\) between the two receivers, as long as \(V_{\rm C}\) is non-vanishing, the argument of \(F\) never becomes 0, thus the maximum value of \(F\) is achieved at a time lag of \(t_{m}\ =\ x_{0}\ V_{0}/\big{(}V_{0}^{2}\ +\ V_{\rm C}^{2}\big{)}\), for which the argument has the lowest value. This maximum value is less than 1. Thus, in addition to \(S_{4}\), there are three more parameters that may be extracted from spaced receiver scintillation data: \(V_{0}\), \(V_{\rm C}\), and \(C_{\rm f}(x_{0},\ t_{m})\). For \(V_{\rm C}\) = 0, this becomes the usual cross-correlation technique for estimating drifts. The situation with  
Figure 3: Smoothed power spectra of filtered amplitude and phase scintillations on a 140 MHz signal transmitted from the geostationary satellite ATS-6 and recorded at the low-latitude station Ootacamund during a 15 min interval starting at 21:13 h local time on 24 October 1975. The two straight lines are parallel to the linear fits to the spectra of phase fluctuations over different frequency ranges, which for weak scintillations have a one-to-one relationship with the scale sizes of the corresponding irregularities. non-vanishing \(V_{C}\) is of interest because it provides an opportunity to study the spatial evolution of the EPB irregularities with time in the non-linear phase of the development of R-T instability. An example of the variation of \(S_{4}\), \(V_{0}\), \(V_{C}\), and \(C_{I}(x_{0},\ t_{m})\) through the course of a scintillation event, recorded at the equatorial station Tirunelveli (geomagnetic latitude: 0.2\({}^{\circ}\) S) in India on a magnetically quiet day, is shown in Figure 4.  
The pattern of local time variations for \(V_{C}\) and \(C_{I}(x_{0},\ t_{m})\) shown in Figure 4 is fairly typical for most magnetically quiet days irrespective of how \(S_{4}\) varies, as it is a fundamental characteristic of the development of R-T instability [47; 48]. This will be discussed in a later section. The parameters \(V_{0}\), \(V_{C}\), and \(C_{I}(x_{0},\ t_{m})\), as computed for each sub-interval of a scintillation event, have also been used in a novel way to determine the functional form of \(F\), and hence the dominant spatial scale \(d_{I}\) in the ground scintillation pattern of intensity variations for each sub-interval of the scintillation event. It is seen from Equation (1) that \(C_{I}(x_{0},\ t_{m})\) is given by  
\[C_{I}(x_{0},\ t_{m})\ =\ F\Big{[}x_{0}^{2}\ V_{C}^{2}\Big{/}\Big{(}V_{C}^{2}\ +\ V_{0}^{2}\Big{)}\Big{]} \tag{2}\]  
Although analyzed scintillation data are always a time series, it is necessary to derive information about the spatial variations in signal intensity in the plane of the receiver in order to relate the scintillations to the irregularities. For this purpose, it is seen from Equation (1) that the spatial correlation function for intensity variations in the ground scintillation pattern is given by \(C_{I}(x,\ 0)\ =\ F\big{(}x^{2}\big{)}\). Subsequently, according to Equation (2), if \(C_{I}(x_{0},\ t_{m})\) is plotted as a function of \(x_{0}\ V_{C}/\sqrt{\big{(}V_{C}^{2}\ +\ V_{0}^{2}\big{)}}\), it would be equivalent to plotting \(C_{I}(x,\ 0)\) as a function of the spatial lag \(x\).