## 2 Materials and Methods
Figure 1: Detrending sTEC to determine depletion in (**a**) PRN 32 (GPS) and (**b**) PRN 89 (Galileo) on 23 April 2023. The upper panels show observed sTEC (black) and sTEC trend with variable window sizes (10 (cyan), 60 (red), 90 (green), and 120 (blue) minutes). The lower panels show detrended sTEC (sTEC depletion) in respective PRNs. The depletion depth (\(\Delta\)(sTEC)) is calculated as in Equation (1):  
\[\Delta(\text{sTEC})=\text{abs}(\text{sTEC}_{\text{minimum}})+\frac{\text{sTEC}_{ \text{dL}}+\text{sTEC}_{\text{dR}}}{2}, \tag{1}\]  
where sTEC minimum is the minimum value in the detrended TEC curve, sTEC, and sTEC, are the nearby maximum values on the left and right of the absolute minimum value in the detrended TEC curve as shown in Figure 2b. The apparent duration or the depletion time (tSTEC) is calculated as in Equation (2). \[\text{t}_{\text{sTEC}}=\text{UT}(\text{sTEC}_{\text{dR}})-\text{UT}(\text{sTEC }_{\text{dL}}), \tag{2}\]  
where UT (sTEC,dL) is the time at the sTEC,dL, and UT (sTEC,dR) is the time at the sTEC, in the TEC detrended curve as shown in Figure 2b. PRNs from all the GNSS constellations fulfilling the threshold values for the indication of plasma bubble occurrence are chosen in this study. TEC depletion is observed in some PRNs that do not fulfil the thresholds of possible plasma bubble occurrence. This depletion may be due to the F layer anomalies, ionospheric density redistribution or MSTIDs. Further, the ionospheric delays corresponding to the frequencies are calculated using the sTEC depletions for the satellite PRNs affected by the EPB. The ionospheric delays corresponding to the depletion depth in any radio signal can be obtained by using Equation (3). \[\text{I}=\frac{40.31071}{\hat{\rho}^{2}}*\Delta(\text{sTEC}) \tag{3}\]  
Figure 2: The observed sTEC (black line), moving average (blue line) and the detrended TEC curves (sTEC depletion; red line with a marker ‘\(\times\)’) for (**a**) PRN 32 (GPS) and (**b**) PRN 89 (Galileo) in the upper panels, followed by the zoomed-in versions of the region of interests in lower panels, indicating the respective TEC depletion depth (\(\Delta\)(sTEC)) and apparent duration (tSTEC) during the geomagnetic storm event on 23 April 2023.  
where 'I' denotes the ionospheric delay in meters, \(\Delta\)(sTEC) is depletion depth in TECU, and f is the frequency of the radio signal in Hz. In this study, the sTEC is used in all the computations and observations which is sometimes mentioned as TEC. The effect of the EPB on the other available frequencies of all the constellations is observed in terms of S4 and \(\sigma_{\varphi}\) that are recorded by the GISTM receiver along with observational TEC. To further substantiate the connection between TEC depletion at the location and prevailing EPBs over the Indian longitude sector on 23 April 2023 geomagnetic storm day, the ROTI variations at the present location (KLEF) and the available geodetic GNSS stations under International GNSS Service (IGS) stations (IISC, HYDE, and LCK3), ranging from near equatorial latitude to outer edge of equatorial ionization anomaly (EIA) crest latitude, are obtained from SIMuRG: System for Ionosphere Monitoring and Research from GNSS [79].