Variations in solar, geomagnetic, and seismic activity can cause deviations in the ionospheric plasma that can be detected as disturbances in both natural and man-made signals. Total electron content (TEC) is an efficient means for investigating the structure of the ionosphere by making use of GPS receivers. In this study, TEC data obtained for eight GPS stations are compared with each other using the cross-correlation coefficient (CC), symmetric Kullback-Leibler distance (KLD), and L2 norm (L2N) for quiet days of the ionosphere, during severe geomagnetic storms and strong earthquakes. It is observed that only KLD and L2N can differentiate the seismic activity from the geomagnetic disturbance and quiet ionosphere if the stations are in a radius of 340 km. When TEC for each station is compared with an average quiet day TEC for all periods using CC, KLD, and L2N, it is observed that, again, only KLD and L2N can distinguish the approaching seismicity for stations that are within 150 km radius to the epicenter. When the TEC of consecutive days for each station and for all periods are compared, it is observed that CC, KLD, and L2N methods are all successful in distinguishing the geomagnetic disturbances. Using sliding-window statistical analysis, moving averages of daily TEC with estimated variance bounds are also obtained for all stations and for all days of interest. When these bounds are compared with each other for all periods, it is observed that CC, KLD, and L2N are successful tools for detecting ionospheric disturbances.