## 1. Introduction

[2] The ionosphere is an important layer of Earth's upper atmosphere that extends from 60 to 1000 km and is ionized to a plasma state primarily by radiation from the sun with density *N*_{e} varying with altitude up to 10^{12} m^{−3}. The determining parameter of the ionospheric plasma is the electron concentration, which is a complex function of variations and coupling in solar, geomagnetic, and seismic activities such as solar flares, sunspot number, solar wind, geomagnetic storms, and earthquakes. An important measurable quantity of the electron density is the total electron content (TEC), which provides an efficient means to investigate the structure of the ionosphere and upper atmosphere. TEC is defined as the line integral of electron density along a raypath or as a measure of the total number of electrons along a raypath. The unit of TEC is given in TECU, where 1 TECU = 10^{16} el*/*m^{2} [*Nayir et al.*, 2007; *Arikan et al.*, 2003]. The variations and disturbances of the ionosphere can be obtained effectively and efficiently by computing and monitoring TEC. In recent decades, the Global Positioning System (GPS), with its network of worldwide receivers, provides a cost-effective solution in estimating TEC (GPS-TEC) and monitoring ionospheric variability over a significant proportion of global landmass [*Nayir et al.*, 2007; *Arikan et al.*, 2003].

[3] The general trends of temporal and spatial variability of the ionosphere depend on Earth's diurnal and annual rotation and the distribution of magnetic field lines of the geomagnetic dipole. Earth's magnetic field is seldom quiet, even when there are no storms. The underlying trends and standard periodical variations make up the dynamics of quiet ionosphere [*Rishbeth and Garriot*, 1969]. It has long been observed that variations in the solar and geomagnetic activity and seismicity can cause deviations from the quiet conditions and these changes can be detected as disturbances in both natural and man-made signal parameters. If the magnetic field is severely disturbed, a magnetic storm is said to occur. The geomagnetic storms can be listed as one of the major sources of severe temporal and spatial variability in the ionosphere. Several empirical indices have been developed to describe the amount of the variability at any given time. These disturbances are due to the coupling of solar activity with Earth's magnetic field that involves highly complicated dynamics in the magnetosphere and ionosphere. A large number of studies in the literature [*Rishbeth and Garriot*, 1969; *Biqiang et al.*, 2007; *Vlasov et al.*, 2003; *Zhang and Xiao*, 2000] investigating the ionospheric disturbances suggest that geomagnetic storms can cause strong disturbances in the electron density distribution and TEC. Also, in recent years, the coupling of seismic activity in the lithosphere with the troposphere and ionosphere has been observed through the variations in electromagnetic signals, Earth's electric and magnetic fields, and the chemical composition of the atmosphere. Recently, there have been some theories that try to explain electromagnetic anomalies associated with preseismic activity and their effects in the ionosphere. The forecast methods [e.g., *Ondoh*, 2000; *Pulinets*, 2004; *Pulinets et al.*, 2004, 2005, 2007; *Liu et al.*, 2000, 2004; *Chuo et al.*, 2001; *Plotkin*, 2003; *Trigunait et al.*, 2004] suggest that, before the strong earthquakes, there are several disturbances in the ionospheric parameters, especially in the critical frequency of the F2 layer (foF2), ion temperatures (*T*_{i}), and TEC.

[4] In the literature, the basic statistical tools that are used to investigate the effect of ionospheric disturbances on ionospheric parameters include but are not limited to relative deviation [*Kouris and Fotiadis*, 2002; *Kouris et al.*, 2006], time derivative analysis [*Ciraolo and Spalla*, 1999], interquartile range analysis [*Liu et al.*, 2004; *Chuo et al.*, 2001; *Lazo et al.*, 2004; *Zhang et al.*, 2004], correlation analysis [*Pulinets*, 2004; *Pulinets et al.*, 2004, 2005, 2007], TEC difference analysis [*Plotkin*, 2003], and ionospheric correction [*Trigunait et al.*, 2004]. All of these methods are applied to severe geomagnetic storms or major earthquakes with magnitudes *M* ≥ 6. Yet the investigated disturbance periods and data sets are still very limited. Also, the reliability and accuracy of the applied statistical tools still need to be reconsidered for a precursor alarm signal before geomagnetic or seismic disturbances.

[5] In statistics and information theory, the Kullback-Leibler divergence is a widely used measure of distance of discrimination between two probability density distributions [*Cover and Thomas*, 2006; *Hall*, 1987; *Inglada*, 2003]. Similarly, the L2 norm is used to define the Euclidian distance between two vectors [*Kreyszig*, 1988]. Sliding-window statistical analysis with moving average and variance bounds is a useful tool in defining the time-varying general trend of the data and characterization of the underlying structure of the disturbances in terms of wide sense stationarity [*Arikan and Erol*, 1998; *Erol and Arikan*, 2005]. In this study, the variability of GPS-TEC is investigated by comparison of the disturbed days with the quiet-day trends of the ionosphere over a large data set using the measures of Kullback-Leibler divergence, L2 norm, and sliding-window statistical analysis for the first time in the literature [*Arikan et al.*, 2009; *Karatay et al.*, 2009a, 2009b]. The correlation coefficients of data sets are also computed in spatial and temporal domains. Six earthquakes with different seismic properties and two very severe geomagnetic disturbances are chosen for investigation in this study. GPS-TEC is computed for 15 days before and after each earthquake (earthquake-days period) for all the GPS stations at various distances from the earthquake epicenter. TEC values are also obtained for the periods when there is no seismic activity but the ionosphere is under the influence of strong geomagnetic disturbances (disturbed-days period) and also for the periods when there are no significant disturbances or seismic activity in the regions of interest (quiet-days period). The results are obtained for three groups of application. In the first group, the statistical tools are applied between neighboring stations for all periods. In the second group, an average quiet-day TEC estimate is obtained for each station and TEC estimates for all periods are compared with this average quiet-day TEC using statistical tools. In the third group, TEC estimates for consecutive days of all periods are compared with each other. The statistical methods used in the study and the results for the data are presented in sections 2 and 3, respectively.