1 Introduction
Earthquakes and tsunamis killed more people than all other types of disasters, claiming nearly 884,000 lives, globally, between 1980 – 2014 (UNISDR et al., 2015). Among these two disasters, tsunamis were the most deadly with an average of 79 deaths for every 1,000 people affected, compared to four deaths per 1,000 in the case of earthquakes (UNISDR et al., 2015). This makes tsunamis almost twenty times more deadly than earthquakes. As there is no mechanism exists at present to forecast or predict the earthquakes and tsunamis, timely detection and early warning are the only alternative to reduce the loss of lives caused by these disasters. Ionospheric studies carried out for the last two decades show that monitoring ionospheric perturbation induced by earthquakes (CIP – Co-Seismic Ionospheric Perturbations) and tsunamis (TIP – Tsunami induced Ionospheric Perturbation) using Global Positioning System (GPS) is a promising tool for the timely detection and early warning (For example, Astafyeva, 2019, Bagiya et al. 2017, Catherine et al., 2015, Jin et al., 2015, Occhipinti et al., 2013, Manta et al., 2020). Further, detection of ionospheric perturbations induced by earthquakes and Rayleigh waves showed the possibilities of ionospheric remote sensing of earthquakes (Ducic et al., 2003, Occhipinti, 2015) and CIPs detected over the epicentral area was found to be useful to determine the seismic source structure and rupture dynamics of the seismic fault (Astafyeva and Shults, 2019, Jin et al., 2015, Occhipinti, 2015). In addition, studying ionospheric perturbations caused by atmospheric events such as tropospheric convections (Azeem and Barlage, 2018), cyclones (Kong et al., 2018), and stratospheric gravity waves (Hoffmann et al., 2018) are also gaining interest among the researchers apart from the popular use of the ionospheric perturbations to study the geomagnetic storms (Prikryl et al., 2013, Cherniak et al., 2015). As far as earthquake studies are concerned, strong motion accelerometers and seismometers are providing reliable information. However, they are limited to land as the observations are predominantly terrestrial. In this scenario, CIPs detected using GPS can be supplemental to seismic observations by providing information over both land and ocean (Occhipinti, 2015). However, distinguishing the ionospheric perturbations associated with earthquakes and tsunamis from the rest is essential to reap the complete benefits of GPS based ionospheric observations for seismic and tsunami studies. Distinguishing the ionospheric perturbations associated with various events from one another is achieved based on the characteristics of the perturbations, namely amplitude, velocity, frequency, and phase. However, accurate detection of the ionospheric perturbations and determining its characteristics fundamentally depends on the methodology employed to derive the perturbations from GPS based Total Electron Content (TEC) measurements (Shimna and Vijayan, 2018; 2020).
Ionospheric perturbations computed hitherto, using GPS based TEC observations sampled at uniform time intervals, implicitly assumed uniform spatial sampling. In reality, distance between the sampling locations or Ionospheric Pierce Points (IPP) are positioned at non-uniform intervals along the tracks of GPS satellites traced by ground-based GPS receivers. This leads to non-uniform spatial sampling of TEC along the satellite track. Eventually, this unaccounted non-uniform spatial sampling introduces falls spatiotemporal gradient (Fig. 1). The falls spatiotemporal gradients caused by such unaccounted non-uniform spatial sampling will get amalgamated in the ionospheric perturbations and cause signal aliasing (Shimna and Vijayan 2020). Such aliasing will mislead the detection of ionospheric perturbations and its characterization. Further, the distance between adjacent IPPs (inter-IPP distances) are nonlinear in time due to the non-uniform spatial sampling and, in general, it is big at low elevations and small at high elevations (Shimna and Vijayan 2020). Generally, the high aliasing at low elevation angles is attributed to elevation-dependent errors, like multi-path. Conventionally, the errors associated with the low elevation observations are alleviated by applying elevation cut-offs. However, discarding low elevation observations are not viable while monitoring ionospheric perturbations of geophysical origin, particularly, caused by earthquakes (Thomas et al., 2018) and tsunamis (Artru et al. 2005). Low elevation observations are vital to detect TIPs generated by tsunamis propagating in deep ocean using onshore GPS receivers. Hence, discarding low elevation observations limit the utility of GPS based ionospheric observations for tsunami and earthquake early warning. In addition, the residual approach used in many studies (for example, Astefyeva et al., 2009; Hickey et al., 2009; Rolland et al., 2011; Tsugawa et al., 2011; Jin et al. 2015; Komjathy et al., 2016; Savastano et al., 2017) in which the perturbation is computed by detrending the TEC time series using a high-order polynomial introduce severe artifacts (refer section 2.2).