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).