2.2 Residual method
The residual method is used in many seismo-ionopsheric and
tsunami-ionospheric studies as an alternative to the differential method
(Astafyeva et al., 2009; Galvan et al., 2011; Tsugawa et al., 2011; Jin
et al., 2015). In this method, ionospheric perturbations, represented as
a residual TEC (rTEC), is obtained by subtracting a high order
polynomial fitted to the TEC time series from the observed TEC values.
– (3)
where Pt is the high order polynomial representing the
trend of vTEC time series along the IPP track formed by
satellite-receiver link. In this work, we employ a
10th order polynomial, following Galvan et al. (2011),
to compute the trend along the arc.
The high-order polynomial is expected to represent the regular
characteristic variations of TEC. However, the order cannot be too high
because it would introduce additional variations in the residuals
(Galvan et al., 2011). Hence, polynomials of varying degrees need to be
applied for several cases and then a polynomial that could fit
reasonably should be selected to represent the trend of each
event-specific LoS-TEC time series. This makes the selection of a
suitable polynomial subjective. Besides, an order of the polynomial is
assumed to be uniform across LoS-TEC of all receiver-satellite pairs for
ease of automation, especially, on computing rTEC in case of dense
networks of GPS receivers like the one in Japan (Galvan et al. 2011).
This arbitrariness in the selection of the polynomial will allow the
errors associated with the misfits to creep into the residual time
series (rTEC) as signal aliasing and artifact. Further, severe misfits
can lead to complete failure in detecting the perturbations. The
post-processing of rTEC to remove the artifacts and aliasing will be
complex and eventually leads to erroneous inferences. Moreover, the
subjective selection of high order polynomial limits the use of the
residual method for monitoring the perturbations in real-time.
Apart from differential and residual methods, methods like variometric
approach (e.g. VARION – Variometric Approach for Real-Time Ionosphere
Observation proposed by Savastano et al. (2017)) uses both differential
and residual approaches together for real-time detection of TIPs. VARION
uses 8th order polynomial to fit the differential TEC
time series, subtract the differential TEC from polynomial fit and
represents the residuals as the variation due to a TID perturbation (see
Savastano et al. (2017) for further details). In such cases, the
obtained ionospheric perturbations will be affected by both aliasing and
artifacts.