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.