6.6 Magnitude of aliasing
Ionospheric perturbations derived using residual method, differential method and SPLA from the GPS observations carried out during tsunami, and earthquake are presented as a function of inter-IPP distance (Fig. 13, left). As expected from the theoretical study carried out by Shimna and Vijayan (2020), in the real data set too the rTEC and dTEC are invariant with inter-IPP distance and gROT varies as a function of distance (Fig. 13, left). Further, the values of gROT obtained in the two geophysical events are confined within the upper and lower theoretical bounds. The theoretical bounds were computed following Shimna and Vijayan (2020). These bounds are computed by considering a spatially homogeneous ionosphere, in which TEC varies at a constant rate (refer Fig. 1). The idea of computing the TB is to set a benchmark for exhibiting the impact of non-uniform spatial sampling (or inter-IPP distance) on ionospheric perturbation measurements. To obtain the TB, we considered a hypothetical ionosphere which is homogeneous in space; but varies at a constant rate (Fig. 1). Then, we computed spatiotemporal gradient of the hypothetical ionosphere measured using non-uniform spatial samples. If the spatiotemporal gradient of such an ionosphere is plotted as a function of inter-IPP distance, the spatiotemporal gradient measured along the track of uniform sampling will be a single value; but, the spatiotemporal gradient measured along the track of non-uniform spatial sampling will decrease gradually with distance (Fig. 1). Based on this idea, the upper (lower) theoretical bounds were computed assuming a constant rate of change of TEC which is equivalent to the maximum (minimum) value of ionospheric perturbation observed during the event. In both tsunami and earthquake cases considered in this study, the highest perturbation was obtained when adopting residual method. Hence, the maximum and minimum values of rTEC was used to compute the theoretical bounds using the following equation.
and
where IPmax and IPmin are maximum and minimum ionospheric perturbations, respectively.
The deviation of the ionospheric perturbations obtained using the three methods from the theoretical bound were quantified to understand the magnitude of aliasing
; – (12)
where δr is deviation relative to theoretical bound, IPn is normalized ionospheric perturbation (dTEC or rTEC or gROT), and TB is theoretical bound.
The rTEC and dTEC deviates away from the theoretical bound with maximum relative deviations (δr ) of 1.08 and 0.69, respectively (Fig. 13, left). However, the maximum deviation of gROT is only 0.33. It shows that SPLA is efficient in removing the impact of non-uniform spatial sampling.
Following Shimna and Vijayan (2020) and based on the confidence obtained from the experimental results (Fig. 13, left), average aliasing per kilometer of inter-IPP distance (Al ) in rTEC, and dTEC are computed by considering gROT as the true value using the perturbations computed at all the IPP points during the two geophysical events.
– (13)
where Al is average aliasing binned per km,IP is either rTEC or dTEC; δd is bin width.
Average aliasing plotted as a function of inter-IPP distance (Fig. 13, right) reveals that the perturbations computed at uniform time interval with the implicit assumption of uniform spatial sampling (rTEC and dTEC) can amount to alter the magnitude of perturbations up to 2 times greater than the perturbations computed by accounting non-uniform spatial sampling interval (gROT). These results reveal the effectiveness of SPLA in detecting aliasing free TIPs and CIPs.