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.