Ionospheric perturbations induced by tsunamis and earthquakes can be used for tsunami early warning and remote sensing of earthquakes, provided the perturbations are characterized properly to distinguish them from the ones caused by other sources. The ionospheric perturbations are increasingly being obtained from Global Positioning System (GPS) based Total Electron Content (TEC) measurements sampled at uniform time intervals. However, the sampling is not uniform in space. The nonuniform spatial sampling along the GPS satellite tracks introduces aliasing if it is not accounted while computing the ionospheric perturbations. All the methods hitherto used to detect the co-seismic and tsunamigenic ionospheric perturbations did not account the nonuniform spatial sampling while computing these perturbations. In addition, the residual approach used to obtain the perturbations by detrending the TEC time series using high-order polynomial fit introduces artifacts. These aliasing and artifacts corrupt amplitude, Signal-to-Noise Ratio (SNR), phase, and frequency of ionospheric perturbations which are vital to distinguish the perturbations induced by tsunamis and earthquakes from the rest. We show that Spatio-Periodic Leveling Algorithm (SPLA) successfully removes such aliasing and artifacts. The efficiency of SPLA in removing the aliases and artifacts is validated under two simulated scenarios, and using GPS observations carried out during two natural disasters – the 2004 Indian Ocean tsunami and the 2015 Nepal-Gorkha earthquake. We, further, studied the severity of aliasing and artifacts on co-seismic and tsunamigenic perturbations by analyzing its characteristics employing SNR, spatiotemporal, and wavelet analyses. The results reveal that removal of aliasing and artifacts using SPLA i) increases the SNR up to ~149% compared to the residual method and ~39% compared to the differential method, ii) distinctly resolves signals from sharp static variations, and iii) detects 50% more co-seismic ionospheric perturbations and 25% more tsunami-induced ionospheric perturbations in the two events studied. Cross-correlation of the perturbation time series obtained using the residual method and SPLA reveals that aliasing and artifacts shift the time of occurrence by -7.64 minutes to +4.21 minutes. Further, the results show that the SPLA efficiently detects the ionospheric perturbations at low elevation angles, thereby removes the need of applying elevation cut-off and increases the area of ionospheric exploration of a GPS receiver.