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 non-uniform spatial sampling along the GPS satellite tracks introduces aliasing if it is not accounted while computing the ionospheric perturbations. At the same time, the residual approach used to obtain the perturbations by detrending the TEC time series using high-order polynomial fits introduces artifacts. These aliasing and artifacts corrupt amplitude, Signal-to-Noise Ratio (SNR), phase, and frequency of the perturbations. We show that adopting Spatio-Periodic Leveling Algorithm (SPLA) successfully removes such aliasing and artifacts while detecting the perturbations using GPS. The efficiency of SPLA in removing aliases and artifacts is validated under two theoretically simulated scenarios, and using GPS observations carried out during the 2004 Indian Ocean tsunami and 2015 Nepal-Gorkha earthquake. Spatiotemporal, SNR, cross-correlation, and wavelet analysis reveal that removal of aliasing and artifacts using SPLA i) increases 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. Comparing the occurrence time of the perturbations 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 perturbations at low elevation angles and removes the need of applying elevation cut-off.