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Abstract

The Earth observation satellite missions play a crucial role in the monitoring and study of various phenomena occurring on the surface of the Earth. Most of these satellites sample the Earth regularly in their orbit, but these observations are non-uniformly distributed on the spatial grid. The biggest challenge in the spectral analysis of these observations is their non-uniform distribution on the spatial grid. The most common technique for spectral analysis on the plane is the Fast Fourier Transform (FFT). The FFT requires the non-equidistant signals to be resampled or interpolated on an equidistant grid. The Lomb-Scargle periodogram approach was developed as an alternative to interpolation-based techniques. The one-dimensional Lomb-Scargle methods have been widely used and explored in various research fields. However, the multidimensional Lomb-Scargle techniques are yet to be fully utilized in the spectral analysis due to their complex nature and high computational demands. In this current work, we intend to explore the Lomb Scargle Periodogram technique for two-dimensional non-uniformly sampled geodetic observations on a two-dimensional torus. To this end, we have applied the Lomb-Scargle periodogram approach to different non-uniform two-dimensional simulated signals.