[G03-2] Time-varying gravity field estimation

[G03-2-05] Amplitude-phase representation of GRACE spherical harmonic spectra

^○Nico Sneeuw¹, Balaji Devaraju² (1.Institute of Geodesy, University of Stuttgart, Stuttgart, Germany, 2.Institute of Geodesy, Leibniz University of Hannover, Hannover, Germany)

Representing the spherical harmonic spectrum of a field on the sphere in terms
of its amplitude and phase is termed as its polar form. While the polar form
of the Fourier spectrum, especially in time-series analysis and image
processing, is well understood, it is an alien concept in geodesy. To this
extent, we first show that spherical harmonic synthesis can be interpreted as
a weighted (by amplitude) sum of rotated (by phase) spherical harmonics. As an
example, we explore the polar forms of the monthly GRACE time-variable gravity
field data before and after filtering. The impact of filtering on amplitude is
well understood, but that on phase has not been studied previously. Here, we
demonstrate that certain class of filters only affect the amplitude of the
spherical harmonic spectrum and not the phase, but the others affect both the
amplitude and phase. Further, we also demonstrate that the filtered phase
helps in ascertaining the efficacy of decorrelation filters used in the
GRACE community.