تجزيه و تجليل حساسيت داده هاي جاذبي براي ماهواره گراني سنجي GRACE-1

Sensitivity analysis of the GRACE in single satellite mode

One of the essential studies, to be carried out before the launch of gravimetric satellites, is their sensitivity to the gravity field of the Earth, which is done based on simulated studies. Besides, as soon as the satellite is launched it is possible to apply the "sensitivity analysis", or "spectroscopic analysis" to the real satelliteʹs observations, to find out which parts of the gravity field spectrum must included in the gravity field model, derived based on the satellite observations. In this paper, 345 days of actual GRACE-1 gravitational potential observations during the year 2004 are used within the "energy integral" approach for sensitivity analysis of the GRACE in a single satellite mode. To setup the observation equations, spherical harmonic expansion to degree and order nmax = 60 is considered. This degree and order of expansion is associated with the spatial resolution of 180° /nmax = 3° of spherical harmonics and results in 180° /nmax /2 = 1.5° as the minimum sampling interval, needed for the observations, based on the Nyquist sampling theorem. Since this sampling interval is granted by the coverage made by the aforementioned 345 days of the GRACE-1 satellite observations, we proceeded into the setup of the observation equations. In this way, 486,743 observation equations are setup for the computation of 3,721 spherical harmonic coefficients up to degree and order nmax = 60 . Having computed the coefficient matrix A of the observation equations, and the weight matrix P of the measurements, the covariance matrix C- = (ATPA)_1 is computed with 483,022 degrees of freedom. Next, the geopotential model EGM96 is considered as the indicator of size of the spherical harmonic coefficients to test the statistical meaningfulness of the coefficients using statistical tests. Based on the computations, the GRACE in the single satellite mode is insensitive to gravity signals up to degree and order nmax = 50