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Recovery of the Earth’s Gravity Field from GOCE Satellite Gravity Gradiometry: A Case Study

Dr Oleg Abrikosov(1)and Dr Peter Schwintzer(1)

(1) GeoForshungsZentrum Potsdam, Telegrafenberg A-17, 14473 Potsdam, Germany


GOCE SGG data were simulated along a 28-day perturbed orbit with an initial semi-major axis of 6621 km, an inclination of 96.5°, and an eccentricity of 0.0045. Based on these data, we have estimated numerically the effects of various (static and time-varying) geopotential constituents on the components of the gravity gradient tensor referred to the RTN (radial – quasi-transversal – normal) local orbit system. We have seen that within the gradiometer’s measurement bandwidth the recovery of harmonic coefficients may be not affected by temporal variations of the gravity field. In fact, the total signal of the sum of considered time-dependent constituents (solid Earth tides up to degree and order 4, ocean tides up to degree 50 and order 39, variable atmospheric potential up to degree and order 50) does not exceed 0.1% of the contribution of the Earth’s static anomalous potential (GPM98CR gravity model up to degree 720). Even maximal amplitudes in the spectra of the gravity gradients generated by the sum of these time-dependent constituents were less than the anticipated measurement error of the diagonal components of the gravity gradient tensor. Therefore, in further simulation we take into account only the Earth’s static potential. The computation of power spectral densities (PSD) of gravity gradients generated by spherical harmonics of various degrees has shown that the amplitudes of all harmonics of degree n>250 are less then the anticipated error of GOCE SGG data. Thus, the static anomalous potential is expected to be recoverable up to degree 250 from the GOCE gradiometry data processing. In order to de-correlate the gravity gradients affected by colored noise, several filter approaches were considered and numerically tested for different sampling rates and different spectral properties of measurement errors (including white noise and noise with PSD presumed for GOCE SGG data). As a result, we come to a simple non-recursive filter technique, which incorporates observation equations for SGG data within a floating time interval of fixed length comparable with the GOCE measurement bandwidth. We have examined this technique for the computation of the filter coefficients based on (1) the a priori given PSD of noise and (2) a PSD of noise estimated from the sum of measured diagonal components of the gradient tensor. Each case gives practically the same results after filtering and does not change the signal/noise ratio. Naturally, the second case is closer to real processing of GOCE SGG data. Independently on sampling rate, no more than 400 data samples are required for a stable computation of the filter coefficients. We have used the proposed filter technique for a least-squares estimation of spherical harmonic coefficients of the Earth’s gravitational potential from 28-day simulated GOCE SGG data disturbed by colored noise. Finally the results of recovering spherical harmonic coefficients at various degrees are discussed.


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Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry