Space gravity spectroscopy: the benefits of Taylor-Karman structured criterion matrices

As soon as a space gravity spectroscopy was successfully performed, for instance by means of semicontinuous ephemeris of LEO GPS tracked satellites, the problem of data validation appeared. It is for this purpose that a stochastic model for the homogeneous and isotropic analysis of measurements, obtained as “directly” measured values in LEO satellite missions (CHAMP, GRACE, GOCE), is studied. An isotropic analysis is represented by the homogeneous distribution of measured values and the statistical properties of the model are calculated. In particular, a correlation structure function is defined by the third order tensor (Taylor-Karman tensor) for the ensemble average of a set of incremental differences in measured components. Specifically, Taylor-Karman correlation tensor is calculated with the assumption that the analyzed random function is of a “potential type”. The special class of homogeneous and isotropic correlation functions is introduced. Finally, a successful application of the concept is presented in the case study CHAMP and a comparison between modeled and estimated correlations is performed.