以Taylor-Kármán結構張量進行GOCE重力梯度變方-協變方之研究

Abstract

This study analyzed stochastic processes of gravity gradients from Gravity-field and steady-state Ocean Circulation Explorer (GOCE) satellite measurements by the fourth-order Taylor-Karman structured covariance tensor. The Taylor-Karman structure is often used in turbulence and is derived based on two assumptions: one is that the random function is of the “potential type”, and the other is that the field is homogenous and isotropic. GOCE carries gravity gradiometers to measure the gravity field signal and provides many different products of Earth's gravity field. In our research, we used EGG_TRF_2 to calculate empirical covariance tensors of Taiwan. We analyzed the stochastic processes of GOCE disturbing gravity gradients by empirical covariance tensors and the fourth-order Taylor-Karman structured covariance tensors. The disturbing gravity gradient field was produced by subtracting the normal gravity gradient field of GRS80 from the GOCE gravity gradient field. In our results, we used three different methods to study stochastic process of the disturbing gravity gradient field: 1. The covariance functions for the components of the covariance tensors of the disturbing gradient field are assumed to be the same; 2. The covariance functions of each component of covariance tensor can be individually chosen; 3. The covariance functions are directionally oriented in the second method. In total, six different stochastic models for building the covariance tensor were used. Results show that the disturbing gravity gradient components have different stochastic properties and the Gauss model and the Markov model of third order are the best covariance functions for use. From our analysis, the Taylor-Karman structured tensors for the stochastic properties are better than the covariance tensors derived from the spatial covariance functions of the anomalous potential.