Abstract
Towards Validation of Satellite Gradiometric Data Using Modified Version of 2nd Order Partial Derivatives of Extended Stokes' FormulaThe satellite gradiometric data should be validated prior to being used. One way of such a validation process is to use some integral estimators which are the second-order partial derivatives of the extended Stokes formula to regenerate the data from the gravity anomaly at the topographic surface. In this paper, we present how least-squares modification methods are used to modify such integral estimators. Our concentration will be on validation of the vertical-horizontal and horizontal-horizontal elements of the gravitational tensor at satellite level. The paper will formulate the elements of the system of equations from which the modification parameters are derived based on all types of least-squares modification. The truncation and Paul's coefficients will also be modelled.
Highlights
Satellite gradiometry is a technique to measure second-order derivatives of the Earth’s gravity field from space
This paper presents the way of using least-squares modification in validation of satellite gradiometric data
6 A DISCUSSION ON VALIDATION OF SATELLITE GRADIOMETRIC DATA Isotropy of the kernel is important in modifying the extended Stokes formula, but such a property is destroyed by taking its horizontal derivative
Summary
Satellite gradiometry is a technique to measure second-order derivatives of the Earth’s gravity field from space. The advantage of the stochastic modifications is to minimize the errors of terrestrial, geopotential coefficients and the truncation of the integral formula simultaneously It considers the quality of the existing data in its modification process as well. We take advantage his results to find a spectral form for the truncation error of the vertical-horizontal gradients It is presented in the following theorem. Equation (5c) is the spectral form of the truncation error of the vertical-horizontal derivative of the extended Stokes formula. Equation (6c) shows that the spectral form of the terrestrial error is derived from the spectrum of the kernel function minus the truncation error coefficients We will take this advantage in the least-squares modification of vertical-horizontal gradient estimators. (12c) taking derivative with respect to v k (rP ) and equating the results to zero and further simplifications the proposition is proved
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