Search

With the advent of geodetic satellite missions mapping almost globally the Earth's gravitational field, new methods and theoretical approaches have been developed and investigated to fully exploit the potential of their new observables. Besides estimating values of numerical coefficients in harmonic series of the gravitational potential, new applications emerged such as data validation and combination. In this contribution, new integral transformations are presented which transform principal components of the terrestrial deflection of the vertical onto disturbing satellite-to-satellite tracking and gradiometric data at altitude. Using spherical approximation, necessary integral kernel functions are derived in both spectral and closed forms. The behaviour of isotropic kernel functions is studied and the new integral transformations are tested in a closed-loop simulation using synthetic terrestrial and satellite data synthesized from a global gravitational model. New integral transformations can be used for data validation and combination purposes. [ABSTRACT FROM AUTHOR]

Integral transformations of gravitational gradients onto a Gravity Recovery And Climate Experiment (GRACE) type of observable are derived in this article. The gravitational gradients represent components of the gravitational tensor in the local north-oriented frame. The GRACE type of observable corresponds to a difference between two gravitational vectors as projected onto the line of sight between the two GRACE satellites. In total, three integral transformations relating vertical-vertical, vertical-horizontal and horizontal-horizontal gravitational gradients with the GRACE type of observable are provided. Spectral and closed forms of corresponding isotropic kernels are derived for each transformation. Special cases show that the integral transformations are general and relate gravitational gradients to many other quantities of the gravitational field, such as the gravitational vector, and its radial and tangential components. Correctness of the mathematical derivations is validated in a closed-loop simulation using synthetic data. [ABSTRACT FROM AUTHOR]

New integral formulas for upward/downward continuation of gravitational gradients onto gravitational gradients are derived in this article. They provide more options for continuation of gravitational gradient combinations and extend available mathematical apparatus formulated for this purpose up to now. The starting point represents the analytical solution of the spherical gradiometric boundary value problem in the spatial domain. Applying corresponding differential operators on the analytical solution of the spherical gradiometric boundary value problem, a total of 18 integral formulas are provided. Spatial and spectral forms of isotropic kernels are given and their behaviour for parameters of a GOCE-like satellite is investigated. Correctness of the new integral formulas and the isotropic kernels is tested in a closed-loop simulation. The derived integral formulas and the isotropic kernels form a theoretical basis for validation purposes and geophysical applications of satellite gradiometric data as provided currently by the GOCE mission. They also extend the well-known Meissl scheme. [ABSTRACT FROM AUTHOR]