Geoid determination by spectral combination of an Earth gravitational model with airborne and terrestrial gravimetry — a theoretical study

Abstract

Today air-gravimetry is a versatile technique to quickly collect gravity data over large regions, where terrestrial gravity data are sparse and/or of poor quality. The method requires the data to be downward continued to sea level for use in geoid determination, an inverse problem operation that calls for smoothing of the data and/or the kernel function involved (in either spectral or space domain). In this purely theoretical study we avoid this separate computational step by performing direct geoid estimation by so-called spectral combination/filtering of the data, which includes terrestrial gravimetry, airgravimetry, an Earth Gravitational Model (EGM) as well as their signal and error degree variances. Each derived geoid estimator is presented as the sum of one or two integral formulas and the harmonic series of the EGM together with the expected mean square error of the estimator. The article is limited to a theoretical study, leaving its practical tests for future investigation.