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Upward continuation of Markov type anomalous gravity potential models
Abstract Linear gravity field state space models are still a useful tool to model the anomalous gravity field in vector gravimetry, airborne gravimetry, inertial geodesy and navigation. This paper deals with an idea ofJordan and Heller (1978) to solve analytically the upward continuation problem of Markov gravity models. In contrary to the standard Markov shaping filter approach the height dependency of the covariance function, i.e. variance factor and correlation length as function of height, is strictly introduced in state space and not neglected. Using some basic integral transforms, a general upward continuation integral is derived for the n-th order Markov process. The upward continuation integral is solved for the special and practically important case of 2nd order Markov process in very detail. This leads to the introduction of the special sine and cosine integral functions into the the mathematical covariance model. The features of the covariance model are analyzed analytically and the height dependency is discussed numerically.
Upward continuation of Markov type anomalous gravity potential models
Abstract Linear gravity field state space models are still a useful tool to model the anomalous gravity field in vector gravimetry, airborne gravimetry, inertial geodesy and navigation. This paper deals with an idea ofJordan and Heller (1978) to solve analytically the upward continuation problem of Markov gravity models. In contrary to the standard Markov shaping filter approach the height dependency of the covariance function, i.e. variance factor and correlation length as function of height, is strictly introduced in state space and not neglected. Using some basic integral transforms, a general upward continuation integral is derived for the n-th order Markov process. The upward continuation integral is solved for the special and practically important case of 2nd order Markov process in very detail. This leads to the introduction of the special sine and cosine integral functions into the the mathematical covariance model. The features of the covariance model are analyzed analytically and the height dependency is discussed numerically.
Upward continuation of Markov type anomalous gravity potential models
Eissfeller, Bernd (Autor:in)
Journal of Geodesy ; 70
1996
Aufsatz (Zeitschrift)
Englisch
BKL:
38.73
Geodäsie
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