Shaping filters and the upward continuation problem |
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| Authors: | K H Neumayer |
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| Institution: | (1) GeoForschungsZentrum Potsdam, GFZ/D-PAF, c/o DLR, D-82230 Oberpfaffenhofen, Germany Tel.: +49 8153 28 1330; e-mail: hans.neumayer@dlr.de, DE |
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| Abstract: | An attempt is made to bridge the gap between closed-form harmonic upward continuation (HUC) of analytic covariance functions
of the disturbing potential of the anomalous local gravity field and the numerical shaping filter construction when the local
gravity vector is modelled in the framework of Kalman filtering. Some fundamental concepts of the local gravity field, interpreted
as a stochastic process that is stationary in the plane and harmonic in the upper half space, are reviewed. The shaping-filter
modelling technique for the local gravity vector is introduced. To determine the relation between the disturbing potential
covariance function and the gravity vector covariance matrix, the role of the so-called admissible pair is established. It
is shown that rescaling an admissible pair leads to an analogue rescaling of the shaping filter matrices derived hereof; no
cumbersome numerical recalculations are necessary. The class of covariance functions whose corresponding shaping filters possess
a closed-form HUC are identified as models whose HUC can be interpreted as a rescaling.
Received: 17 December 1997 / Accepted: 7 September 1998 |
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| Keywords: | , Kalman filter,Shaping filter,Admissible pair,Rescaling,STAG model,Attenuated white noise |
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