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On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity FieldThe well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.
Document ID
20050139755
Acquisition Source
Goddard Space Flight Center
Document Type
Conference Paper
Authors
Chao, Benjamin F.
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Date Acquired
August 23, 2013
Publication Date
January 1, 2004
Subject Category
Geophysics
Meeting Information
Meeting: American Geophysical Union Meeting
Location: San Francisco, CA
Country: United States
Start Date: December 13, 2004
End Date: December 17, 2004
Sponsors: American Geophysical Union
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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