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A characterization of the inverse gravimetric source problem through extremal measures
Author(s) -
Anger Gottfried
Publication year - 1981
Publication title -
reviews of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.087
H-Index - 156
eISSN - 1944-9208
pISSN - 8755-1209
DOI - 10.1029/rg019i002p00299
Subject(s) - inverse problem , inverse , gravitational field , mathematics , heat equation , identification (biology) , measure (data warehouse) , characterization (materials science) , regular polygon , mathematical analysis , computer science , physics , geometry , classical mechanics , botany , database , optics , biology
Most problems in applications are inverse source problems or identification problems. This review deals with a systematic treatment of the nonnegative sources (measures) relative to the Laplace equation and the heat conduction equation producing the same potential outside a domain Ω ⊂ R ³. This set is convex and weakly compact. Therefore the basic theorems on convex sets can be applied to such problems. Sets of extremal measures are characterized by geometric conditions. Almost nothing is known about the structure of the sources which produce the earth’s gravitational field. Therefore these investigations may be of interest for the inverse problem in gravimetry. The following question remains unanswered in this review: to find additional conditions to select uniquely a measure producing the earth’s gravitational field. This question is unanswered in most inverse source problems.