Open AccessThe Theory of Ideal Bodies for Gravity Interpretation
Author(s) -
Parker Robert L.
Publication year - 1975
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1975.tb05864.x
Subject(s) - bounding overwatch , ideal (ethics) , interpretation (philosophy) , bouguer anomaly , ambiguity , mathematics , upper and lower bounds , gravity anomaly , anomaly (physics) , geology , geometry , mathematical analysis , computer science , physics , paleontology , philosophy , epistemology , artificial intelligence , oil field , programming language , condensed matter physics
Summary Ambiguity in gravity interpretation is inevitable because of the fundamental incompleteness of real observations; it is, however, possible to provide rigorous limits on possible solutions even with incomplete data. In this paper a systematic theory is developed for finding such bounds, including an upper bound on depth of burial; the bounds are discovered by constructing the unique body achieving the extreme parameter, e.g. depth; such a body is called the 'ideal' one associated with the given data. Ideal bodies can also be constructed for bounding density, thickness of layer and lateral extent. General properties of ideal bodies are derived and numerical methods for modest numbers of observations are discussed. Some artificial examples, where the buried system is exactly known, are given and it is shown how relatively good bounds can be reached with only a few measurements. A Bouguer anomaly from the Swiss Alps is then considered and it is concluded that the mountain roots are unusually shallow there.