A geometrical interpretation of ideal body problems |
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| Authors: | Stephen P Huestis |
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| Institution: | Department of Geology, University of New Mexico, Albuquerque, New Mexico 87131, USA |
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| Abstract: | Summary. For linear geophysical inverse problems, the exercise of finding a greatest lower bound on the uniform norms of positive solutions fitting N data, is shown to have a geometrical counterpart in the N- dimensional space of N -tuples of real numbers. By application of the Fenchel Duality Theorem, we demonstrate that the problem is equivalent to the discovery of a particular hyperplane tangent to a convex set in this space. As examples in the case of two data, the new formulation is applied to the problems of recovering density information from planetary mass and moment of inertia, and from two vertical gravity anomalies. |
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