Open AccessPositivity constraints in linear inverse problems—II. Applications
Author(s) -
Sabatier P. C.
Publication year - 1977
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1977.tb03682.x
Subject(s) - ideal (ethics) , inverse theory , set (abstract data type) , inverse problem , interpretation (philosophy) , inverse , mathematics , distribution (mathematics) , planar , computer science , algorithm , mathematical analysis , geometry , telecommunications , philosophy , computer graphics (images) , epistemology , surface wave , programming language
Summary. A complete method of solution of linear inverse problems with non‐negativity constraints has been given previously. Here, problems with more particular applications in geophysics are discussed. First, we describe the evolution of the set of solutions when a statistical distribution of the errors is assumed. The theory of ideal bodies, which has been introduced recently by Parker, is then discussed. Conjectures of Parker's are proved. Algorithms to construct ideal bodies for any data set are given. To finish, we study planar diagrams, which nicely illustrate the extent of the set of equivalent solutions by showing two moments of a solution versus each other for all possible solutions. The evolution of these diagrams when a new measurement is made gives a good idea of the interest of this measurement. Three‐dimensional diagrams can be managed in the same way and used for the gravity interpretation.