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Generalized approach to linearized inversion with constraints
Author(s) -
Carrion Philip M.,
de Jesus Carneiro Donizeti
Publication year - 1989
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl016i009p01039
Subject(s) - inversion (geology) , a priori and a posteriori , formalism (music) , computer science , inverse problem , mathematics , algorithm , mathematical optimization , least squares function approximation , geology , mathematical analysis , seismology , art , musical , philosophy , statistics , epistemology , estimator , visual arts , tectonics
In this paper, we will develop a novel formalism for the generalized linear least‐squares inversion with arbitrary a priori information incorporated in the inversion in terms of “soft” and “hard” bounds. The technique can be a valuable tool for solving different problems, including those related to global seismology and high‐resolution crustal imagery, especially when numerical algorithms break down due to the absence of properly chosen constraints. Due to different undesirable events in the recorded data (such as leg jumps, skips, significant noise level) the conventional least‐squares in realistic situations can give erroneous solutions since the model parameters can easily readjust to variations in the measured data and give inaccurate or even non‐physical results. Constrained inversion has been overlooked by geophysicists since the mathematics involved are much more complicated. We show that using the concept of duality, constrained problems can be transformed to unconstrained dual problems and an explicit solution with soft and hard bounds can be found.