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Optimal Solutions to a Linear Inverse Problem in Geophysics

Jordan, Thomas H. and Franklin, Joel N. (1971) Optimal Solutions to a Linear Inverse Problem in Geophysics. Proceedings of the National Academy of Sciences of the United States of America, 68 (2). pp. 291-293. ISSN 0027-8424.

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This paper is concerned with the solution of the linear system obtained in the Backus-Gilbert formulation of the inverse problem for gross earth data. The theory of well-posed stochastic extensions to ill-posed linear problems, proposed by Franklin, is developed for this application. For given estimates of the statistical variance of the noise in the data, an optimal solution is obtained under the constraint that it be the output of a prescribed linear filter. Proper specification of this filter permits the introduction of information not contained in the data about the smoothness of an acceptable solution. As an example of the application of this theory, a preliminary model is presented for the density and shear velocity as a function of radius in the earth's interior.

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Additional Information:Copyright © 1971 by the National Academy of Sciences Communicated by Frank Press, November 16, 1970 T.H.J. is indebted to Don L. Anderson for his guidance and assistance during the course of this research. The stimulating discussions and helpful comments provided by Bernard Minster and Charles Archambeau are also gratefully acknowledged. The normal-mode programs used as subroutines in the inversion computations were written by Martin Smith and utilized techniques developed by Freeman Gilbert. The travel time routines were developed by Bruce Julian. This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract F44620-69-C-0067. Thomas H. Jordan is affiliated with the Seismological Laboratory, Division of Geological Sciences and Joel N. Franklin is a member of the Division of Engineering and Applied Sciences, California Institute of Technology. This work is contribution No. 1933 from the Division of Geological Sciences, California Institute of Technology.
Issue or Number:2
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ID Code:4688
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Deposited On:03 Sep 2006
Last Modified:02 Oct 2019 23:15

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