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The Backup-Gilbert Method and Its Application to the Electrical Conductivity ProblemThe theory of Backus and Gilbert gives a technique for solving the general linear inverse problem. Observational error and lack of data are shown to reduce the reliability of the solution in different ways: the former introduces statistical uncertainties in the model, while the latter smooths out the detail. Precision can be improved by sacrificing resolving power, and vice versa, so that some compromise may be made between the two in choosing the best model. Nonlinear inverse problems can be brought into the domain of the theory by linearizing about a typical solution.

The inverse problem of electrical conductivity in the mantle is used to illustrate the Backus-Gilbert technique; an example of the tradeoff diagram is given.
Document ID
19730002892
Acquisition Source
Ames Research Center
Document Type
Conference Paper
Authors
Robert L Parker
(University of California San Diego San Diego, United States)
Date Acquired
August 7, 2013
Publication Date
August 1, 1972
Publication Information
Subject Category
Electronics and Electrical Engineering
Report/Patent Number
NASA-TM-X-62150
Meeting Information
Meeting: Workshop on the Mathematics of Profile Inversion
Location: Moffett Field, CA
Country: US
Start Date: July 12, 1971
End Date: July 16, 1971
Sponsors: National Aeronautics and Space Administration
Accession Number
73N11619
Distribution Limits
Public
Copyright
Use by or on behalf of the US Gov. Permitted.
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