Generalized nonlinear inverse problems solved using the least squares criterion
Article first published online: 14 JUN 2010
Copyright © 1982 by the American Geophysical Union.
Reviews of Geophysics
Volume 20, Issue 2, pages 219–232, May 1982
How to Cite
1982), Generalized nonlinear inverse problems solved using the least squares criterion, Rev. Geophys., 20(2), 219–232, doi:10.1029/RG020i002p00219., and (
- Issue published online: 14 JUN 2010
- Article first published online: 14 JUN 2010
- Manuscript Accepted: 8 DEC 1981
- Manuscript Received: 15 AUG 1981
We attempt to give a general definition of the nonlinear least squares inverse problem. First, we examine the discrete problem (finite number of data and unknowns), setting the problem in its fully nonlinear form. Second, we examine the general case where some data and/or unknowns may be functions of a continuous variable and where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodifferential equations). As particular cases of our nonlinear algorithm we find linear solutions well known in geophysics, like Jackson's (1979) solution for discrete problems or Backus and Gilbert's (1970) solution for continuous problems.