Abstract
The practical significance of ill-posedness in a data reduction problem is reviewed. Inverse elastodynamic scattering is shown to be ill-posed in general, although suitably restricted problems may be well-posed. These results underscore the need to analyze carefully the errors of data reduction problems in NDE, and to focus attention on final results of an NDE exercise, rather than on intermediate steps.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. A. Lee,Proc. DARPA/AFML Review of Progress in Quantitative NDE, July 1979, p. 459; published as Air Force Wright Aeronautical Laboratories Technical Report AFWAL-TR-80-4078 (July 1980).
A. N. Tikhonov and V. Y. Arsenin,Solutions of Ill-Posed Problems (Winston, Washington, 1977).
D. A. Lee, R. M. Potter, W. Perry, and W. Schmaedeke,Some Practical Aspects of the Treatment of Ill-Posed Problems by Regularization, USAF Aerospace Research Laboratories Report TR-75-0022 (1975).
J. Hadamard,Princeton University Bulletin XIII:49 (1902).
J. A. Ware and K. Aki,J. Acoust. Soc. Am. 45:911 (1968).
V. H. Weston,J. Math. Phys. 13:1952 (1972).
R. J. Krueger,Q. Appl. Math. 34:129 (1976).
G. C. Gaunard and H. Uberall,J. Appl. Mech. (USA)46:957 (1979).
J. D. Achenbach,Wave Propagation in Elastic Solids (North-Holland, Amsterdam, 1973).
M. Redwood,J. Acoust. Soc. Am. 33:527 (1961).
D. Greenspan,Introduction to Partial Differential Equations, Section 3.3 (McGraw-Hill, New York, 1961).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lee, D.A. Ill-posed and well-posed problems in inverse elastodynamic scattering for nondestructive evaluation. J Nondestruct Eval 2, 161–172 (1981). https://doi.org/10.1007/BF00570728
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00570728