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A method which can be used to solve some classes of Integral Equations and is especially useful in implementing certain types of data inversion. It has been applied to invert seismic data to obtain density profiles in the Earth.
References
Backus, G. and Gilbert, F. ``The Resolving Power of Growth Earth Data.''
Geophys. J. Roy. Astron. Soc. 16, 169-205, 1968.
Backus, G. E. and Gilbert, F. ``Uniqueness in the Inversion of Inaccurate Gross Earth Data.''
Phil. Trans. Roy. Soc. London Ser. A 266, 123-192, 1970.
Loredo, T. J. and Epstein, R. I. ``Analyzing Gamma-Ray Burst Spectral Data.'' Astrophys. J. 336, 896-919, 1989.
Parker, R. L. ``Understanding Inverse Theory.'' Ann. Rev. Earth Planet. Sci. 5, 35-64, 1977.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Backus-Gilbert Method.'' §18.6 in
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge
University Press, pp. 806-809, 1992.