Abstract: The problem of determining the internal structure of the earth from the frequencies of free oscillation is considered. The simplified case of a spherically symmetric fluid sphere is examined. An asymptotic analysis implies that a velocity profile that is a small perturbation from a homogeneous fluid is determined, up to a finite number of parameters, by two infinite spectra of appropriate angular orders. A numerical study of the problem for finite spectra indicates what types of spectral data allow a stable reconstruction.!5
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