### ASA 126th Meeting Denver 1993 October 4-8

## 3aAO8. Model eigenfunction perturbations and group speed tomography.

**B. Edward McDonald
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*Naval Res. Lab., Washington, DC 20375
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**Arthur B. Baggeroer
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*MIT, Cambridge, MA 02139
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Certain problems in acoustic thermometry of ocean climate (ATOC) require
evaluating the response of modal group speeds to perturbations in the ocean
sound-speed profile. Two different approaches have been taken recently by
researchers, resulting in two perturbation expressions whose equivalence is not
immediately evident. The first approach, used by Lynch et al. [J. Acoust. Soc.
Am. 89, 648 (1991)], results in an integral equation involving the frequency
derivative of the eigenfunctions. The second approach, under current
investigation, yields an integral equation involving the response of the
eigenfunctions to sound-speed perturbations. The two expressions are shown to
be equivalent by means of their projections onto the set of modal
eigenfunctions. These results are discussed in relation to group travel-time
tomography.