Abstract
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.
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