Abstract
The mathematical basis for a method to invert modal ocean acoustic tomography measurements without explicitly assuming an initial sound-speed profile is described. The method is based on determining the group and phase travel times for each vertical slice through the tomographic region. The group travel times are determined directly as the measurements of modal pulse travel time. The phase travel times are determined by resolving the cycle ambiguities in the phase measurements with constraints connecting the group and phase travel times. Standard tomographic techniques then determine the modal group and phase speeds within the tomographic region, and Abel transforms can be used to determine the symmetric part (the difference between the upper and lower profiles) of the sound channel. As with ray tomography, modal tomographic measurements supply no information about the antisymmetric part of the sound channel (the average of the upper and lower profiles), but determining the lower part of the sound channel can supply the missing information. The lower part of the sound channel can be estimated from climatology or by using arrays to determine local sound-speed profiles from local modal properties and interpolating into the interior of the tomographic region.
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