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Sarkar, J, Cornuelle BD, Kuperman WA.  2011.  Information and linearity of time-domain complex demodulated amplitude and phase data in shallow water. Journal of the Acoustical Society of America. 130:1242-1252.   10.1121/1.3613709   AbstractWebsite

Wave-theoretic ocean acoustic propagation modeling is used to derive the sensitivity of pressure, and complex demodulated amplitude and phase, at a receiver to the sound speed of the medium using the Born-Frechet derivative. Although the procedure can be applied for pressure as a function of frequency instead of time, the time domain has advantages in practical problems, as linearity and signal-to-noise are more easily assigned in the time domain. The linearity and information content of these sensitivity kernels is explored for an example of a 3-4 kHz broadband pulse transmission in a 1 km shallow water Pekeris waveguide. Full-wave observations (pressure as a function of time) are seen to be too nonlinear for use in most practical cases, whereas envelope and phase data have a wider range of validity and provide complementary information. These results are used in simulated inversions with a more realistic sound speed profile, comparing the performance of amplitude and phase observations. (C) 2011 Acoustical Society of America. [DOI: 10.1121/1.3613709]