Kramers–Kronig relationship between ultrasonic attenuation and phase velocity. O'Donnell, M., Jaynes, E. T., & Miller, J. G. The Journal of the Acoustical Society of America, 69(3):696–701, 1981.
Kramers–Kronig relationship between ultrasonic attenuation and phase velocity [link]Paper  doi  abstract   bibtex   
Kramers–Kronig relations linking the attenuation and dispersion are presented for a linear acoustic system. These expressions are used as a starting point to derive approximate, nearly local expressions relating the ultrasonic attenuation at a specific frequency to the local frequency derivative of the phase velocity (i.e., dispersion). The validity of these approximate relationships is demonstrated in several acoustic systems exhibiting substantially different physical properties.
@article{odonnell_kramerskronig_1981,
	title = {Kramers–{Kronig} relationship between ultrasonic attenuation and phase velocity},
	volume = {69},
	url = {http://link.aip.org/link/?JAS/69/696/1},
	doi = {10.1121/1.385566},
	abstract = {Kramers–Kronig relations linking the attenuation and dispersion are presented for a linear acoustic system. These expressions are used as a starting point to derive approximate, nearly local expressions relating the ultrasonic attenuation at a specific frequency to the local frequency derivative of the phase velocity (i.e., dispersion). The validity of these approximate relationships is demonstrated in several acoustic systems exhibiting substantially different physical properties.},
	number = {3},
	urldate = {2012-09-20TZ},
	journal = {The Journal of the Acoustical Society of America},
	author = {O'Donnell, M. and Jaynes, E. T. and Miller, J. G.},
	year = {1981},
	pages = {696--701}
}
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