title: Linking multiple relaxation, power-law attenuation, and fractional wave equations.
abstract: The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by Nachman et al. [J. Acoust. Soc. Am. 88, 1584-1595 (1990)]. Through assumption of a continuum of relaxation mechanisms, each with an effective compressibility described by a distribution related to the Mittag-Leffler function, this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation. This work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling.
authors.affiliation: Department of Informatics, University of Oslo, P.O. Box 1080, NO-0316 Oslo, Norway. svenpn@ifi.uio.no
authors.forename: Sven Peter
authors.initials: SP
authors.lastname: Näsholm
authors.forename: Sverre
authors.initials: S
authors.lastname: Holm
mesh_terms: D000162:Acoustics; D003198:Computer Simulation; D005583:Fourier Analysis; D008962:Models, Theoretical; D009038:Motion; D009716:Numerical Analysis, Computer-Assisted; D013016:Sound; D013997:Time Factors