Send to

Choose Destination

Links from PubMed

See comment in PubMed Commons below
J Acoust Soc Am. 2010 Jan;127(1):542-59. doi: 10.1121/1.3268508.

A unifying fractional wave equation for compressional and shear waves.

Author information

Department of Informatics, University of Oslo, PO Box 1080, NO-0316 Oslo, Norway.


This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

[Indexed for MEDLINE]
PubMed Commons home

PubMed Commons

How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for American Institute of Physics
    Loading ...
    Support Center