Holm Sverre, Näsholm Sven Peter
Department of Informatics, University of Oslo, Oslo, Norway.
Norsar, Kjeller, Norway.
Ultrasound Med Biol. 2014 Apr;40(4):695-703. doi: 10.1016/j.ultrasmedbio.2013.09.033. Epub 2014 Jan 13.
A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.
分析了一组在时间和空间上具有分数阶损耗算子的波动方程。发现分数阶萨博方程、幂律波动方程和因果分数阶拉普拉斯波动方程都是分数阶开尔文 - 沃伊特波动方程和更一般的分数阶齐纳波动方程的低频近似。后两个方程基于分数阶本构方程，而前几个波动方程是出于在医学超声等应用中对幂律衰减进行建模的需求而推导出来的。这对建模和仿真的应用有影响，特别是对于不满足低频近似的应用，如剪切波弹性成像。在这类应用中，基于本构方程的波动方程是可行的。
