Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian
Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian
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DOI：
10.1121/1.3377056
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发表时间：
2010-05-01
影响因子：
2.4
通讯作者：
Cox, B. T.
中科院分区：
文献类型：
--
作者：
Treeby, Bradley E.;Cox, B. T.
在有耗介质中吸收服从频率幂律的波传播的有效模拟在生物医学超声中有许多重要的应用。以前使用时域分数算子的波动方程需要存储在前一个时间步长的完整压力场（这种算子是基于卷积的）。这使得它们不适用于许多感兴趣的三维问题。本文推导了基于分数阶拉普拉斯算子的两个有耗导数算子的波动方程。这些运算符分别考虑所需的幂律吸收和色散，并且可以有效地结合到基于傅立叶的伪谱和k空间方法中，而不会增加它们的时域分数对应物所需的内存。讨论了用三个耦合的一阶本构方程对已开发的波动方程进行编码的框架，并通过若干一维、二维和三维模拟对该模型进行了验证。(C) 2010年美国声学学会。(DOI: 10.1121/1.3377056)
The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations. (C) 2010 Acoustical Society of America. [DOI: 10.1121/1.3377056]