A k-space Green's function solution for acoustic initial value problems in homogeneous media with power law absorption.
A k-space Green's function solution for acoustic initial value problems in homogeneous media with power law absorption.
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DOI：
10.1121/1.3583537
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
B. Treeby;B. Cox
中科院分区：
文献类型：
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作者：
B. Treeby;B. Cox
本文导出了具有幂律吸收的均匀介质中声波初值问题的有效绿色函数解。该解基于无耗介质的齐次波动方程，并增加了两个附加项。这些项取决于分数拉普拉斯算子，并分别考虑幂律吸收和色散。给定压力及其时间导数的初始条件，该解允许使用傅里叶变换和精确的k-时空传播算子在单个步骤中计算任何时间t> 0的压力场。对于规则间隔的笛卡尔网格，前者可以使用快速傅立叶变换有效地计算。由于不需要时间步进，该解决方案有助于在没有稳定性约束的情况下有效地计算一维、二维或三维的压力场。几个计算方面的解决方案进行了讨论，包括使用截断傅立叶级数表示离散的初始条件，平滑的使用，和封装的吸收和分散的属性的影响。
An efficient Green's function solution for acoustic initial value problems in homogeneous media with power law absorption is derived. The solution is based on the homogeneous wave equation for lossless media with two additional terms. These terms are dependent on the fractional Laplacian and separately account for power law absorption and dispersion. Given initial conditions for the pressure and its temporal derivative, the solution allows the pressure field for any time t>0 to be calculated in a single step using the Fourier transform and an exact k-space time propagator. For regularly spaced Cartesian grids, the former can be computed efficiently using the fast Fourier transform. Because no time stepping is required, the solution facilitates the efficient computation of the pressure field in one, two, or three dimensions without stability constraints. Several computational aspects of the solution are discussed, including the effect of using a truncated Fourier series to represent discrete initial conditions, the use of smoothing, and the properties of the encapsulated absorption and dispersion.