A k-space method for coupled first-order acoustic propagation equations.
A k-space method for coupled first-order acoustic propagation equations.
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DOI：
10.1121/1.1421344
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发表时间：
2002-01
期刊：
影响因子：
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通讯作者：
M. Tabei;R. Waag
中科院分区：
文献类型：
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作者：
M. Tabei;R. Waag
提出了一种大规模模拟超声脉冲传播的k空间方法。本方法，它解决了耦合的一阶微分方程的波在非均匀介质中的传播，推导出一个简单的形式类似于以前的有限差分方法与交错的空间和时间网格。与基于二阶波动方程的k空间方法一样，本文方法对均匀介质是精确的，对"慢"[c（r）<or = c0]介质是无条件稳定的，对一般弱散射介质是高精度的。此外，与以前的k空间方法不同，该方法的形式允许直接包含弛豫吸收和完全匹配层（PML）非反射边界条件。数值例子说明了本k空间方法的能力。对于弱非均匀介质，精确的结果得到使用粗糙的时间和空间的步骤比可比的有限差分和伪谱方法。k空间方法的低色散允许与弛豫吸收相关的频率相关衰减和相速度的准确表示。介绍了一种减少吉布斯现象伪影的技术，该技术通过半带滤波来平滑可压缩性和指数标度密度函数。当与这种平滑技术一起使用时，k空间方法为包括不连续性、高对比度不均匀性和小于空间网格分辨率的散射结构的介质提供高精度。
A k-space method for large-scale simulation of ultrasonic pulse propagation is presented. The present method, which solves the coupled first-order differential equations for wave propagation in inhomogeneous media, is derived in a simple form analogous to previous finite-difference methods with staggered spatial and temporal grids. Like k-space methods based on second-order wave equations, the present method is exact for homogeneous media, unconditionally stable for "slow" [c(r) < or = c0] media, and highly accurate for general weakly scattering media. In addition, unlike previous k-space methods, the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer (PML) nonreflecting boundary conditions. Numerical examples illustrate the capabilities of the present k-space method. For weakly inhomogeneous media, accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite-difference and pseudospectral methods. The low dispersion of the k-space method allows accurate representation of frequency-dependent attenuation and phase velocity associated with relaxation absorption. A technique for reduction of Gibbs phenomenon artifacts, in which compressibility and exponentially scaled density functions are smoothed by half-band filtering, is introduced. When employed together with this smoothing technique, the k-space method provides high accuracy for media including discontinuities, high-contrast inhomogeneities, and scattering structures smaller than the spatial grid resolution.