A comparison between phase screen, finite difference, and eigenfunction expansion calculations for scalar waves in inhomogeneous media
A comparison between phase screen, finite difference, and eigenfunction expansion calculations for scalar waves in inhomogeneous media
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非均匀介质中标量波的相位屏、有限差分和本征函数展开计算之间的比较
DOI：
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发表时间：
1994
影响因子：
3
通讯作者：
R. Wu
中科院分区：
文献类型：
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作者：
Yinbin Liu;R. Wu
摘要对二维非均匀介质中标量波传播的相位屏法、四阶有限差分法和本征函数展开法进行了比较，以评估相位屏法的准确性。相位屏法是一种前向传播（单向波）算法。本研究以有限差分法及本征函数展开法作为参考，这两种方法都是全波方程的解。本文对四种模型：（1）多均匀柱体模型，（2）高斯随机介质，（3）指数随机介质，（4）闪烁噪声随机介质，用相位屏法和有限差分法合成地震记录进行了比较。结果表明，弱随机介质（速度扰动≤ 10%）的协议。对于离散的非均匀性，如多均匀圆柱体模型，结果吻合良好，高达50%的速度偏差。在SUN Ⅱ站上，对网格尺寸为1024 × 512的问题，相位屏程序的计算机CPU时间为367秒，比我们使用的FD程序快57倍。对于大型3D问题，预计节省的时间要多得多。对于有吸收和无吸收的单个圆柱散射体，我们用相位屏法和本征函数展开法（精确解）比较了合成地震图。两种方法的一致性表明，相位屏法对非均匀吸收介质也能给出较好的结果。
Abstract Phase screen, fourth-order finite difference (FD), and eigenfunction expansion calculations of scalar wave propagation in two-dimensional (2D) inhomogeneous media are compared to assess the accuracy of the phase screen method. The phase screen method is a forward propagation (one-way wave) algorithm. The finite difference and eigenfunction expansion calculations, which are solutions of full wave equation, are chosen as references in this study. Comparison of synthetic seismograms by phase screen and finite difference methods is made for four kinds of models: (1) multi-uniform-cylinder model, (2) Gaussian random media, (3) exponential random media, and (4) flicker-noise random media. Results show good agreement for weak random media (velocity perturbations ≦10%). For discrete heterogeneities, such as the multi-uniform-cylinder model, the results agree well for up to 50% deviation in velocities. The computer CPU time of the phase screen program for a problem of grid size 1024 by 512 is 367 sec in a SUN SPARC station II, about 57 times faster than the FD program we used. For large 3D problems the time saved is expected to be much greater. For a single cylinder scatterer with and without absorption, we compare synthetic seismograms by the phase screen method and by the eigenfunction expansion method (exact solution). The agreement between the two methods demonstrates that the phase screen method can also give good results for inhomogeneous absorbing media.