Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method
Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method
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DOI：
10.1029/93jb02518
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发表时间：
1994-01
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--
通讯作者：
R. Wu
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文献类型：
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作者：
R. Wu
本文利用弹性瑞利积分和局部弹性玻恩散射理论，在空间域和波数域建立了弹性波在任意非均质介质中单向广角传播的方程组。波数域公式导致单向传播和散射问题的紧凑解。结果表明，由于入射波场与非均质介质的相互作用在空间域和波数域都不是局域的，因此非均质弹性介质中的广角散射不能表示为通过规则相屏。我们更为普遍有效的公式称为“薄板”公式。应用小角度近似后，薄板效应退化为弹性复合屏效应（或“广义相位屏”）。与标量相网相比，弹性复合相网具有以下特点：(1)对于P-P散射和S-S面内散射，弹性复筛分别作为P波和S波的两个单独的标量相屏。相位畸变分别由P波和S波速度扰动决定。(2)对于P-S和S-P转换，屏幕不再是纯相位屏幕，而变得复杂（既有相位项，也有幅度项）；这两种转换均由剪切波速摄动和剪切模量摄动决定。对于泊松固体，S波速度摄动起主要作用。在α0 = 2β0的特殊情况下，S波速度摄动成为两种转换的唯一因素。(3)对于面内S波与面外S波的交叉耦合，薄板公式中只有剪切模量扰动δμ有影响。由于交叉耦合项是小角度散射的高阶小量，因此在复筛法中忽略了交叉耦合项。相对于先前的矢量相屏方法的推导，我们的方法可以正确地处理P波和S波之间的转换以及不同极化S波之间的交叉耦合。对两种特殊情况进行了三维有限差分解和特征函数展开式精确解的比较。一种是对于只有P速度摄动的实心球；另一种只有S速度摄动。弹性复筛法与三维有限差分法和精确解基本一致。在标量波的极限情况下，本文的推导得到了一种更普遍有效的新方法，即标量薄板法。在保持传播项不变的情况下，对相互作用项进行小角度逼近时，薄板法接近于现有的标量广角相屏法。
In this paper a system of equations for wide-angle one-way elastic wave propagation in arbitrarily heterogeneous media is formulated in both the space and wavenumber domains using elastic Rayleigh integrals and local elastic Born scattering theory. The wavenumber domain formulation leads to compact solutions to one-way propagation and scattering problems. It is shown that wide-angle scattering in heterogeneous elastic media cannot be formulated as passage through regular phase-screens, since the interaction between the incident wavefield and the heterogeneities is not local in both the space domain and the wavenumber domain. Our more generally valid formulation is called the “thin-slab” formulation. After applying the small-angle approximation, the thin-slab effect degenerates to that of an elastic complex-screen (or “generalized phase-screen”). Compared with scalar phase-screen, the elastic complex-screen has the following features. (1) For P-P scattering and S-S in-plane scattering, the elastic complex-screen acts as two separate scalar phase-screens for P and S waves respectively. The phase distortions are determined by the P and S wave velocity perturbations respectively. (2) For P-S and S-P conversions, the screen is no longer a pure phase-screen and becomes complex (with both phase and amplitude terms); both conversions are determined by the shear wave velocity perturbation and the shear modulus perturbation. For Poisson solids the S wave velocity perturbation plays a major role. In the special case of α0 = 2β0, S wave velocity perturbation becomes the only factor for both conversions. (3) For the cross-coupling between in-plane S waves and off-plane S waves, only the shear modulus perturbation δμ has influence in the thin-slab formulation. For the complex-screen method the cross-coupling term is neglected because it is a higher order small quantity for small-angle scattering. Relative to prior derivations of vector phase-screen method, our method can correctly treat the conversion between P and S waves and the cross-coupling between differently polarized S waves. A comparison with solutions from three-dimensional finite difference and exact solutions using eigenfunction expansion is made for two special cases. One is for a solid sphere with only P velocity perturbation; the other is with only S velocity perturbation. The Elastic complex-screen method generally agrees well with the three-dimensional finite difference method and the exact solutions. In the limiting case of scalar waves, the derivation in this paper leads to a more generally valid new method, namely, a scalar thin-slab method. When making the small-angle approximation to the interaction term while keeping the propagation term unchanged, the thin-slab method approaches the currently available scalar wide-angle phase-screen method.