Born序列频散方程和Born-Kirchhoff传播算子
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摘要
传统的Kirchhoff传播算子结构简洁,适用于描述横向均匀介质中波的传播.Ray-Kirchhoff传播算子较为精确地描述了波在非均匀介质中传播的运动学特征,其理论上的先天不足依赖于介质的复杂性.本文通过Born序列逼近波在非均匀介质中传播的大角度波分量,提出一种Born-Kirchhoff传播算子,将传统Kirchhoff传播算子的适用范围扩展至非均匀介质,同时描述波的运动学和动力学特征,其精度取决于Born序列逼近的阶数.利用Born序列频散方程,可以精确分析各阶Born-Kirchhoff传播算子对波长、传播角和非均质性的尺度依赖特征,其中,一阶Born-Kirchhoff传播算子的精度高于传统的相屏传播算子.波数域的Born-Kirchhoff传播算子对于高波数波是奇异的,导致波数域数值计算发散,但其空间域版本是非奇异的,无条件数值稳定,可通过Kirchhoff求和数值实施.本文给出各阶Born-Kirchhoff传播算子及其频散方程,可用于不同程度非均匀介质中的波传播模拟,复杂构造地震成像和速度估计.本文利用零阶和一阶Born-Kirchhoff传播算子计算简单二维模型的合成地震图,并与边界元法进行了比较.
Conventional Kirchhoff propagators are conceptually simple and applicable for wave propagation in laterally homogeneous media.Ray-Kirchhoff propagators are kinematically acceptable in the range of seismic frequencies for heterogeneous media, but theoretically suffer congenital deficiencies.In this paper we present a natural way to extend the conventional Kirchhoff propagators to heterogeneous media.The so-called Born-Kirchhoff propagators are designed in the wavenumber domain under Born-series approximation to account for large-angle waves in strong-contrast media.These wavenumber-domain propagators that usually become singular at high wavenumbers can be transformed into the space domain, which are unconditionally stable with the Kirchhoff-summation implementation.Various orders of the Born-Kirchhoff propagators are formulated with a target-oriented flexibility to handle local complex zones for wave propagation, seismic imaging, and velocity estimation.A complete accuracy analysis is conducted by Born-series dispersion equations to characterize the Born-Kirchhoff propagators'scale-dependence on wavelengths, propagation angles, and heterogeneities.Synthetic seismograms for a simple 2D model are calculated with the zeroth-order and first-order Born-Kirchhoff propagators in comparison with those generated by the boundary-element method.
引文
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