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.
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2010年第2期370-384,共15页
Chinese Journal of Geophysics
基金
国家自然科学基金项目(40830423)
中国科学院知识创新工程项目(KZCX2-YW-101)联合资助
