Gaussian beams in inhomogeneous media: A review

The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method, which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are twins, though they differ by names. The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered medium.     

一种层析成像的正演和反演方法

作者在本文中提出了一种层析成像的正演和反演方法，首先对求解区作网络划分，由给定的正演速度模型在网格点上双线性插值，获得整个网格节点的速度分布，然后，对波阵面作一近似，在此基础上，用最小走时最短路径射线追踪法完成正演，反演则是通过正演的方法实现的，理论模型算例表明，本方法效果较好。     

p—范分布的近似表示

p-范分布是一个包含拉普拉斯分布、正态分析、均匀分布等常见分布的分布族。用p-范分布描述观测误差的统计特性，只需假定误差的分布为单峰、对称，因此、p-范分布似然平差可以避免事先假定误差的具体分布模式，而在平差过程中确定未知参数及误差的分布具有自适应的特点。但是p-范分布的密度函数比较复杂，不利于理论分析和实际应用。 的研究表明，p-范分布可以近似地表示为拉普拉斯分布与正态分析或正态分布均均匀分布的线性组全。p-范分布与本文给出的近似分布具有相的前四阶矩。由于拉普拉斯分布。正态分布。均匀分布的密度函数都比较简单，用近似分布代替p-范分布会使相关的问题得到简化。     

各向异性弹性波有限元叠前逆时偏移

利用有限元法和最小走时射线追踪的界面点法，实现了各向异性弹性波的叠前逆时偏移.理论模型资料的偏移结果清晰准确，证实了该系统的可靠性.通过对各向异性模型资料的各向同性偏移处理，发现常规偏移剖面存在较大误差，地质体的垂向深度和横向位置与实际模型有偏离.     

Modeling,ray tracing,and block nonlinear travel-time inversion in 3D

We describe an integrated forward and inverse three-dimensional modeling system that can deal with complex geological structures. The system has been designed to handle large-scale problems by using a distributed approach. It uses seismic ray tracing for forward simulation, time-to-depth mapping, and nonlinear travel-time inversion.A novel decomposition method is our tool to attack large-scale problems in a parallel approach. The system is fully implemented and we demonstrate its performance with synthetic examples.This research was partially supported by the National Science Foundation under SBIR Grant III-9300992.     

关于垂直分量磁变仪的灵敏度问题

目前国内地磁台垂直分量磁变以的灵敏度都普遍偏低，不能适应一些研究工作的需要，必须予以适当的提高，本文在基本不改变仪器固有灵敏度的前提下，采取记录光线二次反射法，以提高仪器的记录灵敏度，利用这种方法既使仪器的灵敏度提高一倍同时又保证了仪器原有的稳定性。     

模拟倾斜界面情况下区域地震范围内的长周期Pnl波

中国大陆地壳厚度的特点是东部地区薄西部地区厚,因此在计算Pnl波的Green函数时进一步考虑了莫霍界面倾斜的影响.本文将广义射线理论推广到倾斜层结构模型,该方法的计算结果与有限差分的计算结果有很好的一致性.理论计算表明,在同一个倾斜结构模型中沿相反方向传播的Pnl波有明显的差异.因此当地壳厚度的变化不能忽略时,根据水平层模型的理论计算结果拟合Pnl波记录时效果不够理想.对菏泽、门源地震资料的处理结果表明,用一个更接近实际地壳的倾斜层模型来拟合Pnl波比用等效厚度平行层模型来拟合要更为合理.