应用地震反演技术预测储层

为了解决开发过程中储层精细刻画难题,提出将曲线重构地震反演技术引入带储层预测工作中,根据曲线不同频带范围对砂岩敏感性特征,开展基于高频恢复、低频补偿原来的曲线重构技术开展地震反演预测.通过对南八区西部的地震反演实例表明:对于大于2m砂岩分辨能力较高的,隔层太小时,两套砂岩只能当一套砂岩组合反演出来;对于小于2米的砂岩,只有当隔层大于4m条件下才能清晰识别.地震反演能很好的推测地下岩层结构和物性参数的空间分布,有效的提高了薄储层预测精度.     

基于POT-GPD模型的地震巨灾风险测度

依据极值理论构建基于GPD的POT模型,对我国1969年至2013年间地震直接经济损失数据进行拟合;选取恰当的阀值,并对模型形状参数及尺度参数进行估计,以此研究地震巨灾损失的尾部特征,从而合理的对地震巨灾风险进行度量,得到损失数据的高分位数;最后,探讨了POT模型在再保险的高超额层选取及定价问题中的应用.     

牛顿拉夫逊算法在ERT反演问题中的应用研究

本文研究了电阻率反演成像(ERT)中的牛顿拉夫逊基础算法及改进问题.利用最小二乘法和Tikhonov正则化等方法将反演算法予以优化,获得了与实验样本结构吻合的碳纤维复合层的电阻率分布图像,推广了牛顿拉夫逊算法的数理反演模型.     

基于遗传算法与牛顿法的联合算法在地表发射率反演中的应用

结合遗传算法全局高效搜索和牛顿法局部细致搜索的优势,充分利用一种算法的优点弥补另一种算法的不足,进而引入一种基于遗传算法和牛顿法的联合算法,并将联合算法应用于反演地表发射率的函数关系中.结果表明,联合算法中由遗传算法提供的初始值使得牛顿法下降的速度快,且很快趋于稳定,达到精度要求;而由任意初始值提供给牛顿法,目标函数下降到一定阶段后反而有所回升,然后才保持稳定,且经和联合算法迭代相同的次数后,目标函数的值仍然非常大,远远达不到要求.因此,从可行性、计算效率上看,联合算法均优于单纯的牛顿法,是一种性能稳定,计算高效的下降方法.     

地下水位变化中的地震信息

为挖掘地下水位中蕴含的地震信息, 我们通过对地下水位与地震事件序列关系的分析提出了一个新统计量, 进而得到一种寻找地震前兆的方法. 数据分析表明这种探索地震前兆方法有应用价值.     

计数测度在无穷级数中的一个应用

通过引入计数测度,将数学分析中的无穷级数和测度论中的抽象积分联系起来,并在此基础上对双重连加号中,连加号的次序可以颠倒这个性质给出了一个证明.     

基于贝叶斯一稀疏约束正则化方法的地震波形反演

将稀疏约束正则化方法应用于地震波形反演问题.为了减弱对稀疏约束项的光滑性要求,引入贝叶斯推断,产生一组收敛于后验分布的采样点.通过数值算例记录了采样点的条件期望、方差、置信区间等具有统计意义的结果.数值结果表明,在没有光滑性的要求下,稀疏约束正则化方法对孔洞模型和分层模型中的介质边缘有良好的识别能力.特别地,当减少观测数据时,稀疏约束正则化方法仍能获得较好的反演结果.     

蚁群算法下断层追踪在井震联合构造解释中的应用——以喇南中东一区萨二油层组为例

蚁群算法是最近十余年刚刚兴起的一种高效的仿生优化算法,算法采用分布式并行计算和正反馈自我催化机制,具有易与和其他算法结合等特点.将其应用于断层追踪能够客观、全面的诠释断层的空间展布情况,有效的提高断层解释精度.以喇南中东一区萨二油层组为例,应用基于蚁群算法下断层追踪方法准确落实目的层段断层展布规律,能够很好地解决原认识在开发过程中所遇到的矛盾,对于深入油层开发、完善注采系统、挖潜剩余油具有一定的指导意义.     

某些数学方法在地震波反演问题求解中的应用

本文以地震波广义散射（包括透射、折射、反射、绕射等）为背景，对其反演问题的发展状况做了一个回顾．文中着重介绍了在地震波逆散射问题研究过程中，各种数学、物理的基本理论和基本假设是如何被应用于非线性偏微分方程这一复杂问题的求解过程的，同时，结合对地震波逆散射问题的认识，简单介绍了与之相关的数学方法及其在应用中存在的问题。     

模糊测度在山区开挖岩体移动分析中的应用

将山区地下开挖所引起的上覆岩土体的移动视为一模糊事件,应用模糊数学中的模糊测度理论,推导了相应的地表下沉及水平移动的理论计算公式,对煤矿开采所引起的地表移动进行了计算分析。通过工程实例计算分析表明,理论计算结果与工程实测资料吻合的很好。     

Density Deconvolution in the Circular Structural Model

We consider deconvolving bivariate irregular densities supported on the circumference of the unit circle. The errors are bivariate, and the observations are available on the plane. Assuming that the estimated density is smooth on the circle, we compute exact asymptotics of the minimax risks and develop asymptotically optimal estimators for the case of normal errors. The proposed estimators are automatically sharp minimax adaptive over a wide collection of smoothness classes. It is shown that the same rates of convergence hold for a variety of different types of error distributions. The interesting feature of the problem is that the optimal rates of convergence do not depend on the error distribution and are determined essentially by the problem geometry.     

Increasing accuracy and efficiency in FE computations of the Leray‐Deconvolution model

This article develops, analyzes, and tests a finite element method for approximating solutions to the Leray‐deconvolution regularization of the Navier‐Stokes equations. The scheme combines three ideas to create an accurate and effective algorithm: the use of an incompressible filter, a linearization that decouples the velocity‐pressure system from the filtering and deconvolution operations, and a stabilization that works well with the linearization. A rigorous and complete numerical analysis of the scheme is given, and numerical experiments are presented that show clear advantages of the scheme. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 720–736, 2012     

信息熵度量风险的探究

本文分析了风险的本质后指出,风险是某一特定行为主体对某一金融投资中损失的不确定性和收益的不确定性的认识。在众多风险度量的方法中,熵函数法有着其独特的度量风险的优势,因此,在本文中重点讨论了熵函数作为风险度量的合理性。同时提出一个新的风险度量模型,剖析其主要的数学特性,阐明该模型可以针对不同行为主体能有效地度量金融风险,并且计算量小,易于操作。     

Preconditioners Based on Fit Techniques for the Iterative Regularization in the Image Deconvolution Problem

For large-scale image deconvolution problems, the iterative regularization methods can be favorable alternatives to the direct methods. We analyze preconditioners for regularizing gradient-type iterations applied to problems with 2D band Toeplitz coefficient matrix. For problems having separable and positive definite matrices, the fit preconditioner we have introduced in a previous paper has been shown to be effective in conjunction with CG. The cost of this preconditioner is of O(n²) operations per iteration, where n² is the pixels number of the image, whereas the cost of the circulant preconditioners commonly used for this type of problems is of O(n² log n) operations per iteration. In this paper the extension of the fit preconditioner to more general cases is proposed: namely the nonseparable positive definite case and the symmetric indefinite case. The major difficulty encountered in this extension concerns the factorization phase, where a further approximation is required. Three approximate factorizations are proposed. The preconditioners thus obtained have still a cost of O(n²) operations per iteration. A numerical experimentation shows that the fit preconditioners are competitive with the regularizing Chan preconditioner, both in the regularizing efficiency and the computational cost. AMS subject classification (2000) 65F10, 65F22.Received October 2003. Accepted December 2004. Communicated by Lars Eldén.     

Abstract Inverse Estimation with Application to Deconvolution on Locally Compact Abelian Groups

Recovery of the unknown parameter in an abstract inverse estimation model can be based on regularizing the inverse of the operator defining the model. Such regularized-inverse type estimators are constructed with the help of a version of the spectral theorem due to Halmos, after suitable preconditioning. A lower bound to the minimax risk is obtained exploiting the van Trees inequality. The proposed estimators are shown to be asymptotically optimal in the sense that their risk converges to zero, as the sample size tends to infinity, at the same rate as this lower bound. The general theory is applied to deconvolution on locally compact Abelian groups, including both indirect density and indirect regression function estimation.     

基于方向信息测度的图像边缘检测

边缘检测是图像处理中—个重要的研究课题．针对传统图像边缘检测算法对噪声敏感的问题,本文在分析图像像素灰度信息的基础上,建立了—个改进的确定方向信息测度的方法,并利用震动滤波对边缘检测图像进行增强,该方法在滤除噪声的同时,能有效地保留图像的基本目标信息,正确提取图像的边缘．     

The Pointwise Densities of the Cantor Measure

Let be the classical middle-third Cantor set and let μ be the Cantor measure. Set s = log 2/log 3. We will determine by an explicit formula for every point x the upper and lower s-densities Θ*^s(μ , x), Θ*^s(μ , x) of the Cantor measure at the point x, in terms of the 3-adic expansion of x. We show that there exists a countable set F such that 9(Θ*^s(μ , x))^{− 1/s} + (Θ*^s(μ , x))^{− 1/s} = 16 holds for x \F. Furthermore, for μ_C almost all x, Θ*^s(μ , X) − 2 · 4^{− s} and Θ*^s(μ , x) = 4^{− s}. As an application, we will show that the s-dimensional packing measure of the middle-third Cantor set is 4^s.     

关于乘积Borel概率测度的一点注记

In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.     

统计测度及它在概率空间的应用

设=2 N,一实值函数μ:→[0,1]称为统计测度.如果若A,B∈,A∩B=,则μ(A∪B)=μ(A)+μ(B)且μ(k)=0.本文得到了统计测度的表示定理及统计测度在概率空间的应用.     

On a Multiparameter Version of Tukey's Linear Sensitivity Measure and its Properties

A multiparameter version of Tukey's (1965, Proc. Nat. Acad. Sci. U.S.A., 53, 127–134) linear sensitivity measure, as a measure of informativeness in the joint distribution of a given set of random variables, is proposed. The proposed sensitivity measure, under some conditions, is a matrix which is non-negative definite, weakly additive, monotone and convex. Its relation to Fisher information matrix and the best linear unbiased estimator (BLUE) are investigated. The results are applied to the location-scale model and it is observed that the dispersion matrix of the BLUE of the vector location-scale parameter is the inverse of the sensitivity measure. A similar property was established by Nagaraja (1994, Ann. Inst. Statist. Math., 46, 757–768) for the single parameter case when applied to the location and scale models. Two illustrative examples are included.