基于迭代再加权最小二乘的地震资料稀疏反演方法硕士学位论文.doc

中文摘要 地震数据反演的目的在于通过求解反射系数序列来反映地下介质的分布规律，这就需从地震数据中可靠地消除地震子波的影响。然而受到有限带宽的影响，往往缺失反射系数序列中的低频和高频信息；同时由于受到不可避免的噪声的影响，反演得到的结果分辨率通常比较低。 本论文的目的在于使用迭代再加权的寻优方法由地震数据得到高分辨率的反射系数序列；该方法通过再加权的方法将稀疏优化问题转化为一系列权不断变化的线性方程组，在保证结果精度的前提下增加了求解的速度。对寻优过程中的线性方程组求解采用针对性的预条件化，并在权重的计算中引入伸缩变换，优化了整个寻优过程的稳定性和求解速度。经过大量的数值试验，得出了合理的参数选择范围，通过与真值的比较以及实际资料处理验证了本方法的实用性。 关键词：波阻抗反演，迭代再加权，Gauss-Siedel迭代，共轭梯度法，预条件化，伸缩变换 ABSTRACT The basic goal impedance inversion is to recover the layered structure of the surface as a function of depth from observed seismic data, which usually expressed as series of reflection coefficients. Such a goal could be achieved when the effects of seismic wavelet is eliminated in an effective way. However, it is hard to get high resolution reflection coefficients series because of the bandlimited effect of seismic data with the resulting loss of low and high frequency information about subsurface structure. The unavoidable noise reduced the resolution,too. The purpose of this dissertation is to invert a high resolution reflection coefficients series from seismic data using iterative reweighted technique. This technique transform the sparse optimization into a series of wighted linear function, speeds up the computing while keep signal-to-noise rate high. In order to stabilize and accelerate the solving,pre-conditioning according to the linear function is used and shrink operator is introduced in computing the weighing. Through lots of numerical experimentations, the range of parameters is settled, and the practicability is conformed together with the real data processing. KEYWORDS: impedance inversion, iterative reweighted, Gauss-Siedel iteration,conjugate gradient method, pre-conditioning, shrink 目 录 第一章 引 言 1 1.1选题依据和研究意义 1 1.2 波阻抗反演研究现状 1 1.3 稀疏反演方法的研究情况 3 1.4 论文结构与主要内容 4 1.5 论文的主要创新点 4 第二章 波阻抗与稀疏反演概述 5 2.1 基本概念 5 2.1.1 常规波阻抗反演技术的基本假设前提 5 2.1.2 波阻抗反演方法的基本原理 5 2.1.3波阻抗反演的分类 10 2.2 稀疏反演方法 11 2.2.1 匹配追踪 11 2.2.2 稀疏反演和压缩感知 12 第三章 迭代再加权最小二乘地震资料稀疏反演方法 17 3.1 迭代再加权方法原理 17 3.2 反射系数稀疏反演的