基于L-BFGS算法的Huber函数全波形反演研究

发布时间：2018-02-11 15:10

本文关键词： 全波形反演随机相位编码技术 L-BFGS算法 Huber函数　出处：《吉林大学》2015年硕士论文　论文类型：学位论文

【摘要】：油气资源目前是世界上最重要的一次能源之一。随着社会的发展，油气勘探逐渐由浅层向深层转移，传统的地震勘探方法的反演深度比较浅，对地下深层反演结果不能满足精度要求。不同于旅行时层析成像和偏移速度分析，全波形反演能够充分利用地震记录中的所有信息，是一种高分辨率的反演方法，具有揭示复杂地质背景下构造与岩性细节的潜力。全波形反演的目标是利用野外采集所得地震记录的振幅、相位等信息恢复得到地下介质的物性参数模型。全波形反演理论的实现是利用一种非线性优化算法将波场残差（实际采集的观测波场与对初始模型正演得到的理论波场之差）对应的目标函数极小化，不断地优化初始模型，最终得到地下介质的速度分布。本论文基于二维声波介质，针对全波形反演计算量大，对内存要求高，，以及实际应用中受噪声影响大的问题做了研究，并提出了一系列的方案加以解决。全波形反演中为了保证反演结果的精度，往往要进行很多次迭代，每次迭代中，需要对参与反演的所有炮集所对应的震源激发位置做波场传播正演模拟，从而导致很大的计算量和内存需求。多炮正演模拟中引入随机相位编码技术，通过将不同位置的多个震源组合成超级炮，大大减少了正演模拟所需要的时间。并且有效的压制了串扰噪声的影响。全波形反演局部优化算法采用L-BFGS算法。L-BFGS局部优化算法对计算机内存的占用少，不需要存储Hessian矩阵，只需要保存少量向量对Hessian矩阵进行更新，并且收敛速度快，计算精度高。实际数据中往往存在噪声，对反演结果影响很大，目标函数基于Huber函数形式的全波形反演同时结合了L1范数抗噪性和L2范数稳定性的优点，在观测地震记录存在噪声的情况下也能得到很好的反演结果。
[Abstract]:Oil and gas resources are currently one of the most important primary energy sources in the world. With the development of society, oil and gas exploration is gradually transferred from shallow to deep layer, and the inversion depth of traditional seismic exploration method is relatively shallow. Different from travel time tomography and migration velocity analysis, full waveform inversion can make full use of all the information in seismic records, so it is a high resolution inversion method. It has the potential to reveal the details of structure and lithology in complex geological background. The goal of full waveform inversion is to use the amplitude of seismic records obtained from field acquisition. The whole wave inversion theory is to use a nonlinear optimization algorithm to calculate the residual error of the wave field (the observed wave field and the theory of forward modeling for the initial model). On the minimization of the objective function corresponding to the difference of wave field, The initial model is continuously optimized and the velocity distribution of underground media is finally obtained. Based on the two-dimensional acoustic medium, this paper studies the problems of large computation amount of full waveform inversion, high memory requirement, and the influence of noise in practical application, and puts forward a series of schemes to solve the problem. In order to ensure the accuracy of the inversion results, many iterations are often carried out in the whole waveform inversion. In each iteration, it is necessary to do forward simulation of the wave field propagation at the source excitation positions corresponding to all the gun sets involved in the inversion. The random phase coding technique is introduced in the forward modeling of multiple guns, and by combining multiple seismic sources in different positions into super guns, It greatly reduces the time required for forward modeling and effectively suppresses the influence of crosstalk noise. The whole waveform inversion local optimization algorithm uses L-BFGS algorithm. L-BFGS local optimization algorithm occupies less memory, does not need to store Hessian matrix, only needs to save a small number of vectors to update the Hessian matrix, and the convergence speed is fast and the calculation accuracy is high. There is always noise in the actual data, which has a great influence on the inversion results. The full waveform inversion of the objective function based on Huber function combines the advantages of L1 norm anti-noise and L2 norm stability at the same time. Good inversion results can also be obtained in the presence of noise in observed seismic records.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.4

【共引文献】