基于贝叶斯—稀疏约束正则化方法的电阻率反演算法研究

发布时间：2018-01-30 08:21

本文关键词： 电阻率反演稀疏约束正则化贝叶斯推断马尔科夫链蒙特卡罗(MCMC)方法　出处：《大连海事大学》2017年硕士论文　论文类型：学位论文

【摘要】：电阻率反演是数学物理反问题中一个重要的不适定问题。电阻率成像的主要原理是:由于所测区域内部结构不同,其导电性不同,利用注入的电流信号与测量得到的所测区周围各个不同方向的数据,重建探测区域内部的电阻率分布图像。本文利用稀疏约束正则化与贝叶斯推断相结合的方法解决电阻率反演问题,贝叶斯推断的引入,减弱了对稀疏约束项的光滑性要求,并且产生了一组收敛于后验分布的采样点。本文分别针对形状规则且具有少个尖角的异常体和形状不规则且具有多个尖角的异常体结构的电阻率模型进行数值模拟,分别得出TV约束和l1约束下有效采样点的期望和标准差,对比这两种约束在同一模型上的反演效果,可得出贝叶斯-稀疏约束正则化方法在处理具有尖、角边界的异常结构的电阻率模型问题时是可行且有效的,且针对第二种电阻率的模型,将加上噪音之后的反演图像和真实图像进行对比,验证了贝叶斯-稀疏约束正则化方法的抗噪能力。
[Abstract]:Resistivity inversion is an important ill-posed problem in the inverse problem of mathematics and physics. The main principle of resistivity imaging is that the electrical conductivity is different due to the different internal structure of the measured area. The injected current signal is used to measure the measured data in different directions around the measured area. This paper uses sparse constraint regularization and Bayesian inference to solve resistivity inversion problem, and Bayesian inference is introduced. It weakens the smoothness requirement of sparse constraints. A set of sampling points converging to a posteriori distribution is generated. In this paper, numerical simulations are carried out for abnormal bodies with a regular shape with few sharp angles and resistivity models with irregular shapes and anomalous bodies with multiple sharp angles. To. The expectation and standard deviation of effective sampling points under TV constraint and L1 constraint are obtained respectively. By comparing the inversion results of these two constraints on the same model, it can be concluded that the Bayesian sparse constraint regularization method has a sharp point in processing. The resistivity model of anomalous structure with angular boundary is feasible and effective, and the inversion image after adding noise is compared with the real image for the second resistivity model. The robustness of Bayesian-sparse constrained regularization method is verified.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8

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