Bayesian框架下的地震盲反褶积算法研究

发布时间：2018-05-27 16:15

本文选题：地震盲反褶积 + 反射系数　；参考：《天津大学》2015年博士论文

【摘要】：地震盲反褶积是指在地震子波和反射系数均未知的情况下,仅利用地震记录实现地震子波和反射系数的有效估计,其目的是从地震记录中分离地震子波,提取高精度的反射系数,改善地震反射系数资料的分辨率,拓宽其有效频谱,保留高频分量,从而能更精确地表征地层结构。地震盲反褶积算法广泛应用于地震信号分析、地质考察、资源探测、石油勘探、海洋地震勘探等领域。本文主要研究基于Bayesian框架下的地震盲反褶积问题,通过建立地震子波、地震记录以及反射系数的相关先验模型,利用参数估计的方法获得反射系数。所做的主要工作如下:(1)研究了变分Bayesian地震盲反褶积算法和稀疏表示的变分Bayesian地震盲反褶积算法,分别建立了地震子波、反射系数和地震记录的分层Bayesian先验模型,推导了算法迭代公式,进行了计算机仿真,结果表明新算法有效分离了地震子波,获得了较高精度的反射系数,改善了均方误差等量化指标。(2)研究了基于部分折叠Gibbs抽样的Bayesian多通道地震盲反褶积算法,讨论了多通道反射系数的马尔可夫贝努利高斯模型,通过部分折叠Gibbs抽样得到反射系数最大后验分布的近似解,进而实现反射系数的估计;同时分析了改进的马尔可夫贝努利高斯模型,研究了局部边缘化Gibbs抽样的Bayesian多通道地震盲反褶积算法。实验结果表明新算法拓宽了地震反射系数资料的有效频谱,提高了地震反射系数的分辨率,改善了损失函数等量化评价指标。(3)研究了基于线性小波和Curvelet变换的两种Bayesian压缩感知地震盲反褶积算法,分析了Bayesian压缩感知框架下反射系数、地震子波以及超参数的先验分布,推导了算法迭代公式,利用期望最大化策略进行参数估计。实验仿真分析表明,新算法改善了反褶积效果,降低了归一化均方误差,提高了地震反射系数的估计精度。
[Abstract]:Seismic blind deconvolution refers to the effective estimation of seismic wavelet and reflection coefficient only by using seismic records when the seismic wavelet and reflection coefficient are unknown. The purpose of the deconvolution is to separate seismic wavelet from seismic record. The high precision reflection coefficient is extracted, the resolution of seismic reflection coefficient data is improved, the effective frequency spectrum is widened, and the high frequency component is retained, thus the stratigraphic structure can be represented more accurately. Seismic blind deconvolution algorithm is widely used in seismic signal analysis, geological survey, resource exploration, petroleum exploration, marine seismic exploration and other fields. In this paper, the seismic blind deconvolution problem based on Bayesian framework is studied. The reflection coefficient is obtained by establishing a prior model of seismic wavelet, seismic record and reflection coefficient. The main work is as follows: (1) the variational Bayesian seismic blind deconvolution algorithm and the sparse representation variational Bayesian seismic blind deconvolution algorithm are studied. The hierarchical Bayesian prior models of seismic wavelet, reflection coefficient and seismic records are established, respectively. The iterative formula of the algorithm is derived and the computer simulation is carried out. The results show that the new algorithm can effectively separate seismic wavelet and obtain a high precision reflection coefficient. The blind Bayesian seismic deconvolution algorithm based on partially folded Gibbs sampling is studied, and the Markov Bernoulli Gao Si model with multi-channel reflection coefficient is discussed. The approximate solution of the maximum posterior distribution of the reflection coefficient is obtained by partially folded Gibbs sampling, and the estimation of the reflection coefficient is realized, and the improved Markov Bernoulli Gao Si model is also analyzed. A blind Bayesian seismic deconvolution algorithm based on locally marginalized Gibbs sampling is studied. The experimental results show that the new algorithm broadens the effective spectrum of seismic reflection coefficient data and improves the resolution of seismic reflection coefficient. Based on linear wavelet transform and Curvelet transform, two blind deconvolution algorithms for Bayesian compression sensing seismic are studied. The prior distributions of reflection coefficient, seismic wavelet and superparameter are analyzed under the frame of Bayesian compression perception. The iterative formula of the algorithm is derived, and the parameter estimation is carried out by using the expectation maximization strategy. The experimental results show that the new algorithm improves the deconvolution effect, reduces the normalized mean square error, and improves the estimation accuracy of seismic reflection coefficient.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：P631.4

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