空间变量结构约束下AVO贝叶斯反演..doc

空间变量结构约束下AVO贝叶斯反演 摘 要 引入来源不同的地下先验信息约束地球物理反演，降低反演解的不确定性程度是地球物理反演研究中一个重要的课题。地质变量是在空间（时间）上展布的变量。地质变量除了具有统计意义上的随机性外，还依赖于空间（时间）位置，具有一定的相关性和结构性。本文引入地质统计学里变差函数的思想，建立关于地下空间变量结构的描述作为先验信息，结合贝叶斯推断理论，通过似然函数建立空间变量和地球物理观测的联系，得到AVO反演解估计后验概率密度的解析形式。选取东海某油田一口实际测井数据进行反演试算，应用区间估计和随机模拟的方法对解估计的不确定性程度进行评价，结果表明在空间变量结构约束下，解估计的不确定性程度低于未受到约束的反演解，验证了此文方法的有效性。 关键词 地质统计学，AVO反演，贝叶斯理论，空间变量结构 AVO Bayesian inversion constrained by spatial variable structure Abstract An important subject in geophysical inversion research is to decrease the uncertainty degree of inverse solution by introducing subsurface priori information from different sources as a constraint of geophysical inversion. Geological variable exhibits spatial (time) variability. Apart from the randomness in terms of statistics, geological variable depends on spatial (time) location as well, possessing certain correlation and structural property. The paper introduces the theory of variogram from geostatics to create a description about the structure of subsurface spatial variable as priori information. Combined with Bayesian inference theory, we establish a relationship between spatial variable and geophysical observation via likelihood function. Finally, we derive the analytical form of AVO inverse solution estimations posterior probability density. Practical logging data from a well located in an oil field in East China Sea is selected to conduct pilot inverse calculation. Afterwards, uncertainty degree of its solution estimation is evaluated by performing interval estimation and stochastic simulation methods. The consequence suggests that with spatial variable structure as constraint, the uncertainty degree of solution estimation is lower than it of inverse solution which is without constraint. Thus, method proposed in this paper is proved to be effective. Keywords Geostatistics, AVO inversion, Bayesian theory, Spatial variable structure 0引言 众所周知，地球物理反问题是一个多解且不适定的问题。对于地震反演来说，其根本目标是利用观测到的地震数据集，求解地下介质的结构与物理参数[]。除了地震数据外，如何让引入更多不同来源的信息