一种改进的贝叶斯反演算法

Improved Bayesian inversion algorithm

贝叶斯反演方法是一种以贝叶斯理论为基础的不确定性反演方法,该方法除了以寻找最优解为目标外同时还能对反演结果进行评价分析,因此在地球物理反演领域中占据重要地位.然而传统的贝叶斯反演算法约束能力一般,存在精度不高的问题.本文为了进一步提高该反演算法的精度,分别从初始反演阻抗模型、先验概率分布以及似然函数三个方面对算法进行了改进,改进点主要包括对初始反演阻抗模型中的随机噪声成分进行butterworth滤波处理使构建的初始阻抗与真实阻抗更加接近从而降低反演的难度,对先验概率分布进行多方法综合处理从而有效避免了单一方法约束能力的不足,对似然函数则引入反演残差与子波的互相关函数将其扩展为一个向量从而可以使其针对每个点进行约束.通过以上改进在一定程度上提高了贝叶斯反演算法的约束能力,并利用改进后的算法进行单道记录反演试算,直观对比分析了反演阻抗与实际阻抗的匹配程度,同时引入误差项加以验证,结果表明改进算法能够在一定程度上提高反演的精度.最后,本文通过抗噪性分析检验了改进算法的稳定性和适用性.

Bayesian inversion method is an uncertainty inversion method based on Bayesian theory.This method not only aims at finding the optimal solution,but also can evaluate and analyze the inversion results,so it occupies an important position in the field of geophysical inversion.However,the traditional Bayesian inversion algorithm has a general constraint ability and has a problem of low accuracy.In order to further improve the accuracy of the inversion algorithm,this paper improves the algorithm from three aspects:the initial inversion impedance model,the prior probability distribution,and the likelihood function.The improvement points mainly include butterworth filtering of the random noise component in the initial inversion impedance model to make the constructed initial impedance closer to the real impedance to reduce the difficulty of inversion.Multi-method synthesis of the prior probability distribution is effectively avoided.The single method lacks the ability to constrain.For the likelihood function,the cross-correlation function of inversion residuals and wavelets is introduced to expand it into a vector so that it can be constrained for each point.Through the above improvements,the constraint capacity of the Bayesian inversion algorithm is improved to a certain extent,and the improved algorithm is used to perform a single-channel record inversion trial calculation.The degree of matching between the inversion impedance and the actual impedance is visually compared and analyzed.At the same time,the error term is introduced to verify the algorithm.The results show that the improved algorithm can improve the accuracy of inversion to a certain extent.Finally,the stability and applicability of the improved algorithm are tested through the anti-noise analysis.