基于贝叶斯理论的薄层反演方法

A thin bed inversion method based on Bayes theory

大量实验表明,地球物理数据符合或近似符合高斯分布,因此可将高斯分布和贝叶斯原理结合并应用于地球物理反演。本文在无噪假设条件下推导出具有明确物理意义的迭代反演算法,基于贝叶斯原理重新推导了迭代反演公式。经3层和12层砂泥岩互层层状介质模型试算与实际应用,其结果均表明,将基于贝叶斯理论的波阻抗反演算法与多道反演思路相结合,具有反演精度高和稳定性好的特点,可明显降低噪声影响,而且运算简单,可有效识别薄层。

Numerous tests indicate that geophysical data conform to or approximately conform to Gaussian distribution,so it is feasible to combine Gaussian distribution with Bayes theory and apply to geophysical inversion.An iterative inversion algorithm with definite physical significance is derived on the assumption of no noise,and an iterative inversion formula is newly derived based on Bayes theory in this paper.Through test results of 3-layer and 12-layer sand shale interbed models with layered medium and actual applied results,it is found that combining wave impedance inversion algorithm based on Bayes theory with multi-trace inversion idea has features of high precision and improved stability,and that influence of noise can be reduced obviously.The calculation is simple and thin beds can be identified effectively based on inversion results.