基于BG理论确定Phillips方法的正则化参数并评价反演结果

<正>则参数的选取在Phillips-Twomey方法中起着关键性的作用,但一方面人们很难确定该参数的选取是否恰当,另一方面在参数选取时存在着很大的主观因素。研究利用Phillips-Twomey方法反演核磁共振横向弛豫时间谱时正则参数的确定,其确定方法是基于BG理论中的折中准则和正则参数最小准则;同时,还利用分辨率矩阵和协方差矩阵来评价反演所得横向弛豫时间谱。数值模拟和岩心分析均表明,基于BG理论的折中准则和正则参数最小准则方法适用于确定Phillips-Twomey方法反演核磁共振横向弛豫时间谱的正则参数r的选取。岩心分析结果表明,该方法反演效果比常规的SVD方法好,并且该方法避免了反演者的主观判断,因此反演结果没有反演者个人偏好影响。

Evaluating regular parameter of Phillips method and assessing inversions based on BG theory

In the Phillips-Twomey method, it is essential to find a suitable regular parameter r. The selection of the parameter r remains practically difficult, and is often biased by researcher ''s subjectivity. Finding a suitable regular parameter r in using Phillips-Twomey method to inverse nuclear magnetic resonance(NMR) logging transverse relaxation time was focused on. The way to finding the suitable r was based on the compromise criterion in BG theory and the r minimal criterion. The inversed transverse relaxation time was also assessed through the resolution matrix and the covariance matrix. Digital simulation and core analysis show that the approach in determining the regular parameter r of the Phillips-Twomey inverse method works very well for the inverse of NMR transverse relaxation time. Core analysis also shows that this method is better than the classical SVD method without subjective bias.