随着测井技术的发展,各大油田采集和存储的测井数据量呈井喷式增长,并存在大量冗余和噪声,在进行油气层识别前必须对测井数据进行压缩和去噪等预处理.低秩矩阵恢复(Low-Rank Matrix Recovery,LRMR)理论将压缩感知(Compressed Sensing,CS)中向量样例的稀疏表示推广到矩阵的低秩情形,从较大但稀疏的误差中恢复出本质上低秩的数据矩阵,可更好地保持数据结构,提高去噪效果.因此将低秩矩阵恢复理论中的去噪方法应用于石油测井中,实现对测井数据的去噪处理.对比研究了加速近端梯度算法(Accelerate Proximal Gradient,APG)、精确增广拉格朗日乘子(Exact Augmented Lagrange Multipliers, EALM)法和非精确增广拉格朗日乘子法(Inexact Augmented Lagrange Multipliers,IALM)在测井数据中的去噪效果,对去噪前后的测井数据分别采用支持向量机(Support Vector Machine,SVM)和相关向量机(Relevance Vector Machine,RVM)进行油气层识别,结果表明,与不去噪情况相比,利用三种算法进行去噪处理后油气层识别精度都有了显著提升.通过参数优化减少迭代次数,可使得IALM算法在运算时间上优于EALM算法和APG算法,明显提高了运算效率.%With the development of well logging techniques,the repository of data in the major oil fields has shown an enormous growth.Presence of redundancy and noise in well logging data requires the data to be compressed and denoised to make it useful for recognition of oil and gas layers.Low-rank matrix recovery (LRMR) theory generalizes the sparse representation of vector samples in compressed sensing (CS) to the matrix of low rank case.This theory considers recovery of the low-rank data matrix from large and sparse errors,leading to better maintenance of data structure and achieving a superior denoising effect.Thus,here we propose a denoising method through low-rank matrix recovery,and application of its three algorithms (accelerated proximal gradient (APG) algorithm,exact augmented Lagrange multiplier (EALM),and inexact augmented Lagrange multiplier (IALM)) to oil well log ging data to improve the denoising effect.Pre-and post-denoising logging data were consequently used in oil and gas layer recognition by support vector machine (SVM) and relevance vector machine (RVM),respectively.Results show that oil and gas layer recognition accuracy is improved remarkably by the three denoising algorithms,compared to when denoising was not applied.IALM algorithm was superior to EALM and APG algorithms,through parameter optimization to reduce the number of iterations,which could obviously improve the operation efficiency.
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