基于矩阵Toeplitz稀疏分解的相对波阻抗反演方法  

Relative acoustic impedance inversion via Toeplitz-Sparse Matrix Factorization

作　　者：汪玲玲[1,2] 高静怀[3,2] 赵谦[1] 徐宗本[1] 姜秀娣 

机构地区：[1]西安交通大学数学与统计学院,西安710049 [2]海洋石油勘探国家工程实验室,西安710049 [3]西安交通大学电子与信息工程学院,西安710049 [4]中海石油研究中心,北京100029

出　　处：《地球物理学报》2017年第2期639-654,共16页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(41404107;41390454;91330204);中国博士后科学基金面上项目(2013M532028)共同资助

摘　　要：针对利用地震道进行相对波阻抗反演中遇到的横向连续性难以保持、初始子波容错度差以及随机噪声干扰影响反演结果等问题,提出了一种基于矩阵Toeplitz稀疏分解的相对波阻抗反演方法.该方法将地震数据剖面的Toeplitz稀疏分解问题分解为两个子反演问题,其一以Toeplitz子波矩阵元素为待反演的参数,用Fused Lasso方法求解,可保证子波具有紧支集且是光滑的;其二以稀疏反射系数矩阵元素为待反演参数,用基于回溯的快速萎缩阈值迭代算法求解,大大降低了目标函数中参数选择的难度.通过交替迭代求解上述两个子反演问题可将地震数据剖面因式分解为一个Toeplitz子波矩阵和一个稀疏反射系数矩阵;然后由反射系数矩阵递推反演可以得到高分辨率的相对波阻抗剖面;利用测井资料加入低频分量后,也可得到高分辨率的绝对波阻抗剖面.Marmousi2模型生成的合成记录算例和实际地震资料算例均表明:本文方法可以从带限地震数据中有效地反演相对波阻抗,反演结果分辨率高并且能够很好地保持地震数据的横向连续性;即使在初始估计子波存在误差和地震数据被随机噪声污染的情况下也能取得较好的效果.We propose a new relative acoustic impedance inversion method based on Toeplitz- Sparse Matrix Factorization （TSMF）, to address the problems of lateral continuity, wavelet estimation error and the effect of noise in the inversion. This method transforms the Toeplitz- Sparse Matrix Factorization of a seismic profile into two subproblems. One takes the elements of the Toeplitz wavelet matrix as parameters to be inverted for, and will be solved by Fused Lasso, which guarantees that the wavelet has compact support and is smooth. The other takes the elements of the sparse reflectivity matrix as parameters to be inverted for, and will be solved by fast iterative shrinkage-thresholding algorithm （FISTA） with backtracking, which makes it easy to choose the parameter for the objective function. The seismic profile can be simultaneously deconvolved into a Toeplitz wavelet matrix and a sparse reflectivity matrix by alternatively solving the above two sub-problems. Then the high resolution relative acoustic impedance can be achieved by recursive inversion using the deconvolved reflectivity matrix. The high resolution acoustic impedance can also be achieved by adding the low-frequency components derived from the well to the relative acoustic impedance. Tests on the synthetic seismic data from the Marmousi2 model and a section of field seismic data demonstrate that the proposed method can effectively derive the relative acoustic impedance from band-limited data with appropriate resolution and lateral coherence, even when the initially estimated wavelet is inaccurate and the seismic data are contaminated by noise.

关 键 词：波阻抗 矩阵分解 稀疏 横向连续性 递推反演 

分 类 号：P631[天文地球—地质矿产勘探]