基于TV约束和Toeplitz矩阵分解的波阻抗反演

Wave impedance inversion based on TV regularization and Toeplitz-sparse matrix factorization

利用波阻抗剖面的非高斯分布特点以及地震子波褶积矩阵的Toeplitz结构,对波阻抗剖面进行全变分(TV)约束,可以在压制随机噪声的同时保持剖面的不连续性,对地震子波褶积矩阵进行Toeplitz稀疏矩阵分解得到地震子波的稀疏表达。地震资料的低频损失导致无法反演出波阻抗的低频背景,故将测井或解释层位信息通过最小二乘法建立约束条件。建立的约束最优化目标函数可以同时反演子波和波阻抗。文中将地震剖面整体处理,反演结果比常规的逐道反演具有更高的精度、横向连续性和抗噪性。

The total-variation(TV)constraint is applied to the wave impedance inversion through the nonGaussian distribution of wave impedance sections and Toeplitz structure of seismic wavelet convolution matrix,which can suppress random noise and retain the discontinuity on impedance sections.The seismic wavelet can be expressed as sparse representation by Toeplitz sparse matrix factorization.As low frequency seismic components is lost,which fails to obtain the low frequency background of the wave impedance,we take well logging or horizon interpretation information as constraints with the least square method.The constrained optimization objective function can simultaneously invert wavelet and wave impedance.Seismic sections processed by the proposed approach have better accuracy,better transverse continuity,and less noise than conventional inversions.