去噪算法驱动的地震反演正则化方法

Seismic inversion regularization method driven by denoising algorithm

地震反演作为重要的定量解释手段,利用观测地震记录、层位信息和测井数据来预测地下弹性参数展布.但是,作为典型的反问题,地震反演具有严重的不适定性,难以获得稳定可靠的解,通常采用正则化的方法进行求解.同样地,作为反问题的地震数据去噪,已进行了广泛深入的研究,许多去噪算法已经成功应用于地震反演中.本文提出一种去噪算法驱动的正则化方法,并将其应用于叠后地震反演.该正则化方法基于反演结果偏差与真实模型呈正交关系的假设条件,构建拉普拉斯正则化项,利用观测地震记录不匹配项和拉普拉斯正则化项来建立地震反演目标函数.在拉普拉斯正则化中需要真实模型,由传统去噪算法作用后的结果替代,因此该方法可以有效结合各种成熟的去噪算法.为了有效求解该目标函数,本文在去噪算法满足齐次性条件的基础上,推导了一种通用的目标函数的导数形式.该导数形式能灵活地结合传统的均值滤波和保边平滑滤波等线性去噪算法,并且可以采用共轭梯度法直接求解.该方法得到的反演结果可以在满足观测记录与合成记录匹配的同时,具备去噪算法期望的特征.本文证明了非局部均值滤波和字典学习去噪算法满足齐次性条件,并在模型测试中,与传统的迭代滤波反演方法比较,验证了该方法的可靠性和稳定性,并且通过实际数据叠后波阻抗反演说明了该方法的实用性.

Seismic inversion,as an important quantitative interpretation method,can predict the distribution of underground elastic parameters by using observed seismic records,horizon information and borehole data.However,as a typical inverse problem,seismic inversion suffers from serious ill-posedness,which makes it hard obtain a stable and reliable solution.Regularization method is usually used to solve this problem.Similarly,seismic data denoising,as a typical inverse problem,has been extensively and deeply studied.Moreover,lots of them have been successfully applied to seismic inversion.In this paper,we propose a denoising algorithm-driven seismic inversion regularization method,and apply it to poststack seismic inversion.The proposed regularization strategy is based on the assumption that the deviation of the inversion results is orthometric with true model.Laplacian regularization is used to achieve this assumption.The objective function of seismic inversion is constructed by using mismatch term of the observed seismic records and Laplacian regularization term.Laplace regularization term requires the true model,which is replaced by traditional denoising results.Therefore,the proposed regularization method can integrate various mature denoising algorithms.In order to effectively solve this objective function,under the condition that the denoising algorithm satisfies or approximately satisfies the homogeneity,this paper derives a general derivative form of the objective function,which can be flexibly combined with a conventional linear denoising algorithm,such as mean filter and edge-preserving smoothing filter.Moreover,the derivative form can be directly solved by conjugate gradient method.The inversion results obtained by this method can not only meet the observation record,but also possess the desired characteristics of the denoising algorithm.This article demonstrates that conventional non-local mean filter and dictionary learning denoising algorithm satisfy the homogeneity nature.In the synthetic test,compared with conventional iterative filter inversion methods,the reliability and stability of the proposed method are verified.The practicability of the proposed method is demonstrated through poststack acoustic impedance inversion of field data.