全域正则化快速匹配追踪稀疏地震反演方法

Sparse seismic inversion method based on full-domain regularized fast matching pursuit

匹配追踪算法(MP)自提出以来便被广泛应用于信号处理领域。文中首先利用时频域褶积算子与初始模型约束构建匹配追踪的冗余字典,在全时频域内筛选出所有可能的匹配原子构成备选原子库;然后利用正则化方法从备选原子库中筛选出能量最大的子集构成最终的匹配原子库,即一次迭代即可筛选出多个匹配原子。据此形成的上述全域正则化快速匹配追踪算法具有计算效率高、鲁棒性强等优点。此外,将初始模型约束与时频域联合反演方法引入反演框架,可有效提高反演结果的精度。对所提方法进行的一维、二维模型及三维实际资料的测试结果表明,全域正则化快速匹配追踪地震反演方法相较于常规匹配追踪的计算效率得到明显提高,反演结果既具有良好的鲁棒性,同时拥有较好的层位边界保真度。

The matching pursuit(MP)algorithm has been widely applied to signal processing since it was proposed.This paper starts with constructing a redundant dictionary for MP by leveraging the initial model constraint and the convolution operator for the time-frequency(TF)domain.All possible matching atoms are then screened out from the whole TF domain to build an alternative atom dictionary.Subsequently,the subset with the highest energy is selected from the alternative atom dictionary by a regularization method to serve as the final matching atom dictionary.In other words,multiple matching atoms can be obtained in one iteration.The full-domain regularized fast MP algorithm thereby obtained offers the advantages of high computational efficiency and robustness.Furthermore,the initial model constraint and the TFdomain joint inversion method are introduced into the inversion framework,which effectively improves the accuracy of the inversion results.The proposed method is tested by 1D and 2D models and 3D field data,and the results indicate that the seismic inversion method based on full-domain regularized fast MP significantly outperforms those based on conventional MP in computational efficiency.The inversion results of the proposed method exhibit favorable horizon boundary fidelity in addition to high robustness.