基于快速匹配追踪的混合域地震稀疏反演方法

匹配追踪稀疏地震反演是基于模型参数L0范数稀疏性度量的高分辨率反射系数反演方法。针对经典匹配追踪反演策略抗噪能力强但计算效率低的问题，通过控制多原子迭代次数和迭代阈值搜索模型最优解，提出基于快速匹配追踪算法的混合域地震稀疏反演方法。首先，在相对纵波阻抗低频模型约束下，构建混合域褶积模型正演算子和正则化方程，低频背景的引入将有效缩小模型参数的搜索空间；然后，在多原子快速匹配追踪反演框架推导混合域稀疏反演目标泛函，提高地层反射系数的恢复效率和收敛精度；最后，利用数据测试及实际地震资料对该方法的预测精度和可靠性进行试验分析，该方法相比常规时间域反演有助于选择高信噪比的频率分量提高算法的抗噪能力，而且在改善反演分辨率的同时避免了匹配追踪算法存在的计算效率低和局部极值的问题。
Seismic inversion utilizing matching pursuit algorithm (FMP-SI) is one of the most effective sparse inversion methods with superior resolution by considering the sparse characteristic on model reflectivity. Considering the excellent anti-noise property and the low computational efficiency of traditional matching pursuit algorithms, we proposed a novel mixed-domain sparse inversion utilizing the fast matching pursuit algorithm to improve the inversion efficiency. Sparse optimal solution of the subsurface reflectivity can be achieved by controlling the number of iterations and iteration's threshold. Firstly, the mixed-domain modeling operator and regularization equation are established by jointing the mixed-domain convolution with the low-frequency constraint, which can reduce the search space of model parameters effectively. In addition, the object function in the mixed-frequency domain can be deduced by a polyatomic fast matching pursuit algorithm. The recovery efficiency and convergence precision of model parameters can be improved. Finally, the feasibility and excellent stability are illustrated by several synthetic simulations and a field case. From the results, we conclude that the proposed method can achieve superior resolution and high anti-noise ability compared with the conventional time domain inversions. Furthermore, the problem of local extremum in single-atom matching pursuit algorithms can be avoided effectively