基于Lp拟范数稀疏约束和交替方向乘子算法的波阻抗反演

 

波阻抗是反映岩性的重要参数之一,该参数可通过叠后反演获得。基于L1范数稀疏约束的正则化方法是目前常用的叠后波阻抗反演算法,但该方法获得的先验信息有限。为了挖掘更多的稀疏先验信息,进一步提高反演结果的精度,引入了基于Lp拟范数(0<p<1)稀疏约束和交替方向乘子算法两项关键技术。前者针对稀疏先验信息挖掘不足问题,采用了比L1范数更为稀疏的Lp拟范数(0<p<1)作为稀疏约束,并加入了初始模型约束构成目标函数;后者针对Lp拟范数无法直接求解问题,采用交替方向乘子算法将目标函数分解为多个可以直接求解的子函数,然后交替求解。将提出的反演方法用于理论模型及实际数据的反演,与传统L1范数稀疏约束的基追踪反演算子相比,新方法得到的反演结果精度更高,并具有一定的抗噪性。

 

Seismic impedance is an important parameter reflecting lithology and can be obtained via post-stack seismic inversion.The regularization method based on the L1 norm sparse constraint is a typically used post-stack inversion algorithm; nonetheless,the prior information yielded by this method is limited.Two key technologies based on the Lp quasi-norm (0<p<1) sparse constraint and an alternating direction multiplier are introduced to mine more prior information and further improve the inversion accuracy.To address the insufficient mining of sparse prior information,the former technology uses the Lp quasi-norm (0<p<1),which is sparser than the L1 norm as a sparse constraint and adds the initial model constraint to form the objective function.As the Lp quasi-norm cannot be solved,the alternating direction multiplier is used to decompose the objective function into multiple sub-objective functions that can be solved directly and then alternately.The proposed inversion method is applied to a theoretical model and actual data.Compared with the conventional basis pursuit inversion algorithm using the L1 norm sparse constraint,the proposed method yields more accurate inversion results and exhibits anti-noise properties.