基于L_p范数稀疏优化算法的重力三维反演

3D inversion of gravity data using L_p-norm sparse optimization

三维密度反演已经成为重力数据定量解释的常规方法,但由于重力数据本身并没有深度分辨率,为了减少由此引起的重力反演的非唯一性,常用的手段是引入额外的先验信息.本文提出了一种重力三维稀疏反演(以下简称稀疏反演)方法,该方法通过求解物性上下界约束时的Lp范数(0≤p≤1)稀疏优化问题,来获得具有尖锐边界的解.与传统的L2范数反演方法相比,稀疏反演方法可以更加有效地利用已知的物性信息,获得深度分辨率更高的反演结果.此外,我们也分析了稀疏反演方法与二值、三值反演算法的等价性以及在实际应用中需要注意的问题.最后,通过模型试验以及矿区实测数据反演验证了稀疏反演方法的有效性.

Three-dimensional inversion for density distribution has become a common tool for quantitative interpretation of gravity data in recent years.However,as gravity data lacks depth resolution,such inversion has severe non-uniqueness.To reduce this problem,the most common approach is to introduce extra prior information.To further perfect this tool,we propose a 3D sparse gravity inversion method which minimizes an L p-norm(0≤p≤1)of the density model subject to bound constraints.Compared with the traditional L 2-norm inversion approach,our method permits to use known physical property information more effectively and produce solutions characterized by sharp boundaries and high depth resolution.To better understand our method,we analyze the equivalence between our method and binary or ternary inversion.Moreover,we also point out several issues of this method that need to be noticed.The validity of our method is tested by both synthetic-and real-data examples.