应用近似L_0范数的稀疏脉冲反演

Seismic sparse spike inversion based on L_0 norm approximation

根据地下地层反射系数是稀疏的假设,本文提出一种新的波阻抗反演方法。首先将地震波阻抗反演中的目标函数表示为L0范数约束下的基追踪问题,并用平滑函数近似表征L0范数;然后将L0范数约束下的基追踪问题转化为无约束最优化问题,并利用基于导数的最优化方法求解无约束优化问题,求取反射系数;最后计算得到波阻抗。模型和实际资料计算结果均表明该方法是可行的。

Under the assumption that the reflectivity is a series of sparse spike,a sparse spike inversion for seismic reflection coefficients is proposed.First the inversion is accomplished by minimizing an objective function which includes a quadratic error term(L2 norm)combined with a sparseness-inducing regularization term(L0 norm).Then the L0 norm is approximated by a smoothing function,so that the L0 penalty becomes differentiable,and the minimization algorithm for continuous functions based on derivative is used to solve the problems.The proposed method is tested on both model data and real field data,and the results show this method is feasible.