中文摘要：

本文考虑地震波形反演问题．为了克服传统的Tikhonov正则化方法过度光滑的弊端，引入了非线性稀疏约束正则化方法，并采用对偶方法求解稀疏约束泛函的极小点．基于二维声波方程波形反演问题进行了数值模拟，针对不同模型对稀疏约束正则化方法进行了测试．结果表明，稀疏约束正则化方法对不连续介质模型的介质边缘具有良好的识别能力．

英文摘要：

This paper studies the problems of seismic wave{orm inversion. In order to overcome the oversmoothness of the traditional Tikhonov regularization, we introduce the nonlinear regularization with sparsity constraints, and adopt the dual method to obtain the minimizer of the functional with sparsity constraints. Numerical simulations are carried out based on waveform inversion of the 2-D acoustic wave equation, and lots of tests are conducted for various models. The numerical results show that the regularization method with sparsity constraints has the ability to recover the boundary of discontinuous media.