中文摘要：

本文研究了地震数据的稀疏分解问题．提出了一种用高斯束稀疏分解表示地震数据的方法．这是一个拟0范数约束优化问题．在求解拟0范数极小化问题的过程中，通过扫描同相轴的方法实现高斯束稀疏分解，数值实现上提出了使用一种快速单调下降的梯度优化方法．本文提出的稀疏优化方法同时具有去噪的功能，数据模拟试验表明了本方法的可行性和可靠性．

英文摘要：

We study seismic data decomposition problem in this paper. Seismic data representation using Gaussian beams are proposed. This is an 10 quasi-norm constrained minimization problem. In solving the 10 quasi-norm minimization, scanning event in phase is proposed and a gradient descent method of rapid monotonic decrease is utilized. The sparse optimization method proposed in this paper possesses the ability to remove noise and is validated with numerical simulations.