L1范数约束被动源数据稀疏反演一次波估计

对于被动源地震数据,运用常规的互相关算法得到的虚拟炮记录中,不仅含有一次波反射信息,还包括了表面相关多次波.然而,通过传统的被动源数据稀疏反演一次波估计(EPSI)方法,可以求得只含有一次波,不含表面相关多次波的虚拟炮记录.本文改进了传统的被动源数据稀疏反演一次波估计问题的求解方法,将被动源稀疏反演一次波估计求解问题转化为双凸L1范数约束的最优化求解问题,避免了在传统的稀疏反演一次波估计过程中用时窗防止反演陷入局部最优化的情况.在L1范数约束最优化的求解过程中,又结合了2DCurvelet变换和小波变换,在2DCurvelet-wavelet域中,数据变得更加稀疏,从而使求得的结果更加准确,成像质量得到了改善.通过简单模型和复杂模型,验证了本文提出方法的有效性.

Estimating primaries by sparse inversion of passive-source seismic data with L1-norm constraint

This work has improved the original algorithm to estimate primaries by sparse inversion of passive-source seismic data through replacing the original algorithm to solve the convex optimization problem with L1-norm constraint. It avoids using a time-window to prevent the inversion from into local optimization situations when estimating primaries by sparse inversion. Moreover, during the solving of the optimization problem with L1-norm constraint, 2D Curvelet transform and wavelet transform are used at the same time. In 2D Curvelet and wavelet domains, the data become more sparse, then the results obtained are more accurate and the quality of imaging is improved.First, the method of convex optimization problem with L1-norm constraint is introduced to solve the problem of estimating primaries by sparse inversion of passive-source seismic data, instead of the steepest descent method under L0-norm constraint. Second, 2D Curvelet transform and wavelet transform are combined during the sparse inversion. In the 2D Curvelet-wavelet domain, the data become more sparse. Comparing with 3D Curvelet transform, the velocity of 2D Curvelet-wavelet transform is improved. Third, a simple model and a complex model are used to simulate the passive seismic data. The method of convex optimization problem with L1-norm constraint and that combined with 2D Curvelet transform and wavelet transform are used to estimate primaries from the passive seismic data, respectively. At last, comparison with the results obtained by the traditional LSQR algorithm illustrates that the method proposed is feasible and effective.The method of estimating primaries by sparse inversion can directly estimate primaries from the passive seismic data, and obtain the virtual-shot gathers which are free of the surface-related multiples. Under the assumption that the data is sparse, this work uses the method of convex optimization problem with L1-norm constraint to replace the traditional one to estimate primaries, which avoids using a time-window to prevent the inversion from into local optimization situations during sparse inversion, and improves the precision of the primaries estimated. It also suppresses artificial influence and improves the imaging quality.Comparing with the result obtained by lsqr algorithm shows the accuracy and superiority of the convex optimization problem with L1-norm constraint. During sparse inversion by L1-norm inversion, 2D Curvelet transform and wavelet transform are combined to make the data more sparse, and improve the precision of primaries estimated. At the same time, the artificial influence suppression is improved further.Comparing with the traditional method to estimate primaries, the convex optimization problem with L1-norm constraint can avoid using a time-window to prevent the inversion from into local optimization situations, and the primaries estimated become more accurate. 2D Curvelet transform and wavelet transform introduced make the data sparse, and improve the precision of primaries estimated.