压缩感知高分辨率接收函数叠加成像及其应用

High-resolution receiver function imaging based on Compressive Sensing and its application

接收函数成像方法纵向分辨能力高,而其水平分辨能力很大程度上取决于地表观测台站分布.经典共转换点(Common Conversion Point,CCP)叠加成像方法应用中,如果存在台站稀疏区,往往需要统一选取较大尺度叠加半径以获得连续的成像剖面.这不仅造成台站密集区域成像分辨率损失,且使成像界面产生明显的叠加痕迹.本文结合压缩感知理论和经典CCP成像方法实现提高空间分辨率的接收函数成像.我们假设地下界面在局部范围内变化较缓慢、形态特征稳定,那么接收函数信号相应具有一定的稀疏特性.基于此假定,首先通过压缩感知稀疏促进算法从稀疏、不规则分布的地震台阵接收函数重构出密集、规则化的“虚拟台阵”接收函数.之后,利用重构得到的“虚拟台阵”接收函数,采用小尺度叠加半径进行共转换点叠加成像获得高分辨率转换界面成像剖面.特别地,我们在叠加成像前进行了叠前成像点振幅补偿处理,以克服台站分布不均匀导致的成像能量不均衡问题.台站越稀疏的区域,其振幅补偿值越高.本文方法可以极大减少经典CCP成像方法实际应用中为了兼顾台站稀疏区域采用大尺度叠加半径所造成的空间分辨率损失和“阶梯状”界面的叠加痕迹,在保证台站密集区高分辨率成像结果的同时有效提高台站稀疏区的成像分辨率并提升成像质量.数值模拟测试和华北克拉通科学台阵观测数据应用结果表明,压缩感知接收函数叠加成像方法可以实现可靠的高分辨率深部转换界面成像,在高分辨率深部结构研究中具有广阔的应用前景.

The classical Common Conversion Point(CCP)receiver function imaging method has high vertical resolution while its horizontal resolution is highly affected by distribution of seismic stations.Thus,in practical applications,the classical CCP imaging method have to use large-scale stacking boxes to obtain continuous and smooth image under the station-sparsely-distributed area,which may result in the resolution loss in dense station area and obvious stack traces in the image profile.In this article,we introduce Compressive Sensing theory into CCP imaging to implement a high-resolution receiver function imaging.Firstly,we assume that interfaces have stable local spatial features and that the receiver functions,accordingly,have fine sparsity.We then build dense,regularized virtual seismic array and reconstruct the receiver functions for the virtual stations by CS-based sparsity promoting inversions.Then,the reconstructed receiver functions of virtual stations are used in the following CCP stack imaging with small-scale stacking boxes to obtain high-resolution image profile.Particularly,pre-stack amplitude compensation process is implemented before the stacking to balance the image energy due to the uneven distribution of the stations.Higher compensation value for the image point means less distribution of the stations near the image point.Our developed approach can highly reduce the aforementioned spatial resolution loss and the stacking traces and thus effectively improve the imaging quality.The synthetic test and the application to the Northern ChinArray seismic data demonstrated that,the CS-based receiver function imaging can implement reliable and effective high-resolution receiver function imaging,and thus has wide application prospects in high-resolution deep structure studies.