基于正交秩-1矩阵追踪的天然地震数据重建研究:以加州San Jacinto断层密集地震台阵为例

由于受地理环境和采集成本等因素的影响,采集到的天然地震数据往往呈现不规则和不完整分布,将直接影响到后续的天然地震数据处理效果,因此需要对缺失数据进行重建.本文将一种基于降秩补全理论的正交秩-1矩阵追踪算法(Orthogonal Rank-One Matrix Pursuit,OR1MP)应用于加州San Jacinto断层带的天然地震数据重建.首先将空间数据的每个频率切片进行Hankel预变换,获取具有低秩结构特征的预变换矩阵,缺失地震道和随机噪声会增加数据预变换矩阵的秩,然后运用OR1MP算法进行降秩处理,最后做反Hankel变换,得到频域上的重建数据.OR1MP算法对2D和3D的加州San Jacinto断层带的天然地震数据实验结果表明,OR1MP算法能够有效地增加地震体的峰值信噪比,能较好地实现对天然地震信号的重建.

Reconstruction of natural earthquake data based on Orthogonal Rank-one Matrix Pursuit and its application to dense seismic array around the San Jacinto Fault Zone in California

Restricted by harsh field environment and data collection costs, the natural earthquake data is often irregularly and incompletely distributed in space, which will adversely affect the subsequent seismic data processing and analysis. Therefore, it is necessary to reconstruct and regularize the earthquake data. In this paper, an orthogonal Rank-One Matrix Pursuit (OR1MP) algorithm based on the theory of reduced rank completion is introduced and applied to the reconstruction of natural earthquake data of the San Jacinto fault zone in California. First, Hankel pre-transforms should be performed on each frequency slice of the spatial data, resulting in a pre-transformed matrix with low-rank structure. Missing seismic traces and random noise will increase the rank of the pre-transformed data matrix and the OR1MP algorithm is then used to reduce the rank. Finally, an inverse Hankel transform is conducted to reconstruct data in the frequency domain. The experimental results on 2D and 3D earthquake data from San Jacinto fault zone in California show that the peak signal-to-noise ratio of the seismic data can be greatly improved through the OR1MP algorithm and the earthquake signals can be well reconstructed.