Robust and Fast Algorithms for Singular Spectral Analysis of Seismic Data

Abstract

As discussed and demonstrated in the previous chapters, researchers have vigorously exploited the proficiency of the SSA based methods for time series analysis. Although the SSA method is well proven for variety of applications in signal analysis, its applicability for handling large data is hampered due to the huge computational time and memory requirements for the singular value decomposition (SVD) of Hankel matrix (Trajectory matrix). The SVD scheme is the main computational process of SSA and for an n × m matrix, it requires O (nm²) floating point operations (Rokhlin et al. 2009). As the length of the data record increases, the size of the trajectory matrix and therefore time and memory required for SVD computation increases rapidly. Consequently, this limits the applicability of SSA based methods. Recently some researchers (Xu and Qiao 2008; Mahmoudvand and Zokaei 2012) have devised methods to reduce the floating point operations (FLOPS) in SVD computation of square Hankel matrix to reduce the computational cost (compared to classical O(n³) method). Further, Oropeza and Sacchi (2011), Tiwari and Rajesh (2014) and Rajesh and Tiwari (2015) have discussed fast and robust algorithms to reduce the computation cost involved in SVD of Hankel matrices to use in singular spectrum based seismic data processing methods. These methods are discussed in the following sections.