Application of Robust Principal Component Analysis to Seismic Data Processing

The Singular Value Decomposition (SVD) is a useful tool in seismic data processing and has been applied in many problems. In the past several years, there is a growing interest in the application of extensions of the ordinary SVD to treat seismic data. For instance, recent works have shown that the combination of SVD with an Independent Component Analysis (ICA) approach can provide interesting results in problems such as wavefield separation. In this work, we investigate the application of new decomposition framework, known as robust principal component analysis (PCA). This method, which can also be seen as an extension of the SVD approach, searches for a data representation composed of a sparse term and a low-rank term. We show by means of simulations that such a feature lead to better results than those obtained by the SVD and SVD-ICA approaches in the task of separating hyperbolic events from horizontal ones in noisy data. Moreover, the robust PCA decomposition provided a good trade-off between computational complexity and precision in the separation of two close events.