SEISMIC WAVE SEPARATION BY MEANS OF ROBUST PRINCIPALCOMPONENT ANALYSIS L. T. Duarte 1 , E. Z. Nadalin 2 , K. Nose Filho 2 , R. A. Zanetti 2 J. M. T. Romano 2 , M. Tygel 3 1-School of Applied Sciences, University of Campinas (UNICAMP), Brazil 2-School of Electrical and Computer Engineering, University of Campinas (UNICAMP), Brazil 3-Department of Applied Mathematics, IMECC, University of Campinas (UNICAMP), Brazil leonardo.duarte@fca.unicamp.br, nadalin@dca.fee.unicamp.br, knfilho@dmo.fee.unicamp.br, rzanetti@gmail.com romano@dmo.fee.unicamp.br, tygel@ime.unicamp.br ABSTRACT In this work, we investigate the application of the recently in- troduced signal decomposition method known as robust prin- cipal component analysis (RPCA) to the problem of wave separation in seismic data. The motivation of our research comes from the observation that the elements of the decom- position performed by RPCA can be associated with partic- ular structures that often arise in seismic data. Results ob- tained considering two different situations, the separation of crossing events and the separation of diffracted waves from reflected ones, confirms that RPCA is a promising tool in seismic signal processing, outperforming the classical singu- lar value decomposition (SVD) and the extension of the SVD based on independent component analysis in most cases. Index Terms— Seismic signal processing, robust princi- pal component analysis, wave separation, SVD. 1. INTRODUCTION The separation of the different types of waves present in seis- mic data is a very relevant task in seismic signal process- ing [1]. This is specially true when seismic prospecting is considered, since a reliable interpretation of individual waves is crucial to identification of key geological structures in the subsurface under analysis. For instance, the separation of diffracted waves from reflections can be of use to identify stratigraphic traps, such as geological faults, in which hydro- carbons is often accumulated [2]. Classically, wave separation (or event separation) is per- formed by filtering methods such as the 2-D Fourier trans- form (or f-k filtering, as is known among geophysicists) and the Radon transform [3]. A third route to wave separation, which is the one we are interested in here, is the Singular Value Decomposition (SVD) [4]. This method has been inten- sively applied in different contexts, such as wavefield separa- tion of normal moveout (NMO)-corrected common-midpoint (CMP) gathers, residual static corrections [5], diffraction sep- aration [6] and ground-roll attenuation [7]. Although computationally efficient, the use of SVD to perform wave separation has some limitations. For instance, the estimation obtained by the SVD may not be good when there are crossing events, as well as the presence of horizontal and non-horizontal events in the same data. Such a drawback can be attributed [8] to the fact that SVD imposes orthogonal- ity to all the elements present in the decomposition, which is implicitly equivalent to enforcing decorrelation in the separa- tion process. To overcome these limitations, extensions of the SVD have been proposed. In [8], for instance, a modified ver- sion of the SVD based on Independent Component Analysis (ICA) was introduced. In this approach, higher-order statis- tics of the data are also taken into account, which results in a better performance both in wave separation [8] and signal-to- noise enhancement of pre-stack seismic gathers [9]. In this work, we aim to extend the SVD approaches in seismic signal processing upon the incorporation of the re- cently introduced decomposition framework known as robust principal component analysis (RPCA) [10, 11]. Roughly speaking, RPCA aims at decomposing the observed multidi- mensional data as a sum of a low-rank matrix and a sparse matrix. The key aspect here is that such a decomposition perfectly matches some situations typical of wave separa- tion. More specifically, we compare RPCA with SVD and the SVD-ICA methods in two situations of great interest in seismic signal separation. The paper is organized as follows: In Section 2, we in- troduce the problem and briefly describe the three separation strategies considered in our work. In Section 3, a set of nu- merical experiments illustrates our proposed procedures. Fi- nally, Section 4 states our conclusions. 2. WAVE SEPARATION METHODS 2.1. Preliminaries: seismic data Seismic data comprise an ensemble of traces, i.e., signals recorded in time at a given receiver location, due to a given 20th European Signal Processing Conference (EUSIPCO 2012) Bucharest, Romania, August 27 - 31, 2012 © EURASIP, 2012 - ISSN 2076-1465 1494