ICA and Factor Analysis Application in Seismic Profiling

We study the problems of stacking in seismic profiles. ICA is considered first as it has been a well studied subject in recent years. In contrast to PCA, the objective of ICA is to extract components with higher-order statistical independence. However ICA clearly has the disadvantage of not taking nonstationarity into consideration, typically experienced in the seismic data processing problems. In this paper we examine instead the use of factor analysis as an alternative but effective way of enhancing the seismic profiles rather than using the conventional Stacking method. Factor analysis is a way to fit a model to multivariate data to estimate the interdependence. In a factor analysis model, the measured variables depend on a smaller number of unobserved (latent) factors. Because each factor might affect several variables in common, they are known as common factors. Each variable is assumed to be dependent on a linear combination of the common factors, and the coefficients are known as loadings. Each measured variable also includes a component due to independent random variability, known as "specific variance"because it is specific to one variable. Contrary to stacking, Factor analysis takes into consideration the scaling of the latent signal and makes explicit use of the second order statistics, obtaining high signal to noise ratio. Moreover, it is compared with principal component analysis and Independent Analysis in processing the synthetic Marmousi dataset.