Application of quaternion algorithms for multicomponent data analysis: a review

In this paper we illustrate the applications of three algorithms of multicomponent seismic data processing, velocity analysis, deconvolution, and seismic wavefield separation, that we implemented by means of quaternion algebra. After a brief introduction on quaternions and a review of these methods, we focus our description on the applications to actual multicomponent seismic data sets. Quaternion velocity analysis results in an improved resolution and distinction of the velocity trends associated with the various wave phases, while the extension of the classical Wiener deconvolution demonstrates the better performance of the quaternion filter on the multicomponent traces compared to the scalar filters. Wavefield separation by means of quaternion SVD makes it possible to discern body waves from surface waves based on their different polarization characteristics and eventually leads to their effective separation.