Application of quaternion algorithms for multicomponent data analysis: a review.

In this paper we illustrate the applications of three algorithms of multicom- ponent seismic data processing, velocity analysis, deconvolution, and seismic waveeld separation, that we implemented by means of quaternion algebra. Af- ter a brief introduction on quaternions and a review of these methods, we focus our description on the applications to actual multicomponent seismic datasets. Quaternion velocity analysis results in an improved resolution and distinc- tion of the velocity trends associated with the various wave phases, while the extension of the classical Wiener deconvolution demonstrates the better per- formance of the quaternion lter on the multicomponent traces compared to the scalar lters. Waveeld separation by means of quaternion SVD makes it possible to discern body waves from surface waves based on their dierent polarization characteristics and eventually leads to their eective separation. From these experiences it turns out that the superior performance of the quaternion approaches is due to the ability of quaternions to naturally represent vectorial data.