Multicomponent velocity analysis with quaternions

Multicomponent seismic data are acquired by orthogonal geophones that record a vectorial wavefield. Since the single component recordings are not independent, the processing should be performed jointly for all the components. A way to achieve this goal is to exploit quaternions, hyper-complex numbers that due to their very nature are apt to represent multidimensional data. In fact, quaternion algebra allows us to extend coherence functionals used for scalar observations to multicomponent data. Therefore by means of quaternions we implement semblance and other methods based on matched filtering and on the data covariance properties. As an application we show the results from a quaternion velocity analysis carried out combining information from the geophones and from the hydrophones of an ocean bottom cable (OBC) survey, and thus recognizing the true vectorial nature of the incoming wavefield. This also allows one to relax, at least partially, vector fidelity constraints. We demonstrate that quaternion velocity analysis yields an improved resolution with respect to the single component velocity analysis for any coherence functional chosen and that it simultaneously evidences velocity trends pertaining to different wave modes. This facilitates the interpreter in the estimation of interval Vp/Vs by means of event correlation, and in making use of a priori information from VSP and well logs. It also speeds up the velocity picking that can be performed in a single pass on a multicomponent velocity panel, rather than once for each single component velocity panel.