Instantaneous polarization attributes and directional filtering

We introduce a systematic definition of instantaneous attributes for an arbitrary multicomponent seismic signal. The definition is a natural generalization of known complex trace attributes of a one-component signal. Instantaneous amplitude and all polarization parameters are defined as invariants of ''instantaneous phase rotation.'' The principal feature of our approach is the unique definition of the instantaneous phase for a signal with any number of components. Plots of subtle polarization parameters of multicomponent seismic data are easily obtained using conventional seismic plotting routines. We illustrate our approach on a synthetic example and apply it to real 3-component, wide-angle crustal data. Plots of polarization attributes provide evidence for shear-wave splitting in an Sg arrival. Having determined the instantaneous polarization vector, we design a new type of time-domain spatial directional filter. The filter enhances linearly polarized events with specified instantaneous polarization. The filter can work with any number of components in the data, has no user-specified parameters, and is controlled only by the signal. We conclude that rigorously defined instantaneous phase, amplitude, and polarization attributes provide new effective means for the visualization, analysis, and processing of multicomponent signal.