Complex component analysis of shear‐wave splitting: theory

SUMMARY The use of complex arithmetic is a natural way to treat vectorially polarized data, where the real and imaginary components can be taken as two perpendicular axes. This transforms multicomponent data from conventional Cartesian coordinates to polar coordinates, and allows the calculation of instantaneous amplitude and instantaneous polarization. We call this technique complex component analysis. Wave motion can be represented by instantaneous attributes which show distinct features characteristic of the type of wave motion. It is particularly informative to examine shear-wave splitting by instantaneous attributes. The instantaneous amplitude of shear-wave splitting has a number of local maxima, and the instantaneous polarization has a combination of rectangular and semitriangular shapes. Shearwave splitting can be identified from displays of instantaneous amplitude and polarization, where the polarization of the faster split shear wave and the delay between the two split shear waves can be quantified from colour-coded displays. The instantaneous attributes can be displayed as wiggle-lines of amplitude superimposed on a colour-coded polarization, where the use of colour improves the indentification and quantification of shear-wave splitting.