The title should say it all. The justification is given in Stachnik et al . (2012):
This function [Cross-correlation coefficient] is useful because it is bounded on the interval −1
to 1, but it is difficult to find a maximum
because the autocorrelation of the radial component ($S_{rr}$ ) in
the denominator varies with the numerator. This can result in
a range of back azimuths with similar values near the maxi-
mum. Thus a second normalization is used:
$C_{z ̄r} = S{ z ̄r}/S_{zz}$
which has a well-defined maximum value and is used to select
the appropriate azimuth
The flat tops he alludes to are quite obvious in Fig. 3 of the 2019 SRL paper. It's easy to see why: an idealised Rayleigh wave with zero energy on the transverse would lead to a rectangular function of cross-correlation coefficient as dependent on trial orientation angle, ie. CC coefficient would be either -1 and 1. Using the vertical component normalisation instead leads to a more sinusoidal curve with a more clearly defined maximum (if you just pick the maximum, you could also ignore the normalisation entirely).
The title should say it all. The justification is given in Stachnik et al . (2012):
The flat tops he alludes to are quite obvious in Fig. 3 of the 2019 SRL paper. It's easy to see why: an idealised Rayleigh wave with zero energy on the transverse would lead to a rectangular function of cross-correlation coefficient as dependent on trial orientation angle, ie. CC coefficient would be either -1 and 1. Using the vertical component normalisation instead leads to a more sinusoidal curve with a more clearly defined maximum (if you just pick the maximum, you could also ignore the normalisation entirely).