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Suggestion: in orientation search, use cross-correlation normalised by Z power instead of CC coefficient #29

@ftilmann

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@ftilmann

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).

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