[Users] Phase rotation?

[Arnaud Huck]

Dear OpendTect Users,
Thanks to supplemental informations from one of our users, please find 
below the workflow to apply any phase rotation to your seismic data:

Indeed, a phase shift of angle "epsilon" can be represented as a linear 
combination of the trace itself with its Hilbert transform:

trace (PR=epsilon) = trace * cos(epsilon) + Hilbert(trace)*sin(epsilon)

Applying this formula is very easy in the OpendTect attribute engine, 
using the following two attributes:
1) Compute the Hilbert transform of the signal using the Instantaneous 
Hilbert attribute.
2) Define in a mathematics attribute the following formula:
    x0*cos(c0)+x1*sin(c0)
where
   x0 is the input volume
   x1 is the Hilbert transform (first attribute)
   c0 is the angle epsilon, in radians

In order to use epsilon (c0) in degrees, the formula need to be changed to:
   x0*cos(c0*PI/180)+x1*sin(c0*PI/180)

Using the evaluate attribute option, the phase rotation can be evaluated 
for many angles very quickly, for instance using a starting value of 0, 
a step of 15 (degrees) and 25 slides. This monitors the phase rotation 
between 0 and 360 degrees.

Best regards,
Arnaud.

-- dGB Earth Sciences B.V.
-- Nijverheidstraat 11-2, 7511 JM Enschede, The Netherlands
-- mailto: arnaud.huck at dgb-group.com, http://www.dgb-group.com
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PS: Many thanks to Julian Cabrera for his contribution!