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Hilbert Transform, Trace Attributes, and Time-Frequency Domain

A number of classical techniques for representing instantaneous trace attributes have been created over the years. Many of these techniques involve the construction of a quadrature trace to be used as the imaginary part of a ``complex trace'' (with the real part, being the real data). The quadrature trace is created with the Hilbert transform following the construction of the so-called ``allied function.'' This representation permits ``instantaneous amplitude, phase, and frequency'' information to be generated for a dataset, by taking the modulus, phase, and time derivative of the phase, respectively. An alternate approach is to perform multi-filter analysis on data, to represent it as a function of both time and frequency.

Tools in SU which perform these operations are

To generate the Hilbert transform of a test dataset, try
% suplane | suhilb | suxwigb title="Hilbert Transform"  &
This program is useful for instructional and testing purposes.

To see an example of ``trace attributes'' with ``suattributes'' it is necessary to make data which has a strong time-frequency variability. This is done here with ``suvibro'' which makes a synthetic vibroseis sweep. Compare the following:

% suvibro | suxgraph title="Vibroseis sweep" &
% suvibro | suattributes mode=amp | suxgraph title="Inst. amplitude"  &
% suvibro | suattributes mode=phase unwrap=1.0 | suxgraph title="Inst. phase"  &
% suvibro | suattributes mode=freq | suxgraph title="Inst. frequency"  &
which show, respectively, instantaneous amplitude, phase, and frequency.

To see the synthetic vibroseis trace in the time-frequency domain, try the following:

% suvibro | sugabor | suximage title="time frequency plot"  &
The result is an image which shows the instantaneous or apparent frequency increasing from 10hz to 60hz, with time, exactly as stated by the default parameters of ``suvibro.''

See the demos in $CWPROOT/src/demos/Time_Freq_Analysis and $CWPROOT/src/demos/Filtering/Sugabor for further information.


next up previous contents
Next: Radon Transform - Tau_P Up: General Operations on SU Previous: 2D Fourier Transforms   Contents
John Stockwell 2007-04-10