# Coherency attribute stacks

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

The various measures of coherency discussed in this section to compute velocity spectrum can also be used to generate coherency attribute stacks. These stacks are obtained as follows:

1. Choose a specific measure of coherency — stacked amplitude (equation 16), normalized stacked amplitude (equation 18), unnormalized crosscorrelation sum (equation 19), normalized crosscorrelation sum (equation 20), energy-normalized crosscorrelation sum (equation 21), or semblance (equation 22).
2. Compute velcoity spectra at selected CMP locations along the line and pick rms velocity functions.
3. By interpolating between the vertical functions, derive an rms velocity section.
4. Extract vertical rms velocity functions from the velocity section at each CMP location along the line traverse.
5. Apply moveout correction to CMP gathers using the extracted vertical functions.
6. Now, compute not just the stacked amplitudes (equation 16), but also the coherency attributes using equations (18) through (22) and thus obtain the coherency attribute sections.

Figure 3.2-41 shows portions of coherency attribute sections associated with a field data set. These sections, in conjunction with conventional stack, may be useful in enhancing fault patterns associated with structural plays and identifying amplitude anomalies associated with stratigraphic plays. Note the discriminating power of semblance for the most coherent reflection events in the section. Conventional CMP stacking seems to yield the most robust section that preserves reflections and diffrations. The coherency attribute sections based on crosscorrelation show an apparent higher frequency content compared to the stacked and normalized stacked sections.

Figure 3.2-41  Coherency attribute sections: (a) stack (equation 16), (b) normalized stack (equation 18), (c) unnormalized crosscorrelation (equation 19), (d) normalized crosscorrelation (equation 20), (e) energy-normalized crosscorrelation (equation 21), and (f) semblance (equation 22).

## Equations

 ${\displaystyle S=\sum \limits _{i=1}^{M}f_{i,t(i)},}$ (16)

 ${\displaystyle NS={\frac {\sum \nolimits _{i=1}^{M}f_{i,t(i)}}{\sum \nolimits _{i=1}^{M}|f_{i,t(i)}|}},}$ (18)

 ${\displaystyle CC={\frac {1}{2}}\sum \limits _{t}\left\{\left[\sum \limits _{i=1}^{M}f_{i,t(i)}\right]^{2}-\sum \limits _{i=1}^{M}f_{i,t(i)}^{2}\right\},}$ (19a)

 ${\displaystyle CC={\frac {1}{2}}\sum \limits _{t}\left[S_{t}^{2}-\sum \limits _{i=1}^{M}f_{i,t(i)}^{2}\right],}$ (19b)

 ${\displaystyle NC=MF\sum \limits _{t}\sum \limits _{k=1}^{M-1}\sum \limits _{i=1}^{M-k}{\frac {f_{i,t(i)}f_{i+k,t(i+k)}}{{\sqrt {\sum \nolimits _{t}f_{i,t(i)}^{2}\sum \nolimits _{t}f_{i+k,t(i+k)}^{2}}},}}}$ (20)

 ${\displaystyle EC={\frac {2}{(M-1)}}{\frac {CC}{\sum \nolimits _{t}\sum \nolimits _{i=1}^{M}f_{i,t(i)}^{2}}}.}$ (21)

 ${\displaystyle NE={\frac {1}{M}}{\frac {\sum \nolimits _{t}\sum \nolimits _{i=1}^{M}f_{i,t(i)}}{\sum \nolimits _{t}\sum \nolimits _{i=1}^{M}f_{i,t(i)}^{2}}}.}$ (22a)

 ${\displaystyle EC={\frac {1}{M-1}}(M\times NE-1).}$ (22b)