In the special case, that all sedimentary layers are horizontal, a time slice of an undisturbed horizontal layer shows a constant amplitude, and, within the time slice, discontinuities create standard amplitude edges. The amplitude edges could be enhanced by standard edge enhancement techniques applied to individual time slices. Instead, I chose trace correlation to compute discontinuity attributes of horizontally layered seismic images.

Correlation measures horizontal alignment
of one-dimensional arrays (traces).
The standard normalized correlation between two one-dimensional arrays,
*f _{1}* and

(6) |

(7) |

To simplify plots of correlation coefficients, I map the coefficient range from [-1,1] to [0,2] so that pixels of correlation 1 - perfect correlation - plot as and less well-correlated regions show positive amplitudes. Hence, I first subtract 1 from each pixel value and then multiply it by -1.

To compute the local correlation of a nonstationary image volume,
I split the image into small patches,
compute the generalized correlation within the patch,
set all patch pixels to its correlation value *c*
and merge the individual patches to a single output quilt^{}.
The correlation
within a patch measures the similarity among its traces *f*_{i},
the one-dimensional vertical array of
all pixels of identical horizontal location.
Perfectly horizontal layers result
in a correlation coefficient of 1 and are mapped to a pixel
value of .

The patch size is determined by a trade-off between resolution and data nonstationarity on one side and the need to capture sufficient statistical information in a patch on the other. Since each patch is filled with a single correlation coefficient, the procedure can only resolve two discontinuities if they are separated by more than the size of a patch. Besides loss of resolution, a large patch may capture nonstationary data and yield incorrect statistical estimates. On the other hand, a small patch may not contain enough data to gather reliable statistics in the presence of noise.

3/8/1999