where u is the image data, the superscript H represent the Hilbert transform, p and q are the dips of elliptic plane along x and y axes direction, respectively. In order to suppress a possible high coherency value around the zero-crossing location, the average semblance is calculated along a time window that ranges from upper K to lower K.
Figure 2 Elliptic analysis window centered about an analysis point including J traces.
As evident in equation (1), the coherency analysis requires average semblances for various dips (Figure 3). The method of choosing the dips is important not only for the computational cost, but also to obtain an even distribution of dips. I used a ``Chinese checker'' tessellation Marfurt et al. (1998) to find a finite number of discrete angle combinations. Then the coherency value at each location was determined by choosing a maximum value among the semblance values for various dips as follows:
Figure 3 Calculation of coherency over an elliptical analysis window with apparent dips Marfurt et al. (1998).
This coherency evaluation is performed for the Boonsville image and the result is shown in Figure 4. In Figure 4, the coherency values are shown in grey scale so that the dark represent low coherency and the bright represent high coherency. A comparison of Figure 4 to Figure 1, shows that the coherency cube more clearly reveals the discontinuities in the seismic image. It shows not only the discontinuities that were obvious, but also the ones that are hard to recognize in the seismic image.