Quantifying the significance of coherence anomalies

Semblance and other coherence measures are routinely used in seismic processing, such as velocity spectra analysis, in seismic interpretation to estimate volumetric dip and to delineate geologic boundaries, and in post-stack and prestack data conditioning such as edge-preserving structure-oriented filtering. Although interpreters readily understand the significance of outliers for such measures as seismic amplitude being described by a Gaussian (or normal) distribution, and root-mean-square amplitude by a log-normal distribution, the measurement significance of a given coherence of poststack seismic data is much more difficult to grasp. We have followed early work on the significance of events seen in semblance-based velocity spectra, and we used an F-statistic to quantify the significance of coherence measures at each voxel. The accuracy and resolution of these measures depended on the bandwidth of the data, the signal-to-noise ratio (S/N), and the size of the spatial and temporal analysis windows used in their numerical estimation. In 3D interpretation, low coherence estimated not only the seismic noise but also the geologic signal, such as fault planes and channel edges. Therefore, we have estimated the S/N as the product of coherence and two alternative measures of randomness, the first being the disorder attribute and the second estimate based on eigenvalues of a window of coherence values. The disorder attribute is fast and easy to compute, whereas the eigenvalue calculation is computationally intensive and more accurate. We have demonstrated the value of this measure through application to two 3D surveys, in which we modulated coherence measures by our F-statistic measure to show where discontinuities were significant and where they corresponded to more chaotic features.