Analysis of fault scaling relations using fault seismic attributes

We have studied three-dimensional fault geometries through a geologically integrated analysis of fault seismic attribute volumes. We used a series of coherence (semblance) and filtered coherence attribute volumes with parameters optimised for imaging faults in the studied seismic volumes. Fault geometric attributes such as along strike segment length and displacement were measured on fault seismic attributes. The scaling relationships of fault geometric attributes were studied using statistical methods such as the Bayesian information criterion, the likelihood ratio test, and the bootstrap method. Univariate distributions of fault segment length and maximum displacement show a truncated power law for most of the fault data. The statistical results indicate a piecewise-linear relation with two slopes between depth and fault segments lengths: depth and mean displacement. For these relations, we observe consistent increases in fault segment lengths and mean displacements from the lower tip of the fault at depth toward a point of inflection at shallower depth at the vertical section. From that point, a reduction in fault segment lengths and mean displacements toward the upper tip of the fault at the shallower depth occurs. Fault segmentation along strike increases toward the lower and upper tips of the fault, but the maximum number of segments are located near the lower tip of the fault in two of the studied faults. The fault segment length is maximum, where the number of segments (along strike) is least close to the middle of the fault in the vertical section.