Fault scaling relates fault size and frequency in one form or another. There are a lot data and theoretical arguments for a relationship between slip and fault length, fault rock thickness, and fault damage zone thickness (see the Table in Figure 1 from Scholz, 2002). Many of these studies conclude a fractal relationship of cL(n), 'n' being the power and 'c' is a constant. However, there is also substantial scatter in almost all the original data in log-log plot to make these relationships more complex and ambiguous.

Figure 1. Table showing scaling relationship of fault length (L), displacement (D), process zone width (P), and cataclasite zone width (T). From Scholz (2002).

One of the motivations to study fault scaling is to predict fault properties where data are not available (Yielding, 1996). In particular, it helps filling the gap among different data sets obtained by different methods as illustrated in Figure 2. As shown by the plot, core data is limited by the size of the cores, which is around 0.1 m in diameter and seismic and well log data have resolutions on the order of several meters. There is a large gap between these two data sets. Thus, scaling relationships can be utilized to populate subsurface rock volumes lacking data on fracture presence and attributes.

Figure 2. Cumulative frequency plot for fault size for faults detected on well core, seismic data, and well log correlation. The gap between the two data sets is highlighted by a vertical stripe of gray-shading. From Yielding, et al. (1996).