Changes in fault length distributions due to fault linkage

Fault linkage plays an important role in the growth of faults. In this paper we analyze a published synthetic model to simulate fault linkage. The results of the simulation indicate that fault linkage is the cause of the shallower local slopes on the length–frequency plots. The shallower local slopes lead to two effects. First, the curves of log cumulative number against log length exhibit fluctuating shapes as reported in literature. Second, for a given fault population, the power-law exponents after linkage are negatively related to the linked length scales. Also, we present datasets of fault length measured from four structural maps at the Cantarell oilfield in the southern Gulf of Mexico (offshore Campeche). The results demonstrate that the fault length data, corrected by seismic resolution at the tip fault zone, also exhibit fluctuating curves of log cumulative frequency vs. log length. The steps (shallower slopes) on the curves imply the scale positions of fault linkage. We conclude that fault linkage is the main reason for the fluctuating shapes of log cumulative frequency vs. log length. On the other hand, our data show that the two-tip faults are better for linear analysis between maximum displacement (D) and length (L). Evidently, two-tip faults underwent fewer fault linkages and interactions.