Quantifying Natural Fault Geometry : Statistics of Splay Fault Angles

We propose a new approach to quantifying fault system geometry, using an objective fit of the fault geometry to a test function, specifically here a fault branch. Fitting a “Y” shaped object using a cost function to dextral faults in California, we find a number of significant results arising from using a systematic, objective, quantitative approach. (1) The largest angle of the branch structure is generally very close to 180°, implying the branch is a splay fault off the primary throughgoing fault. (2) The distribution of the smallest angle, the splay angle, has a peak near ± 17°, symmetric about the primary fault. (3) These features appear independent of scale. These results are not yet explained by any theory, and pose new questions and constraints for the physics of fault system formation and behavior. Introduction Faults do not act as isolated objects, but rather as parts of complex fault systems. Quantifying the geometry of fault systems remains an important and in many ways an unsolved problem. Here, we propose a new approach to the problem, using objective criteria to match geometrical objects to mapped faults. Specifically, we focus on a geometrical object of a branching fault, and numerically fit with a cost function the mapped fault system to this geometrical object. This approach allows for a systematic, unbiased, quantitative measure of a significant aspect of fault system geometry. We examine the particular geometrical object of fault branches for a few reasons. One reason is it is a geometrical object which does not have an explicit scale, and since fault structures appear similar from ranges of hundreds of meters to hundreds of kilometers, we would like to find scale-independent measures of geometry—and, moreover, test the apparent scale invariance. Fault branches are not, of course, the only relevant geometrical irregularities—fault stopovers (Wesnousky 2006) and bends (King and Nabelek 1985) being other examples. These geometrical