Displacement/Length Scaling Relationships for Normal Faults; a Review, Critique, and Revised Compilation

The relationship between normal fault displacement (D) and length (L) varies due to numerous factors, including fault size, maturity, basin tectonic history, and host rock lithology. Understanding how fault D and L relate is useful, given related scaling laws are often used to help refine interpretations of often incomplete, subsurface datasets, which has implications for hydrocarbon and low-carbon energy applications. Here we provide a review of D/L scaling laws for normal faults, discuss factors that could influence these relationships, including both geological factors and errors in measurement, and provide a critique of previously published D/L databases. We then present our newly assembled database of 4059 normal faults from 66 sources that include explicit information on: 1) fault length and displacement, 2) host rock lithology, 3) host basin tectonic history, and 4) maturity, as well as fault D and L through time when these data are available. We find an overall scaling law of D = 0.3L0.92, which is similar to previously published scaling equations and that varies in response to the aforementioned geological factors. Our data show that small faults (<1 m length) tend to be over-displaced compared to larger faults, active faults tend to be over-displaced compared to inactive faults, and faults with stiffer host rock lithologies, like igneous and carbonate rocks, tend to be under-displaced with respect to faults within softer, more compliant host rocks, like clastic sedimentary rocks. Our dynamic D/L through time data show that faults follow the hybrid fault growth model, i.e., they initially lengthen, during which time they will appear under-displaced, before accumulating displacement. To the best of our knowledge, this is the first comprehensive, integrated, critical study of D/L scaling laws for normal faults and the factors influencing their growth. These revised relationships can now be utilized for predicting fault length or displacement when only one variable is available and provide the basis for general understanding D/L scaling laws in the context of normal fault growth. This underpinning database is open-access and is available for analysis and manipulation by the broader structural geology community.