A scaling relationship for the width of secondary deformation around strike-slip faults

Simple mechanical arguments suggest that slip along interlocked, rough faults, damages surrounding rocks. The same arguments require that the scale of secondary damage is proportional to the size of geometric irregularities along the main fault. This relationship could apply at all scales, but has, so far, been difficult to observe at the 10s to 100 s of km scales of large, natural faults, often because large-scale deformation is distributed across wide, complex plate-boundary fault systems, like the San Andreas Fault. The geometry and geology of another large-scale plate-boundary strike slip fault—the Queen Charlotte Fault (QCF)—is, in contrast, especially simple. Here, we show that observations of secondary deformation are well-aligned with predictions of stress variations caused by geometric irregularities along the QCF, suggesting a geometric relationship between primary fault geometry and secondary deformation. The analytic stress solution reveals that the highest stresses and highest likelihood of failure are confined to a zone of influence (ZOI) with a width quantified by $\mathrm{ZOI}=\lambda /2\pi$, where λ is the wavelength of geometric variations along the main fault. This simple model is consistent with ∼100-km-scale observations along the QCF and can theoretically be used to predict the width of secondary deformation at all scales.