Length-displacement scaling and fault growth

Following an earthquake in a fault zone, commonly the co-seismic rupture length and the slip are measured. Similarly, in a structural analysis of major faults, the total fault length and displacement are measured when possible. It is well known that typical rupture length-slip ratios are generally orders of magnitude larger than typical fault length-displacement ratios. So far, however, most of the measured co-seismic ruptures and faults have been from different areas and commonly hosted by rocks of widely different mechanical properties (which have strong effects on these ratios). Here we present new results on length-displacement ratios from 7 fault zones in Holocene lava flows on the flanks of the volcano Etna (Italy), as well as 10 co-seismic rupture length-slips, and compare them with fault data from Iceland. The displacement and slip data from Etna are mostly from the same fault zones and hosted by rocks with largely the same mechanical properties. For the co-seismic ruptures, the average length is 3657m, the average slip 0.31m, and the average length-slip ratio 19,595. For the faults, the average length is 6341m, the average displacement 73m, and the average length-displacement ratio 130. Thus, the average rupture-slip ratio is about 150-times larger than the average length-displacement ratio. We propose a model where the differences between the length-slip and the length-displacement ratios can be partly explained by the dynamic Young's modulus of a fault zone being 101-2-times greater than its static modulus. In this model, the dynamic modulus controls the length-slip ratios whereas the static modulus controls the length-displacement ratio. We suggest that the common aseismic slip in fault zones is partly related to adjustment of the short-term seismogenic length-slip ratios to the long-term length-displacement ratios. Fault displacement is here regarded as analogous to plastic flow, in which case the long-term displacement can be very large so long as sufficient shear stress concentrates in the fault.