Length-displacement scaling of thrust faults on the Moon and the formation of uphill-facing scarps

Fault populations on terrestrial planets exhibit a linear relationship between their length, L, and the maximum displacement, D, which implies a constant D/L ratio during fault growth. Although it is known that D/L ratios of faults are typically a few percent on Earth and 0.2-0.8% on Mars and Mercury, the D/L ratios of lunar faults are not well characterized. Quantifying the D/L ratios of faults on the Moon is, however, crucial for a better understanding of lunar tectonics, including for studies of the amount of global lunar contraction. Here, we use high-resolution digital terrain models to perform a topographic analysis of four lunar thrust faults - Simpelius-1, Morozov (S1), Fowler, and Racah X-1 - that range in length from 1.3 km to 15.4 km. First, we determine the along-strike variation of the vertical displacement from ≥ 20 topographic profiles across each fault. For measuring the vertical displacements, we use a method that is commonly applied to fault scarps on Earth and that does not require detrending of the profiles. The resulting profiles show that the displacement changes gradually along these faults' strike, with maximum vertical displacements ranging from 17 ± 2 m for Simpelius-1 to 192 ± 30 m for Racah X-1. Assuming a fault dip of 30° yields maximum total displacements (D) that are twice as large as the vertical displacements. The linear relationship between D and L supports the inference that lunar faults gradually accumulate displacement as they propagate laterally. For the faults we investigated, the D/L ratio is ∼2.3%, an order of magnitude higher than theoretical predictions for the Moon, but a value similar for faults on Earth. We also employ finite-element modeling and a Mohr circle stress analysis to investigate why many lunar thrust faults, including three of those studied here, form uphill-facing scarps. Our analysis shows that fault slip is preferentially initiated on planes that dip in the same direction as the topography, because the reduced overburden increases the differential stress on prospective fault planes, and hence, promotes failure. Our findings highlight the need for quantifying vertical displacements of more lunar thrust-fault scarps with the methodology employed in this study, rather than relying only on measurements of local relief, which result in D/L ratios that tend to be too low.