MAGNITUDE OF THEORETICAL MAXIMUM MOONQUAKES ON SMALL LUNAR LOBATE SCARPS

Lunar lobate scarps (LS) are small-scale surface-cutting thrust faults found primarily in the highlands. Recent work using high-resolution Lunar Reconnaissance Orbiter imagery has increased the number of known lobate scarps, showing an approximately global distribution. Lobate scarps appear to be among the youngest endogenic features on the Moon. Current age estimates of the lobate scarps range from 1 Ga to 100 Ma. Their presence suggests late-stage thermal cooling and contraction of the Moon and implies recent seismic activity. Using a published catalog of locations and lengths of lobate scarps (Banks et al., 2012), we calculate the seismic moment and corresponding moment magnitude for each of the 79 faults.

Seismic moment (M₀) and moment magnitude (M_w) for a quake are related to the elastic properties of the rock, the size of the slipped region on the fault, and the amount of displacement. To obtain M₀ and M_w, fault depth T, dip angle δ, fault length L, and displacement D are needed for each fault. LS lengths range from 0.6 to 21.6 km, with an average of 6 km. A range of values for the depth of faulting of 0.5 to 4 km and thrust fault dip angle (20º–40º) is adopted for this study. As the displacement along the subjacent thrust faults cannot be directly measured, D-L scaling is used to calculate the displacement for each of the lobate scarps. The relationship between displacement and length is given by D = γL, where γ is the displacement-length ratio. We investigate a range in γ values between 10^-1 and 10^-3 to account for uncertainty associated with measuring the lengths and maximum relief of the lunar lobate scarps.

M₀ and M_w increase with increasing T, decrease for decreasing γ, and decrease with increasing δ. Minimum values are obtained for the combination of δ = 40º and T = 0.5 km and maximum values for δ = 20º and T = 4 km. Average M₀ ranges from 1.51 × 10²⁴ to 2.27 × 10²⁸ ergs and M_w ranges from 5.1 to 7.9.

The largest theoretical maximum lobate scarp moonquake calculated here is on the order of the 1906 San Francisco earthquake (Mw = 7.9), indicating that these relatively small structures could theoretically release a large amount of stored energy over the entire Moon, suggesting that potentially a large amount of accumulated stress was released through these quakes, which makes these small structures important to recent lunar evolution.