Standardized representation of lunar lobate scarp topography-initial re-

Introduction: Lobate fault scarps (LS) are prevalent tectonic landforms across the lunar surface. They are the surface expressions of low-angle thrust faults formed by the contraction of the crust principally from long-term interior cooling [1, 2, 3, 4] and along with orbit recession and tidal deformation [5, 6, 7]. They are among some of the youngest landforms on the Moon (< 1 Ga) based on their crisp appearance, absence of superposed craters, and model age estimates [4, 8, 9, 10, 11, 12]. The crisp morphologies and the survival of small (several to tens of meters width) graben on the back-limb of scarps suggest that many of the scarps have been active in the last 50 Ma, possibly even currently active [13, 14, 6]. Over 3500 lobate scarps have been identified on the Moon, ranging from up to ∼22 km in length and have a cross-sectional topographic maximum relief between ∼5 m and ∼150 m [15, 6]. Scarps have asymmetric profiles with a steeply dipping scarp face and a gently sloping back-limb. The topographic shape of the fault scarp cross section (LS profile hereafter), which varies across the length of the fault directly affects our understanding of the compressive (and extensional) kinematics that led to the lobate scarp morphology. The LS profile is defined by the geometric and kinematic properties of the fault, such as the depth of faulting, dip of the fault plane, and cumulative fault slip. To characterize the kinematic properties, measurements of topographic features from LS profile are required [5, 16]. For example, the relief (R) of the LS profile is related to the vertical displacement (D) which in turn is used to estimate the displacement length (DL ) ratio for the fault. A method that can robustly model the LS profile and is easily applicable across the entire fault length can offer significant advantages in the characterization of lobate scarps and would also provide additional constraints on forward mechanical models [5, 16]. Earlier work [17] has shown that elevation profiles of relatively smooth topographic features can be efficiently represented mathematically by Chebyshev approximation coefficients. For example, topography of nearly all lunar craters can be efficiently represented by only 17 Chebyshev coefficients [17]. In this representation, individual Chebyshev polynomial functions are scaled and summed to approximate the true elevation profile. The scaling factors are the Chebyshev coefficients which then represent the shape. In this abstract, we propose a novel method for standardized representation of lunar lobate scarp topograFigure 1: LROC NAC images showing selected lobate scarps (A) Racah X-1 (-10.1 N, 176.1 E; M143459779), (B) Mandel’shtam-6 (5.8 N, 161.5 E; M161252379), (C) Feoktiskov (32 N, 140.6 E, M; M151956846), and (D) Oppenheimer F (-34.2 N, -160.9 E; M151568945).