Morphometric Laws for Small Martian Craters (D < 50 m): a Case Study on Landslide Deposits

Introduction: Since the 60’s, extensive surveys with orbiters have produced large quantity of data on planet Mars, including very high resolution products (e.g. [1-2]) that allow precise studies of the surface geomorphology. Quantitative approaches such as morphometry have been broadly used on orbital imagery to produce impact craters scaling laws [3-5]. These laws are needed to quantify erosion (e.g. [6]), and by extension to better understand the surface processes that occur on the red planet. However, only one study has focused on crater diameters below 1 km [5] and scaling laws for diameters below 50 m have not been investigated yet. In our study, we counted the craters and measured their depths and diameters on landslide deposits located in Valles Marineris [7]. We produced a scaling law of depth d as a function of diameter D for craters below 50 m.

Methods: We used High Resolution Imaging Science Experiment (HiRISE, [1]) products to count all the craters in a specific area. We focused on ESP_024255_1750, a HiRISE image and the associated Digital Elevation Models (DEM, [2]), which both have a resolution of 0.5 m/pixel. We mapped the landslide deposits, which are restricted to the northern part of the image, at the base of the canyon walls. The data have been studied with Geographical Information System (GIS) Arcmap 10.8. We first counted all the craters at the surface and made diameters measurement using the HiRISE image. Then, depths have been measured following our handmade model through the ModelBuilder tool. The model fitted a local surface for each crater from elevations encompassing the crater rims, on a 3 m buffer area. We finally subtracted the elevations from the local surface and the DEM to obtain the crater depth.

Results and discussion: We counted 32128 craters of all diameters on ESP_024255_01750 within the landslide region. We reduced this count to keep all the craters with D > 10 m and excluded the negative depths that are due to DEM vertical uncertainties. This yielded a final count of 1252 craters. We fitted the freshest craters to get the morphometry under the form d = cD^α following the methods from Boyce and Garbeil, 2007 [3] (figure 1). This produced the following expression:

d = [0.137±0.290] D^{[0.862±0.419]} ,

where d and D are depths and diameters in meters. Parameter α is slightly lower than the value found in Watters et al., 2015 (α = 0.205±0.012, [5]), highlighting that craters are shallower in this range of diameters. Parameter c has an intermediate value between those from Watters et al., 2015 (c = 1.012±0.009 [5]) and Garvin et al., 2003 (c = 0.81 [4]). These results have to be compared with our previous results in which we found a higher value for c (c = 1.014, Millot et al., 2024, conference paper submitted to the 10^th International Conference on Mars [8]) on Interior Layered Deposits (ILDs, e.g. [9]), light-toned sedimentary rocks that are known to be easily erodible [6]. These differences highlight the impact of terrains on the scaling laws. Finally, parameters c and α have high uncertainties due to the small area involved in the count: we expect these uncertainties to decrease if we include more landslide areas in the counting. Given  the very large number of craters comprised within a single region restricted to the northern part of a HiRISE image, next studies will involve machine learning algorithms (e.g. [10]) to perform automatic segmentation and mapping of the impact craters. These tools will be mandatory to refine our results over larger regions, and reconcile local and global scale analyses of the Martian surface.

Figure 1: Log-log plot of depth d versus diameter D for the crater dataset on the landslide. Plain black points are included in the linear regression (red dashed line). The gray points are other craters from the dataset. The scaling law is displayed under the logarithmic form, with r² value to quantify the regression robustness.

References: [1] McEwen A. S. et al. (2007) JGR: Planets, 112, E5. [2] Kirk R. L. (2008) JGR: Planets, 113, E3. [3] Boyce J. M. and Garbeil H. (2007) Geophysical Research Letters, 34, 16. [4] Garvin J. B. et al. (2003) Sixth International Conference on Mars, Abstract #3277. [5] Watters W. A. et al. (2015) JGR: Planets, 120, 2, 226-254. [6] Kite E. S. and David P. M. (2017) Icarus, 286, 212-222. [7] Quantin C. et al., (2004) Icarus, 172, 2, 555-572. [8] Millot C. et al. (2003) Submitted to Tenth International Conference on Mars, Abstract #3355 [9] Mangold N. et al. (2008) Icarus, 194, 2, 519-543. [10] C. Lee (2019), PSS, 170, 16-28.