Depth to Diameter Measurements of Mercurian Mature Complex Craters

Introduction: Previous crater studies of Mercury utilized shadow measurement techniques to determine some crater characteristics [1-5]. Shadow measurements of crater topography yield accurate relative heights, but are limited to craters that have shadows that reach the crater center. Pike [5] collected morphologic characteristics of 316 impact craters on Mercury. Craters were classified into seven groups (similar to lunar classes) and seven crater attributes were recorded for each crater measured [5]. Pike [5] resolved ambiguity in previous measurements of the depth to diameter ratio (d/D), and also better quantified the diameters at which transitions in crater morphology occurred [5]. We present new crater depth and diameter measurements from digital elevation models derived from Mariner 10 images. We add to and improve the fundamental dataset of crater characteristics provided by Pike [5] by using newly-derived data not available when Pike performed his study and by using a technique not dependent on shadow measurement. Background: In the preliminary stages of this study, Wilkison et al. [6,7] analyzed crater d/D ratios for immature (9.5 km to 29 km in diameter) and mature (30 km to 175 km in diameter) complex craters from the Discovery quadrangle of Mercury. The d/D results from the pilot study [7] agree with those of Pike [5] for mature complex craters. However, the d/D results for immature complex craters differed significantly from that of Pike [5], a result of smoothing due to an effect of the stereo matching process. The smoothing effect may be reduced by using smaller correlation box sizes within the stereo matching process used to create the digital elevation models. However, smaller correlation box sizes increase the spatial resolution, but also increase the topographic noise. Therefore, an optimized patch size of 21x21 pixels was used in this study in order to minimize smoothing and introduce a minimum amount of noise. Even at this correlation box size, some smoothing of crater topography within the immature complex category may occur. Therefore, we focus this study primarily on measuring the d/D ratios of mature complex craters. Methods: Digital elevation models were constructed using Mariner 10 stereo pairs and stereomatching software, SMTK [8]. The topographic data has 1-2 km spatial resolution and vertical resolution better than 1 km. This data allows for the measurement of a greater number of crater depths because it does not depend on shadows reaching the center of the crater. We measured the depths and diameters of 173 mature complex craters within the Tolstoj, Discovery, and Michaelangelo quadrangles of Mercury (i.e. Figure 1). To determine the mean crater depth we used a firstorder fit to the rim surface, and then determined the maximum depth under the rim. Results: We measured the depths and diameters of 173 mercurian complex craters. The least squares regression to the d/D data is: d = 0.339D. A total of 58 mature complex craters were measured by Pike [5], and the least squares regression to the Pike d/D data is: d = 0.353D. The d/D data shows agreement in overall slope with that of Pike’s [5] measurements (Figure 2). However, comparison of the lines graphically (Figure 3) reveals that some of our measurements appear to be slightly lower than that of Pike [5].