Mars crater production function based on mapped crater populations

Absolute ages provide vital information in establishing the geological history of the Solar System’s solid bodies. For extraterrestrial bodies, only the Moon has been sampled in a few areas for radiometric dating in the laboratory. For the unsampled areas on the Moon, the widely used surface dating method is based on the crater size–frequency distribution (CSFD) technique. However, there are no returned Martian samples, so the above method cannot be directly applied for Mars. The Martian isochrons have usually been derived based on the production function (PF) and chronology function (CF) of the Moon. Many uncertainties cast a shadow on the reliability of the current Martian isochrons (e.g., the maximum age difference is up to ~1.0 Ga from meteor flux ratios of 2.04 and 3.0). Thus, obtaining the Martian crater PF directly from remote sensing observations is a necessary and significant task. In a research article recently published in Space: Science & Technology, researchers from Chinese Academy of Sciences and Freie Universitaet Berlin utilized a high-resolution Context Camera (CTX) mosaic and selected 17 regions from diverse geological units and ages across Mars’s surface to establish an observed Martian crater production function (PF). With the radiometric ages of the samples returned by future Mars sample return missions, this research could become the basis for establishing a new chronology system for Mars.

First, the used dataset and methodology are introduced. Four datasets were used in this research. First, the high-resolution images (at a resolution of 5.0 m/pixel) obtained by CTX, onboard the Mars Reconnaissance Orbiter, were used to map the craters and the corresponding counting areas. The Martian geological map by Tanaka et al. was used in initially selecting and mapping the counting areas in this research. A global mosaic, at a resolution of 100 m/pixel, obtained by the Thermal Emission Imaging System (THEMIS) onboard Mars Odyssey is used to further refine the initially mapped counting areas. The High Resolution Stereo Camera + Mars Orbiter Laser Altimeter blended digital elevation model (200 m/pixel) was used to evaluate the topography in delineating the counting areas. To establish the Martian crater PF, the following steps were taken. The first step is to select the crater counting areas, which must be homogeneous in terms of rock type, formation age, and topography. In the Martian geological map by Tanaka et al., the Martian surface was divided into 7 types of units, of which the volcanic units, impact units, and highland units in the geological map were used to establish the crater counting areas (Fig. 1). The next step is to map the craters in the counting areas. All of the craters within the selected counting areas were mapped manually according to the CTX mosaic. Then, the CSFD is obtained with a bin size of 2^1/4 through the software Craterstats. Furthermore, the spatial randomness of crater distributions within each counting area was assessed. If the overlapping portions of the CSFDs from different counting areas are of similar shape, they can be normalized into one curve, i.e., the PF. The F test, the t test, and the Durbin–Watson (DW) test were employed to evaluate the goodness of the fitting, the significance of the coefficients in the fitted function, and the autocorrelation between different coefficients, respectively.

Then, the CSFD and PF results are presented. As for CSFDs in the volcanic units, the volcanic units from Hesperian and Amazonian volcanic units are selected to establish the crater PF. As for CSFDs in the impact units, the CSFD of a pristine crater is obtained by counting the craters superposed on its continuous ejecta. The Mohawk crater and Davies crater are selected in establishing PF. As for CSFDs in the highland units, one counting area from the Late Noachian highland (lNh) unit and another counting area from the Early Hesperian highland (eHh) unit are selected in establishing the Martian crater PF. All in all, 17 counting areas are selected from the volcanic units, impact units, and highland units in this study. Within these counting areas, the mapped 38,479 craters (0.016 to 108.0 km in diameter) and the corresponding CSFDs are analyzed in the software Craterstats. There are a total of 93 overlapping diameter ranges of the CSFDs from different geological units and/or ages, and a Pearson correlation analysis of these overlapping ranges were conducted. The result reveals that even the smallest correlation coefficient is 0.945, and the majority (92.5%, 86 out of 93) of the correlation coefficients are greater than 0.98. This indicates a strong correlation between the CSFDs of different geological units and/or ages at the same diameter range on the logarithmic scale, so that the CSFD curves from different units and/or ages can be normalized by shifting them vertically. All of the CSFDs are normalized to the CSFD in the Hesperian volcanic unit Hve, which has the largest diameter range (i.e., 0.016 to 36.223 km), and the number of the overlapping diameter bins between it and the CSFDs of all other regions ranged from 1 to 13. The final equation is as follows: logN = a₀ + a₁logD + a₂(logD)² + a₆(logD)⁶. Fig. 2 A shows the fitted results along with the 95% CI, and Fig. 2 B shows the distribution of fitted residuals with 2 horizontal dashed lines representing ±1σ of the residuals.

Finally, the discussion is carried out. Fig. 3 compares the obtained Martian PF curve with previous crater PFs derived from lunar surface dating models. It can be observed that the obtained results show evident difference compared with previous PFs. To validate our model, the CSFDs obtained from different regions on Mars are compared with results from references in Fig. 3. In fact, discrepancies between the previous Mars crater PF curves and the actual observations have also been identified during the dating process. Due to the uncertainties in the previous Mars crater PFs, they have undoubtedly had a significant impact on the results of earlier Martian dating. Nevertheless, there is no doubt that the Mars crater PF curve presented in our study will yield results that are more consistent with the observed crater populations.