Geometric relationships of pristine Martian complex impact craters, and their implications to Mars geologic history

Based on the depths of pristine complex craters on Mars, we have estimated the final, post- modification phase depth ( d(r)) to diameter ( D) function of Martian complex craters. We suggest that the d(r)/ D function determined here holds globally for complex craters >similar to 12 km diameter. The global nature of this function may be due to the stability of slopes in the highly fractured rock that makes up the steep interior walls of post- modification phase craters. The stability of such slopes should be controlled mainly by such factors as the nature of the fractures and not target strength. This function is an essential benchmark for studies that utilize crater geometry as their basis. For example, the function can be used in gradation history of Mars to predict the magnitude of degradation. For instance, an example 20- km- diameter, Middle/ Early Noachian- age crater that initially formed in the mid- latitudes of Mars with a depth of 1800 m ( instead of 1404 m as predicted by the fresh craters function) has lost similar to 1450 m of its depth over its history, similar to 350 m in the Noachian, similar to 400 m during an intense episode of degradation at the end of the Noachian, and similar to 700 m thereafter. No evidence of the period of intense degradation is found in the high- latitudes, although those regions appear to have been affected by a process that reduced crater depth soon after they form.