Embayed Craters on Venus: How Do They Correspond to the Catastrophic and Equilibrium Resurfacing Models?

Introduction: The style and rate of resurfacing on Venus is among the key problem in the geologic history of this planet. There are two alternative models of resurfacing. The first is the model of catastrophic resurfacing [1]. It states that at some specific point (say, ~500 Ma ago) the entire surface of Venus was renewed and the observable population of crates began to accumulate. The model of equilibrium resurfacing [2] states that both endogenous processes (volcanism and tectonics) and exogenous impact cratering acted in a balanced way and that it is unnecessary to call on major cataclysms involving either volcanism or tectonism to explain the observed geological history of Venus. Both models are based on two observations thought at the time of Magellan to characterize the Venus crater population: (1) the spatial distribution of craters may be indistinguishable from complete spatial randomness and (2) only a small proportion of craters is modified by volcanic flows and/or tectonic structures. The spatial randomness of the distribution of craters had been tested in different ways and by different groups of researchers [2-4]. A careful geologic analysis of the morphology of craters revealed that only ~6.2 % of the Venus craters are embayed from outside and 9.6 % of the craters are tectonized [1]. These characteristics of the distribution and morphology of the craters place some constraints on the model of equilibrium resurfacing and are the starting points of the catastrophic resurfacing model. Limits of the equilibrium model: Phillips et al. [2] describe the parameters of the equilibrium model under the restriction of spatially randomly distributed craters. The craters considered as dimensionless points and the successive and randomly distributed resurfacing events have been modeled as two-dimensional circular areas. These areas could either completely cover (erase) the craters or did not affect them. The model predicts that the craters remain to be randomly distributed if the diameter of the resurfacing areas is either smaller than about 4 (~420 km) or larger than about 74 (~7700 km). If the characteristic size of the resurfacing areas falls between these limits the restriction of the randomness of the craters is violated. Proportion of modified craters: The above estimates were made without considering the size distribution of the craters. When the craters are not treated as dimensionless points, however, the problem of embayed and/or tectonized craters becomes an important issue of the equilibrium model. The proportion of modified craters in the framework of this model can be estimated by the functions that describe the probabilities that a resurfacing event completely erases a crater, deforms it, or leaves it unaffected [2, Appendix C]. These are decreasing functions of the size of the resurfacing event: The smaller events are more effective in the partial embayment/deformation of the craters and the larger events more effectively erase the craters completely. Thus, when the events are smaller the larger fraction of embayed/tectonized craters appears. Figure 1 shows these functions that were constructed based on the size distribution of observable volcanic features on Venus taken from the global geologic map of Venus [5]. The upper branch takes into account the assumption that multiple resurfacing events never completely erase a crater and overestimates the proportion of affected craters [2]. For the lower branch the assumption is that that two resurfacing events completely erase a crater. It underestimates the proportion of the modified craters [2]. The expected fraction of the modified craters is between these branches. The proportion of all volcanically embayed craters from exterior is ~0.066 (Fig. 1).