Abstract
Through analysis of a large number of Monte Carlo and Markov Chain simulations, a model for determining crater accumulation and crater obliteration histories has been derived. The model generally applies to populations of large craters. It predicts that the following relationships hold for subequilibrium-density crater populations: (1) the more negative the production function's exponent, α, ( N∼ D α ) the lower the crater density at which the population size-frequency distribution will significantly depart from its production function; (2) the more negative the production function's exponent, the less obliteration a crater population will sustain after a set number of impacts. Application of the model to the lunar highlands implies (1) the production function for the large craters is highly structured, resembling the observed size-frequency distribution and not the function N∼ D −2; (2) even the densely cratered highlands have not attained crater saturation or equilibrium. Direct simulations of the highlands' crater population supports the model's implications.
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