The inner solar system cratering record and the evolution of impactor   populations
  We review previously published and newly obtained crater size-frequency distributions in the inner solar system. These data indicate that the Moon and the terrestrial planets have been bombarded by two populations of objects. Population 1, dominating at early times, had nearly the same size distribution as the present-day asteroid belt, and produced the heavily cratered surfaces with a complex, multi-sloped crater size-frequency distribution. Population 2, dominating since about 3.8-3.7 Ga, has the same size distribution as near-Earth objects (NEOs), had a much lower impact flux, and produced a crater size distribution characterized by a differential -3 single-slope power law in the crater diameter range 0.02 km to 100 km. Taken together with the results from a large body of work on age-dating of lunar and meteorite samples and theoretical work in solar system dynamics, a plausible interpretation of these data is as follows. The NEO population is the source of Population 2 and it has been in near-steady state over the past ~3.7-3.8 gigayears; these objects are derived from the main asteroid belt by size-dependent non-gravitational effects that favor the ejection of smaller asteroids. However, Population 1 were main belt asteroids ejected from their source region in a size-independent manner, possibly by means of gravitational resonance sweeping during giant planet orbit migration; this caused the so-called Late Heavy Bombardment (LHB). The LHB began some time before ~3.9 Ga, peaked and declined rapidly over the next ~100 to 300 megayears, and possibly more slowly from about 3.8-3.7 Ga to ~2 Ga. A third crater population (Population S) consists of secondary impact craters that can dominate the cratering record at small diameters. 
Robert G. Strom, Renu Malhotra, Zhiyong Xiao, Takashi Ito, Fumi   Yoshida, Lillian R. Ostrach
astro-ph.EP