Using the Melosh Model of Acoustic Fluidization to Simulate Impact Crater Collapse on the Earth and Moon

The formation of complex craters requires some form of transient weakening of target rocks. Acoustic fluidization is one proposed mechanism applied in many numerical simulations of large crater formation. In a companion paper, we describe implementing the Melosh model of acoustic fluidization in the iSALE shock physics code. Here, we explore the effect of Melosh model parameters on crater collapse and determine the range of parameters that reproduce observed crater depth-to-diameter trends on the Earth and Moon. Target viscosity in the Melosh model is proportional to the vibrational wavelength, $\lambda$ , and the longevity of acoustic vibrations is $\propto \lambda Q$ ( $Q$ -quality factor). Our simulations show that $\lambda$ affects the size of the fluidized region, its fluidity, and the magnitude of the vibrations, producing a variety of crater collapse styles. The size of the fluidized region is strongly affected by the $Q$ . The regeneration factor, $e$ , controls the amount of (re)generated acoustic energy and its localization. We find that a decrease in $e$ leads to less crater collapse and that there are trade-offs between $e$ and $Q$ . This trade-off contributes to the more realistic $Q$ values than those used in the Block model. The diffusion of vibrations in regions with high stress and strain is controlled by the scattering term, $\xi$ . Compared to the Block model, the Melosh model results in a shallower zone of weakening in complex craters and enhanced strain localization around the crater rim. The parameter set that produces best depth-diameter trends is $\lambda$ = 0.2 $\times$ impactor radius, $Q$ = 10-50, $e$ = 0.025-0.1, and $\xi$ = 10- ${10}^5$ $m^2{s}^{-1}$ .