Globally smooth approximations for shock pressure decay in impacts

New forms of empirical formulae that provide an approximate description of the decay of shock pressure with distance in hypervelocity impacts are proposed. These forms, which are intended for use in applications such as large-scale mantle convection models, are continuous and smooth from the point of impact to arbitrarily large distances, thereby avoiding the need to divide the domain into different decay regimes and yielding the maximum pressure in a self-consistent way without resorting to the impedance-match solution. Individual fits for different impact velocities as well as a tentative general fitting formula are given, especially for the case of dunite-on-dunite impacts. The temperature effects resulting from the shock are estimated for different decay models, and the differences between them are found to be substantial in some cases, potentially leading to over- or underestimates of impact heating and melt production in modeling contexts like mantle convection, where such parameterizations are commonly used to represent giant impacts.