  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.
