# Globally smooth approximations for shock pressure decay in impacts

## TL;DR

This paper introduces new smooth empirical formulas for modeling shock pressure decay in hypervelocity impacts, improving accuracy and consistency for applications like mantle convection modeling.

## Contribution

It presents novel continuous and smooth decay formulas that eliminate regime divisions and self-consistently determine maximum pressure, with specific fits for dunite impacts.

## Key findings

- Different decay models significantly affect estimated impact heating.
- The proposed formulas provide a unified approach avoiding regime boundaries.
- Temperature estimates vary substantially depending on the decay model.

## Abstract

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.