Seismic Coda Envelope as a Distance Proxy for Lunar Impact Localization

Meteoroid impacts are frequent on the Moon and provide valuable natural seismic sources for probing the lunar interior. However, accurately locating lunar impacts remains challenging because intense scattering within the highly fractured lunar crust obscures direct P- and S-wave arrivals. Coda-based localization methods exploit scattered energy, but their accuracy has so far been limited by the parameterization of the method. In this study, we reformulated a coda-based localization approach within the framework of seismic quanta scattering theory by introducing four distance proxies: peak amplitude, rise time, differential arrival time, and the overall coda shape. By jointly combining these proxies, we obtain locations that agree well with independent travel-time-based solutions. We then apply the method to locate forty-nine high-amplitude local impact events recorded by the Apollo seismic network, while also estimating their localization uncertainties and impact momenta. Our results demonstrates that coda waves contain robust distance information even in a strongly scattering lunar crust, enabling reliable impact localization and providing new constraints on the connection between seismic source properties and impact crater formation.