The transition from ballistic to diffuse wavefields on Earth, its Moon and Mars.

Seismograms on Mars and Earth's Moon display extended coda, relative to many terrestrial seismograms, that are attributed to strong scattering of elastic waves by crustal regions. The varying duration of these planetary coda hints at a spectrum of scattering strengths on planetary bodies from Earth (weak) to its moon (strongest). Quantifying the scattering strength of a medium, within this spectrum, is therefore desirable for probing interior structure and mapping the complexity of different media. However, assumptions required in common models and metrics of scattered wavefields, such as the Born approximation, diffusion equations, equipartitioning and coda-Q, render them inapplicable to an entire spectrum of scattering behaviour and strength.

Here we utilise quantitative measures of scattering whose assumptions do not limit them to a sub-region of the spectrum of scattering strength. Correlation-coefficient analysis and multi-scale entropy techniques are applied to terrestrial, Lunar and Martian seismograms, demonstrating their applicability as measures of wavefield diffusivity and complexity. Our results indicate non-diffuse characteristics are present within some bandwidths of Lunar coda, and we observe the highest waveform complexities in Martian examples. We discuss the potential of applying these techniques in future coda studies to map the statistical complexity of planetary interiors.