Seismic codas on the Earth and the Moon: a comparison

The phenomenon of the seismic coda, which is composed of seismic energy delayed by scattering, is seen on both the Earth and the Moon. On the Moon the scattered coda is very large relative to body wave arrivals with a delay of the time of maximum energy, whereas on Earth scattered codas are relatively small and show no delay of the energy maximum. In both cases the form of the coda is controlled by three distance scales, the mean free path L, which is the average distance seismic energy travels before it is scattered, the attenuation distance $\text{x1}$, which is the average distance seismic energy travels before it is attenuated, and the source-receiver distance R. Two coda models are discussed based on these parameters; a strong scattering (diffusion) model, and a weak scattering (single scattering) model. A discussion of the diffusion scattering model indicates that if $\text{x1/L ? 1}$, diffusion scattering is an appropriate model, but if $\text{x1/L ? 1}$, single scattering is the appropriate model, within the appropriate range of R. A survey of the literature indicates that for the frequency range 0.5–10 Hz, diffusion scattering is important in lunar codas, but for the frequency range 1–25 Hz single scattering is important in terrestrial codas. Another important effect of attenuation is the elimination of scattering paths much longer than $\text{x1}$. On the Moon, this means that seismic energy in the coda can only propagate directly in the near-surface strong scattering zone between surface sources and the seismometer for source-seismometer separations of the order of $\text{(x1L)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$; otherwise, scattering is limited to regions near the source and the receiver. On Earth, this effect probably prevents multiple scattering.