Origin of coda waves: Source, attenuation, and scattering effects

Coda waves from small local earthquakes are interpreted as backscattering waves from numerous heterogeneities distributed uniformly in the earth's crust. Two extreme models of the wave medium that account for the observations on the coda are proposed. In the single backscattering model the scattering is considered to be a weak process, and the loss of seismic energy by scattering is neglected. In the diffusion model the seismic energy transfer is considered as a diffusion process. Both models lead to similar formulas that allow an accurate separation of the effect of earthquake source from the effects of scattering and attenuation on the coda spectra. A unique difference was found in the scaling law of earthquake source spectra between central California and western Japan, which may be attributed to the difference in inhomogeneity length of the earth's crust. The Q of coda waves in the two regions is strongly frequency dependent with values increasing from 50–200 at 1 Hz to about 1000–2000 at 20 Hz. This observation is interpreted as a combined effect of variation of Q with depth and frequency-dependent composition of coda waves described below. The turbidity coefficient of the lithosphere required at 1 Hz to explain the observed coda as body wave scattering is orders of magnitude greater than previously known values such as those obtained by Aki (1973) and Capon (1974) under the Montana Lasa from the amplitude and phase fluctuations of teleseismic P waves. From the high attenuation and turbidity obtained at this frequency we conclude that at around 1 Hz the coda is made of backscattering surface waves from heterogeneities in the shallow, low-Q lithosphere. The high Q observed for the coda at frequencies higher than 10 Hz, on the other hand, eliminates the possibility that these waves are backscattering surface waves. We conclude that at these high frequencies the coda must be made of backscattering body waves from heterogeneities in the deep lithosphere. The low turbidities found for deep earthquake sources under western Japan are consistent with this model of coda wave generation.