A finite-difference algorithm is used to generate synthetic seismograms for waves propagating through two-dimensional random media. The media have a significant component of their material properties varying randomly over length scales smaller than the seismic wavelength and are meant to approximate the heterogeneity of the crust and upper mantle. The finite-difference technique retains all multiply scattered and diffracted waves, and also accounts for transmission losses.
The synthetic seismograms clearly exhibit coda and apparent attenuation caused by scattering. For a medium with a white wavenumber spectrum of velocity fluctuations, the coda is higher frequency than the initial pulse. The apparent attenuation is greatest when the scatterer size is comparable to the seismic wavelength. The spectra of the coda generally increase in frequency as the scatterers decrease in size. Examples demonstrate how scattering can produce spectra with broad peaks and sharp fall-offs that can make the determination of the source spectra and corner frequencies of small earthquakes extremely difficult.