ATTENUATION OPERATORS AND COMPLEX WAVE VELOCITIES FOR SCATTERING IN RANDOM-MEDIA

The concept of attenuation operators and complex velocities is applied to scattering attenuation in two and three dimensions, using the mini mum-phase assumption for the attenuation operator. Acoustic 2D finite- difference computations of synthetic seismograms show, that the attenu ation operator describes well the decay and lowpass filtering of the a veraged wave form, which follows from averaging travel-time-corrected wave forms along the wave front. In the case of exponential random med ia, analytical forms of the attenuation operators and complex velociti es are available. The complex velocities are incorporated into the ref lectivity method. As an application, synthetic seismograms are present ed for the S-n wave, attenuated by lithospheric velocity and density f luctuations. The limitations of attenuation operators and complex velo cities for scattering are also discussed. With these quantities it is not possible to model phenomena related to the scattered waves themsel ves, such as amplitude and travel-time fluctuations along the wave fro nt, codas and precursors.