Scattering attenuation of 2D elastic waves: Theory and numerical modeling using a wavelet-based method

The passage of seismic waves through highly heterogeneous media leads to significant scattering of seismic energy and an apparent attenuation of seismic signals emerging from the heterogenous zone. The size of this scattering attenuation depends on the correlation properties of the medium, the rates of P- and S-wave velocities, and frequency content of the incident waves. An estimate of the effect can be obtained using single scattering theory (first-order Born approximation) for path deviations beyond a minimum scattering angle; smaller deviations require consideration of multiple scattering or a representation in terms of travel-time perturbations. Although an acoustic treatment provides a quantitative reference, full elastic effects need to be taken into consideration to get an accurate attenuation rates. The use of a wavelet-based modeling technique, which is accurate and stable even in highly perturbed media, allows an assessment of the properties of different classes of stochastic media (Gaussian, exponential, von Karman). The minimum scattering angle for these stochastic media is in the range of 60° to 90°. The wavelet-based method provides a good representation of the scattered coda, and it appears that methods such as finite differences may overestimate scattering attenuation when the level of the heterogeneity is high.