SEISMIC ATTENUATION BY SCATTERING - THEORY AND NUMERICAL RESULTS

Estimates of seismic wave attenuation are strongly affected by scattering. Scattering is an important effect caused by interaction of seismic wavefields with inhomogeneities of hydrocarbon reservoirs, Earth's crust and mantle. In order to study the contribution of scattering to apparent attenuation we consider plane-wave propagation in acoustic 2-D and 3-D inhomogeneous media. Different attenuation estimates result depending on what wavefield function is being averaged during corresponding processing. By wave-theoretical analysis and high-order finite difference modelling in two dimensions we show that scattering attenuation estimates derived from the mean of amplitude spectra and from the mean logarithm of amplitude spectra depend on travel distance. For not too long travel distances, where the coherent part of the wavefield dominates, we give an analytical description of these estimates. In 2-D and 3-D the relations are established between the autocorrelation functions of velocity fluctuations of a random medium and the autocorrelation functions of amplitude and phase fluctuations on a receiver line perpendicular to the general propagation direction of an originally plane wave. For long distances, where the wavefield fluctuates strongly, we show that both mean logarithm of amplitude and logarithm of mean amplitude tend to constants. They differ approximately by a factor two in both scattering regimes. The scattering attenuation coefficient of the meanfield is not dependent on travel distance. We compared our theoretical results with numerical calculations and found excellent agreements. The concept presented clarifies the nature of seismic Q estimations in the presence of scattering and can help to yield statistical earth models from seismic data.