Seismic waves in randomly heterogeneous media: multiple scattering dispersion and attenuation

摘要

We investigate the problem of plane-harmonic wave propagation in a randomly heterogeneous elastic medium with spatially correlated material properties: density ρ(x) and Lame coefficients (λ(x), μ(x))-We solve analytically, in frequency-wavenumber space, the plane compressional wave propagating orthogonally to strata in a perfectly stratified (1D) random medium. We evaluate the solution explicitly for given structures of the random coefficients. We also average the solutions analytically to obtain the "effective" complex wave velocity. The mean seismic wave is affected by significant heterogeneity-induced dispersion and attenuation at moderate frequencies, f < 2000 Hz, based on cross-well seismic data in a fractured limestone formation. Finally, we extend the 1D stochastic solution to the multidimensional case: we develop a solution for plane-harmonic P- and S-waves propagating in a statistically non-isotropic 2D medium. Synthetic seismograms and velocity distribution maps are generated and compared to cross-well seismic data.