Effects of multi-scale velocity heterogeneities on wave-equation migration

Velocity models used for wavefield-based seismic imaging represent approximations of the velocity characterizing the area under investigation. The real subsurface velocity can at best be approximated by the combination of a known background velocity and unknown multi-scale heterogeneities. Here, we model the multi-scale heterogeneity assuming a fractal behavior and compare this type of heterogeneity with conventional correlated Gaussian random distributions. Data simulated for the various heterogeneity distributions are characterized by spectra with different shapes when analyzed in the log-log domain. For example, Gaussian distributions are characterized by exponential functions and fractal distributions are characterized by linear functions with fractional slopes. These properties hold for both data and migrated images after deconvolution of the source wavelet. Exploiting the distinctions between the various kinds of heterogeneities, we can use leastsquares fitting to ascertain characteristics and parameters of heterogeneity from the seismic data and migrated images.