Fractal heterogeneities in sonic logs and low-frequency scattering attenuation

Cycles in sedimentary strata exist at dierent scales and can be described by fractal statistics. We use von K arm an's autocorrelation function to model het- erogeneities in sonic logs from a clastic reservoir and propose a nonlinear pa- rameter estimation. Our method is validated using synthetic signals, and when applied to real sonic logs, it extracts both the fractal properties of high spatial frequencies and one dominant cycle between 2.5 and 7 m. Results demonstrate non-Gaussian and antipersistent statistics of sedimentary layers. We derive an analytical formula for the scattering attenuation of scalar waves by 3D isotropic fractal heterogeneities using the mean eld theory. Penetration of waves exhibits a high-frequency cuto sensitive to heterogeneity size. Therefore shear waves