Fractal heterogeneities in sonic logs and low-frequency scattering attenuation

Abstract

Cycles in sedimentary strata exist at different scales and can be described by fractal statistics. We use von Kármán’s autocorrelation function to model heterogeneities in sonic logs from a clastic reservoir and propose a nonlinear parameter estimation. Our method is validated using synthetic signals. When applied to real sonic logs, it extracts the fractal properties of high spatial frequencies and one dominant cycle between 2.5 and [Formula: see text]. Results demonstrate non-Gaussian and antipersistent statistics of sedimentary layers. We have derived an analytical formula for the scattering attenuation of scalar waves by 3D isotropic fractal heterogeneities using the mean field theory. Penetration of waves exhibits a high-frequency cutoff sensitive to heterogeneity size. Therefore, shear waves can be attenuated more than compressional waves because of their shorter wavelength.