Thomas J. Browaeys and Sergey Fomel
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,
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 field theory.
Penetration of waves exhibits a high-frequency cutoff sensitive to heterogeneity size.
Therefore shear waves can be more attenuated than compressional waves because of their shorter wavelength.
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