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Geophysics / Volume 74 / Issue 2 / TECHNICAL PAPERS / THEORY

Fractal heterogeneities in sonic logs and low-frequency scattering attenuation

Geophysics 74, WA77 (2009); doi:10.1190/1.3062859

Published 11 March 2009

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ABSTRACT

REFERENCES (61)

CITING ARTICLES

Thomas J. Browaeys¹ and Sergey Fomel¹
¹University of Texas at Austin, John A. and Katherine G. Jackson School of Geosciences, Bureau of Economic Geology, Austin, Texas, U.S.A. E-mail: jules.browaeys@beg.utexas.edu; sergey.fomel@beg.utexas.edu.

Cyclesin sedimentary strata exist at different scales and can bedescribed by fractal statistics. We use von Kármán's autocorrelation functionto model heterogeneities in sonic logs from a clastic reservoirand propose a nonlinear parameter estimation. Our method is validatedusing synthetic signals. When applied to real sonic logs, itextracts the fractal properties of high spatial frequencies and onedominant cycle between 2.5 and 7 m. Results demonstrate non-Gaussian andantipersistent statistics of sedimentary layers. We have derived an analyticalformula for the scattering attenuation of scalar waves by 3Disotropic fractal heterogeneities using the mean field theory. Penetration ofwaves exhibits a high-frequency cutoff sensitive to heterogeneity size. Therefore,shear waves can be attenuated more than compressional waves becauseof their shorter wavelength. ©2009 Society of Exploration Geophysicists