From the Bureau of Economic Geology, The
University of Texas at Austin (www.beg.utexas.edu).
For more information, please contact the author.
Bureau Seminar, March 06, 2009
Fractal heterogeneities in sonic logs and low-frequency scattering attenuation
Bureau of Economic Geology
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 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 attenuated more than compressional waves because of
their shorter wavelength.