HR: 1340h
AN: S53B-1262 [Abstracts]
TI: Fractal Heterogeneities in Sonic Logs and Low Frequency Scattering Attenuation
AU: * Browaeys, T J
EM: jules.browaeys@beg.utexas.edu
AF: University of Texas at Austin,
John A. and Katherine G. Jackson School of Geosciences,
Bureau of Economic Geology, University Station, Box X, Austin, TX 78713-8972, United States
AU: Fomel, S
EM: sergey.fomel@beg.utexas.edu
AF: University of Texas at Austin,
John A. and Katherine G. Jackson School of Geosciences,
Bureau of Economic Geology, University Station, Box X, Austin, TX 78713-8972, United States
AB:
Wave propagation in a heterogeneous medium involves seismic attenuation and dispersion
by scattering. The nature of subsurface heterogeneities
has been recognized to satisfy fractal properties.
We model the velocity heterogeneities by the von Kármán spatial autocorrelation function
depending on the length b (larger size of fractal heterogeneities), the Hurst exponent,
and the standard deviation of the velocity variations.
The nonlinear parameters estimation on four sonic VP and VS logs data
from a clastic overburden in Canada reveals the spatial frequency domain
of validity for the fractal description and the presence of several low cycles.
We attempt to identify the different scales of the sedimentation process
in the well log signal as proposed by O'Doherty and Anstey.
Our inversion result shows a good agreement with the fractal model at scales
smaller than 10 meters but the importance of local cycles at low spatial frequency.
For long wavelengths compared to the size of heterogeneities,
the scattering is in the Rayleigh diffusion regime in which
the wavefield is dominantly backscattered.
This regime is relevant for the frequency band of seismic surveys
in our fractal heterogeneities model.
High frequencies, required to improve resolution,
undergo a more complex loss of energy by intrabed multiples
as the wavelengths become similar to the heterogeneities scale.
We use analytical derivations of the scattering attenuation
based on the mean wavefield theory,
whose validity is restricted to the low frequency band, i.e. for
small heterogeneities compared to the seismic wavelength.
The result estimates the attenuation by 3-D scattering
of a scalar wave from isotropic fractal heterogeneities
correlated by the von Kármán function.
We determine that the loss of resolution with depth is more severe for a
high Hurst exponent (smoother medium), for shear waves compared
to compressional wave due to their smaller wavelength,
and extremely sensitive to the characteristic size b of the fractal heterogeneities.
The depth of penetration of the wave decreases dramatically with increasing frequencies.
We evaluate the shift of the dominant frequency with depth for a Ricker wavelet
propagating in the 3-D fractal heterogeneous medium.
These results advise to use low frequency seismic for deep targets
under a strongly heterogeneous overburden. The presence of quasi-cycles in the sonic log
data at large spatial scales calls for more sophisticated seismic scattering methods
accounting for the medium's periodicity.
DE: 0935 Seismic methods (3025, 7294)
DE: 3255 Spectral analysis (3205, 3280)
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 5144 Wave attenuation
DE: 7260 Theory
SC: Seismology [S]
MN: 2007 Fall Meeting