Fractal heterogeneities in sonic logs and low-frequency scattering attenuation |

Different scattering regimes exist when waves propagate in heterogeneous media, according to the ratio of the wavelength, , to the size, , of heterogeneities. The formalism including the different scattering regimes, when heterogeneities are modeled by spherical inclusions, is the Mie scattering theory. Recent experimental results (Le Gonidec and Gibert, 2007) on sonic-wave reflectivity in a granular medium, made up of beads of size in a water tank, illustrate this classification :

- for low frequencies, when , backward scattering is dominant, the Born approximation can be used, and the regime is Rayleigh scattering;
- for wavelengths similar in size to heterogeneity, when , lateral scattering is important, multiples should not be neglected, and the regime is called resonant scattering; and
- for high frequencies, when , waves are scattered mainly forward, and localization theory and the Rytov formalism are appropriate.

schemescatter3dgg,schemescatterd,schemescatter3d
Schematic comparison of single scattering effects,
during a vertical wave propagation in sediments,
between a realistic geological structure (a) and two end-member models:
horizontal layers with propagation including 1D scattering (b)
and isotropic heterogeneities with 3D scattering (c).
Figure 5. |
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Fractal heterogeneities in sonic logs and low-frequency scattering attenuation |

2013-03-02