On the distribution of seismic reflection coefficients and seismic amplitudes
- Commonwealth Scientific and Industrial Research Organization, Glen Waverly, Victoria (Australia). Division of Petroleum Resources
- Univ. of Melbourne, Parkville, Victoria (Australia). Dept. of Mathematics
Reflection coefficient sequences from 14 wells in Australia have a statistical character consistent with a non-Gaussian scaling noise model based on the Levy-stable family of probability distributions. Experimental histograms of reflection coefficients are accurately approximated by symmetric Levy-stable probability density functions with Levy index between 0.99 and 1.43. These distributions have the same canonical role in mathematical statistics as the Gaussian distribution, but they have slowly decaying tails and infinite moments. The distribution of reflection coefficients is independent of the spatial scale (statistically self-similar), and the reflection coefficient sequences have long-range dependence. These results suggest that the logarithm of seismic impedance can be modeled accurately using fractional Levy motion, which is a generalization of fractional Brownian motion. Synthetic seismograms produced from the authors` model for the reflection coefficients also have Levy-stable distributions. These isolations include transmission losses, the effects of reverberations, and the loss of resolution caused by band-limited wavelets, and suggest that actual seismic amplitudes with sufficient signal-to-noise ratio should also have a Levy-stable distribution. This prediction is verified using post-stack seismic data acquired in the Timor Sea and in the continental USA. However, prestack seismic amplitudes from the Timor Sea are nearly Gaussian. They attribute the difference between prestack and poststack data to the high level of measurement noise in the prestack data.
- OSTI ID:
- 100751
- Journal Information:
- Geophysics, Vol. 60, Issue 4; Other Information: PBD: Jul-Aug 1995
- Country of Publication:
- United States
- Language:
- English
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