On the distribution of seismic reflection coefficients and seismic amplitudes

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. The distribution of reflection coefficients is independent of the spatial scale 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 a model of the reflection coefficients also have Levy-stable distributions. The difference between prestack and poststack data is attributed to the high level of measurement noise in the prestack data. -from Authors