Statistical modeling of seismic reflectivities comparing Lévy stable and Gaussian mixture distributions

Abstract

The goal of this work is to compare statistical modeling of seismic reflectivities using two heavy-tailed models: Levy stable distributions and Gaussian mixture distributions. Distributions of various parameters, such as reflectivities are required inputs for many Monte Carlo simulations in statistical rock physics analyses for reservoir characterizations as well as formulating seismic inverse problem with non-Gaussian priors. Gaussian mixture models can provide an equally good fit to heavy-tailed reflectivity data as stable distributions, but with a larger number of fitting parameters. Monte Carlo simulations from stable distributions have a tendency to have more extreme outliers than simulations from Gaussian mixture models. Hence problems related to non-physical values, infinite moments, and ad-hoc fixes (truncation, deletion, etc.) tend to occur more often with stable distributions than Gaussian mixture models simulations