On inferring the noise in probabilistic seismic AVO inversion using hierarchical Bayes

A realistic noise model is essential for trustworthy inversion of geophysical data. Sometimes, as in case of seismic data, quantification of the noise model is non-trivial. To remedy this, a hierarchical Bayes approach can be adopted in which properties of the noise model, such as the amplitude of an assumed uncorrelated Gaussian noise model, can be inferred as part of the inversion. Here we demonstrate how such an approach can lead to substantial overfitting of noise when inverting a 1D reflection seismic NMO data set. We then argue that usually the noise model is correlated, and suggest to infer the amplitude of a correlated Gaussian noise model. This provides better results than assuming an uncorrelated model. In general though, the results suggest that care should be taken using the hierarchical Bayes approach to infer the noise model.