Estimation of a non‐stationary prior covariance from seismic data

Abstract

ABSTRACTNon‐stationarity in statistical properties of the subsurface is often ignored. In a classical linear Bayesian inversion setting of seismic data, the prior distribution of physical parameters is often assumed to be stationary. Here we propose a new method of handling non‐stationarity in the variance of physical parameters in seismic data. We propose to infer the model variance prior to inversion using maximum likelihood estimators in a sliding window approach. A traditional, and a localized shrinkage estimator is defined for inferring the prior model variance. The estimators are assessed in a synthetic base case with heterogeneous variance of the acoustic impedance in a zero‐offset seismic cross section. Subsequently, this data is inverted for acoustic impedance using a non‐stationary model set up with the inferred variances. Results indicate that prediction as well as posterior resolution is greatly improved using the non‐stationary model compared with a common prior model with stationary variance. The localized shrinkage predictor is shown to be slightly more robust than the traditional estimator in terms of amplitude differences in the variance of acoustic impedance and size of local neighbourhood. Finally, we apply the methodology to a real data set from the North Sea basin. Inversion results show a more realistic posterior model than using a conventional approach with stationary variance.