Statistical rock physics inversion of elastic and electrical properties for CO2 sequestration studies

Abstract

SUMMARY We present a statistical rock physics inversion of the elastic and electrical properties to estimate the petrophysical properties and quantify the associated uncertainty. The inversion method combines statistical rock physics modeling with Bayesian inverse theory. The model variables of interest are porosity and fluid saturations. The rock physics model includes the elastic and electrical components and can be applied to the results of seismic and electromagnetic inversion. To describe the non-Gaussian behaviour of the model properties, we adopt non-parametric probability density functions to sample multimodal and skewed distributions of the model variables. Different from machine learning approach, the proposed method is not completely data-driven but is based on a statistical rock physics model to link the model parameters to the data. The proposed method provides pointwise posterior distributions of the porosity and CO2 saturation along with the most-likely models and the associated uncertainty. The method is validated using synthetic and real data acquired for CO2 sequestration studies in different formations: the Rock Springs Uplift in Southwestern Wyoming and the Johansen formation in the North Sea, offshore Norway. The proposed approach is validated under different noise conditions and compared to traditional parametric approaches based on Gaussian assumptions. The results show that the proposed method provides an accurate inversion framework where instead of fitting the relationship between the model and the data, we account for the uncertainty in the rock physics model.