Bayesian Seismic–Petrophysical Inversion for Rock and Fluid Properties and Pore Aspect Ratio in Carbonate Reservoirs

Abstract

Seismic characterization of carbonate reservoirs is a challenging task due to the complex structure of carbonate rocks, where the seismic response is affected by multiple factors such as pore volume and shape as well as changes in mineralogy due to dolomitization and silicification. Hence, the prediction of petrophysical properties from seismic data is often uncertain. For this reason, we propose a statistical inversion method for the estimation of rock properties, where we combine Bayesian inverse theory with geophysical modelling. The geophysical model aims to compute the seismic response based on the rock and fluid properties and pore structure of the carbonate rocks, and it includes rock physics and the amplitude variation with offset models for the seismic response. The Bayesian formulation allows for the solution of the associated inverse problem by computing the posterior distribution of rock and fluid properties and pore structure of the rocks conditioned by the measured geophysical data. The novelty of the proposed method is that the rock physics model can be any petroelastic relation, without requiring any linearization. For the application to the carbonate reservoir, we adopt the self-consistent inclusion model with ellipsoidal pore shapes and Gassmann's equation for the fluid effect; however, the inversion can be applied to any rock physics model. The statistical model assumes that the prior probability distribution of the model variables is a Gaussian mixture model such that distinct petrophysical characteristics can be associated with geological or seismic facies. The result of the proposed inversion is the most likely reservoir model of rock and fluid and pore geometry parameters, for example, porosity, pore aspect ratio, and water saturation and the uncertainty of the model predictions. The method is demonstrated and validated on synthetic and real examples using well logs and two-dimensional seismic sections from a pre-salt dataset in Brazil.