Bayesian linearized petrophysical AVO inversion

Abstract

Seismic reservoir characterization aims to provide a 3D model of rock and fluid properties based on measured seismic data. Petrophysical properties, such as porosity, mineral volumes, and water saturation, are related to elastic properties, such as velocity and impedance, through a rock-physics model. Elastic attributes can be obtained from seismic data through seismic modeling. Estimation of the properties of interest is an inverse problem; however, if the forward model is nonlinear, computationally demanding inversion algorithms should be adopted. We have developed a linearized forward model, based on a convolutional model and a new amplitude variation with offset approximation that combined Gray’s linearization of the reflectivity coefficients with Gassmann’s equation and Nur’s critical porosity model. Physical relations between the saturated elastic moduli and the matrix elastic moduli, fluid bulk modulus, and porosity are almost linear, and the model linearization can be obtained by computing the first-order Taylor series approximation. The inversion method for the estimation of the reservoir properties of interest is then developed in the Bayesian framework. If we assume that the distributions of the prior model and error term are Gaussian, then the explicit analytical solution of the posterior distribution of rock and fluid properties can be analytically derived. Our method has first been validated on synthetic seismic data and then applied to a 2D seismic section extracted from a real data set acquired in the Norwegian Sea.