Time-lapse amplitude variation with offset inversion using Bayesian theory in two-phase media

Abstract

In time-lapse seismic analysis, the Zoeppritz equations are usually used in the time-lapse amplitude variation with offset (AVO) inversion and then combined with a rock-physical model to estimate the reservoir-parameter changes. The real-life reservoir is a two-phase medium that consists of solid and fluid components. The Zoeppritz equations are a simplification, assuming a single-phase solid medium, in which the properties of this medium are estimated by effective parameters from the combined components. This means that the Zoeppritz equations cannot describe the characteristics of the seismic reflection amplitudes in the reservoir in an accurate way. Therefore, we develop a method for time-lapse AVO inversion in two-phase media using the Bayesian theory to estimate the reservoir parameters and their changes quantitatively. We use a reflection-coefficient equation in two-phase media, a rock-physical model, and the convolutional model to build a relationship between the seismic records and reservoir parameters, which include porosity, clay content, saturation, and pressure. Assuming that the seismic-data errors follow a zero-mean Gaussian distribution and that the reservoir parameters follow a four-variable Cauchy prior distribution, we use the Bayesian theory to construct the objective function for the AVO inversion, and we also add a model-constraint term to compensate the low-frequency information and improve the stability of the inversion. Using the objective function of the AVO inversion and the Gauss-Newton method, we derived the equation for time-lapse AVO inversion. This result can be used to estimate the reservoir parameters and their changes accurately and in a stable way. The test results from the feasibility study on synthetic and field data proved that the method is effective and reliable.