Development of optimal models of porous media by combining static and dynamic data: the porosity distribution

This paper is part of a project, the goal of which is the development of the optimal spatial distributions of the porosity and permeability of a large-scale porous medium by using complementary static and dynamic data for the medium. The data include limited measurements of the porosity, which the method honors (preserves) in the optimal model and utilizes its correlation function, together with the first-arrival (FA) times, at a certain number of receivers, of seismic waves that have propagated in the medium and the time dependence of the pressure of a fluid flowing in the medium. The method uses the simulated-annealing (SA) technique in order to develop the optimal model. In the present paper we utilize the porosity and FA times data in order to develop the optimal spatial distribution of the porosity. This is accomplished by combining the SA method with a simulator that solves for the numerical solution of the acoustic-wave equation from which the FA times are estimated, limited porosity, and FA times data. We show that the optimal model not only honors the data, but also provides accurate estimates of the porosities in the rest of the porous medium. The efficiency of the computations is discussed in detail.