Joint and simultaneous inversion of petrophysical properties of reservoir rocks using parallel niche generic algorithm

In a geophysical inversion process, the observed data is transformed to the meaningful properties of earth. For inversion of petrophysical properties, we need a rock physics model that links the petrophysical properties to the elastic properties of rock. The more accurate the model, the more reliable the results. There are a variety of procedures in which can invert petrophysical properties of earth through seismic data. Those procedures include experimental and empirical methods (In these methods, seismic data is assumed to be a function of some special petrophysical features of a zone), statistical methods and theoretical methods such as Biot model. Such theoretical method predicts elastic properties of rocks such as velocities and quality factors as functions of physical properties of rock and fluid. Here, we use BISQ  (Biot-Squirt flow) model for inversion of petrophysical properties of reservoir rock. The BISQ describes seismic wave propagation in a fluid saturated poroelastic medium. This model consists of both Biot and squirt flow models and its accuracy is confirmed by several researchers versus other models. The model is developed for several anisotropic media too. Biot model relates the attenuation of seismic wave to parallel motion of fluid in a solid frame; while, the squirt flow model relates it to local motion of fluid. It is proven that both mechanisms exist during seismic wave propagation and BISQ model is correct for both of them, simultaneously. In a petrophysical properties inversion process, there are two vital elements. First one, as described before, is using a rock physical model and the other one is mathematical method by which we solve an optimization problem that minimizes misfit between observed and predicted data. Here, we choose PNGA (Parallel Niche Genetic Algorithm) because of nonlinearity of BISQ model. Moreover, PNGA as an evolutionary algorithm, has capability of dealing with multi-objective optimization problems. We apply the mentioned method on both synthetic and real data. The inversion results show acceptable correlation with the used quantities in generation of synthetic and well logs.