| Description |
The generalized effective-medium theory of induced polarization (GEMTIP) provides fundamental equations, which describe in analytical form the relationships between the petrophysical parameters of the rocks and their complex resistivity (CR) as a function of frequency. These relationships can be used to determine the petrophysical properties of the rocks from the observed CR data. However, for the three-phase ellipsoidal GEMTIP model, the inversion of the CR data has proven to be very challenging due to nonuniqueness and instability of this problem. In a number of practical situations, the gradient-type methods may experience significant difficulties due to existence of many local minima in the search space. In this thesis, the inversion methods for the GEMTIP modeling of heterogeneous rock samples are developed based on the genetic algorithms. I have conducted the synthetic study to prove that the pure genetic algorithm can be used for the GEMTIP inversion. However, it is showed that this method is not an ideal solution. To improve the inversion method, a hybrid adaptive genetic algorithm with simulated annealing (SAAGA) for the GEMTIP inversion was developed. The synthetic study demonstrated that this method provided an effective solution for the GEMTIP inverse problems and made it possible to find the global minimum in the space of GEMTIP model parameters. The case study included interpretation of the practical CR curves for different mineral rock samples. This case study demonstrated the advantage of the developed method over the global minimum search (GMS) method and pure genetic algorithm with the SAAGA method. Finally, I have developed a modified hybrid genetic algorithm based on the SAAGA method and three-point crossover operation. The case study indicated that, by using the SAAGA with multipoint crossover operation the inversion results were significantly improved compared to the GMS method and SAAGA method. |
