Institute of Geophysics, University of TehranJournal of the Earth and Space Physics2538-371X41420151222Application of different inverse methods for combination of vS and vGPR data to estimate porosity and water saturationApplication of different inverse methods for combination of vS and vGPR data to estimate porosity and water saturation89945722510.22059/jesphys.2015.57225FARamin VarfinezhadM.Sc. Graduate, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran0000-0001-9360-4978Mohamd Kazem HafiziProfessor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran0000-0002-5634-1141Hosein HashemiAssistant Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran0000-0002-6734-9317Journal Article20150706Inverse problem is one of the most important problems in geophysics as model parameters can be estimated from the measured data directly using inverse techniques. In this paper, applying different inverse methods on integration of S-wave and GPR velocities are investigated for estimation of porosity and water saturation. A combination of linear and nonlinear inverse problems are solved. Linear least-squares and conjugate gradient are used as linear techniques, whereas grid search and Newton methods are selected as nonlinear ones. It is understood that vS depends on density and Lame Constant (shear modulus) and vGPR on dielectric constant. This combination seems to be logical. Shear modulus is related to porosity using Bruggemanâ€™s rule. Density and dielectric constant is also related to porosity and water saturation. This implies that vS and vGPR are bivariate functions of porosity and water saturation, which are our unknown model parameters. The model parameters are estimated to minimize the cost functional ora system of the equations. In order to convert the nonlinear problem into the linear form, taking logarithm and changing variables were used. The problem was convex, which was inferred from the linear form, so there was just one local minimum as the global minimum of the problem. The grid search method shows that porosity and water saturation cannot be estimated by vGPR or vS uniquely. The results of the four methods were compared with each other and a good agreement was observed.Inverse problem is one of the most important problems in geophysics as model parameters can be estimated from the measured data directly using inverse techniques. In this paper, applying different inverse methods on integration of S-wave and GPR velocities are investigated for estimation of porosity and water saturation. A combination of linear and nonlinear inverse problems are solved. Linear least-squares and conjugate gradient are used as linear techniques, whereas grid search and Newton methods are selected as nonlinear ones. It is understood that vS depends on density and Lame Constant (shear modulus) and vGPR on dielectric constant. This combination seems to be logical. Shear modulus is related to porosity using Bruggemanâ€™s rule. Density and dielectric constant is also related to porosity and water saturation. This implies that vS and vGPR are bivariate functions of porosity and water saturation, which are our unknown model parameters. The model parameters are estimated to minimize the cost functional ora system of the equations. In order to convert the nonlinear problem into the linear form, taking logarithm and changing variables were used. The problem was convex, which was inferred from the linear form, so there was just one local minimum as the global minimum of the problem. The grid search method shows that porosity and water saturation cannot be estimated by vGPR or vS uniquely. The results of the four methods were compared with each other and a good agreement was observed.https://jesphys.ut.ac.ir/article_57225_e0f85c2be4519bea2495b29ae8d1dce5.pdf