Forward and inverse modelling of electrical properties of some sandstone rocks using renormalisation group method
Electrical properties of some sandstone rocks (conductivity and dielectric constant) were investigated as a function of frequency (100 Hz to 100 kHz). Such heterogeneous specimens contain semiconducting constituents (silt and clay) and insulating constituents (sand, air, and carbonates). A theoretical pseudo-random renormalisation group method was used to predict the electrical properties of such random mixture. Four phases were used in the model to consider the detailed texture of the constituent materials. The measured electrical properties (conductivity and dielectric constant) versus frequency of these samples were analysed to predict the texture or connections of these four phases. From the analysis, these four phases were suggested to be (1) carbonates, (2) sand coated with clay and coated with air, (3) carbonates coated with clay and coated with air, and (4) pure sand. The forward problem predicts the electrical properties versus frequency using the pseudo-random renormalisation group method for certain concentrations of the constituent materials distributed among the random four phases. The forward model is used to fit the measured response to obtain the expected concentrations of rock constituents in the proposed four phases using a parameter search method (inverse problem). The obtained accordance between the experimental and modelled characteristics in much of the frequency band used suggests that the pseudo-random renormalisation group method with the supposed four phases reasonably represents the main mineralogical composition of the rock.