Poroelasticity and rock-physics templates

Abstract Two common rock-physics templates that are used to identify the geologic facies and fluid trends derived from well log or prestack inverted seismic data involve crossplotting the VP/VS ratio against acoustic impedance, IP (the product of P-wave velocity VP and density ρ) and μρ against λρ, wherein λ and μ are the Lamé coefficients extracted from the P- and S-wave velocity, called the LambdaMuRho (LMR) method. Using well-log examples from an Alberta gas well and a deeper North Sea oil well, we show how to superimpose the constant μρ and λρ curves on a VP/VS versus IP crossplot, which produce the orthogonal trends of stiffness or porosity (from μρ) and fluid saturation (from λρ) that match the data trends reasonably well. We then consider the related technique of KMuRho (KMR), wherein K represents the bulk modulus and show how to superimpose the constant Kρ trends on a VP/VS versus IP crossplot. Again, we obtain the orthogonal trends of stiffness or porosity (from μρ) and fluid saturation (from Kρ), but the fit to our real data examples is less accurate than with LMR. Using the Biot-Gassmann poroelasticity theory, we generalize the LMR and KMR approaches into a technique we call FluidMuRho (FMR). In the FMR techniques, we introduce two new fitting parameters, f and d, wherein f is a fluid term derived from the Biot-Gassmann theory, and d is the dry rock VP/VS ratio squared. When we superimpose the fluid trends from the FMR technique on our two well-log data sets and adjust the f and d parameters, we achieve accurate fits to the data sets. Finally, we apply the FMR technique to a seismic case study from the Gulf of Mexico. In an appendix, we compare the FMR technique to the empirical curved pseudo-elastic impedance and pseudo-elastic impedance for lithology methods.