Poroelasticity and rock-physics templates Available to Purchase

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.