Application of the power mean to modeling the elastic properties of reservoir rocks

Abstract

The relationship between seismic velocity and porosity is one of the most important research topics in exploration geophysics. A strong correlation, if it exists, can be very useful for quantitative seismic interpretation of direct hydrocarbon indicators. The Voigt and Reuss bounds are often plotted alongside the data for quality control and interpretation. The relative position of the data within the bounds may supply important information regarding the pore shape, stress condition, lithology, and diagenesis of porous rocks. It is found that the Voigt bound and Reuss bound are actually special cases of the weighted power mean, with the power parameters being 1 and −1, respectively. The geometric mean is a special case of the power mean with the power parameter being zero. The power mean is a monotonic function of the power parameter. For the construction of a rock physics template, the region between the Voigt and Reuss bounds can be evenly divided by varying the power parameter between −1 and 1. The power mean can be a very useful tool for modeling the elastic properties of rocks. We have demonstrated the potential applications of the power mean in the studies of velocity-porosity relation, effective media, and pore fluids effect on seismic velocities.