Predicting elasticity in nonclastic rocks with a differential effective medium model

Abstract

Can a theoretical inclusion model — specifically, the differential effective medium (DEM) model — match experimental velocity data in rocks that are not necessarily made of inclusions, such as clastics? It is indeed possible in some cases by using an almost constant inclusion aspect ratio (AR) within wide ranges of porosity and mineralogy. We approach this question by using empirical velocity-porosity equations as proxies for data. By finding a DEM inclusion AR to match these equations, we find that the required range of AR is narrow. Moreover, a constant AR of about 0.13 can be used to accurately match empirical relations in competent sand, shale, and quartz/calcite mixtures. This finding can be utilized practically to predict [Formula: see text] from [Formula: see text]; describe velocity-frequency dispersion between low-frequency and ultrasonic experiments; predict the dry-frame elastic properties from ultrasonic data on liquid-saturated samples where Gassmann’s fluid substitution is not applicable; predict the attenuation of P-wave velocity; and establish tight constraints for ranges of possible variation of [Formula: see text] and [Formula: see text] at a given porosity in some mineralogies. When we apply this approach to laboratory data rather than empirical equations, we confirm a positive answer to the main question, with all applications of this result still valid.