Ultrasonic velocities in sands—revisited

Abstract

Ultrasonic compressional and shear‐wave velocities of isotropic sands are shown to be dependent on their mineralogy, their porosity, their fluid content, and their state of consolidation, under fixed temperature and pressure conditions. This leads to a distinction between two broad classes of sands: those that are well consolidated, and those that are loosely consolidated. Changes in elastic velocities reflect changes in the ratio of bulk and shear moduli to density in response to lithologic variations. We decouple the two effects by examining changes in elastic moduli with respect to changes in lithology, and we observe three main points: (1) For consolidated sandstones, the effects of mineralogy and porosity can be approximated both empirically and theoretically by a modified isostrain theory: the dry bulk and shear moduli of the rock aggregate follow a “mixing law,” being linear combinations of the respective moduli of the individual constituents. The dry elastic moduli of families of clean sands and shaley sands are linear functions of porosity, with decreasing y‐axis intercepts as their clay‐to‐sand ratio increases. (2) Loosely consolidated sands and sandy shales appear to follow a behavior closer to that of the isostress theory for suspensions: the reciprocals of the bulk and shear moduli of the rock aggregate are linear combinations of the reciprocal moduli of their individual constituents. In general, the elastic moduli of poorly lithified sands are less sensitive to changes in mineralogy and porosity than those of consolidated sandstones. (3) For high permeability sands like the loosely consolidated sands of Troll, the Biot‐Gassman theory is a good approximation to the effects of fluids on seismic velocities. With our understanding of elastic moduli, we then show that dry ratios [Formula: see text] increase with porosity and clay content.