Time-average equation revisited

Abstract

Expressions that relate velocity to porosity and to pore-fluid compressibility are among the most important deliverables of rock physics. Such relations are used often as additional controls for inferring porosity from well logs, as well as in-situ indicators of pore fluid type. The oldest and most popular is the Wyllie et al. (1956) equation: [Formula: see text]where [Formula: see text] is the measured traveltime of a P-wave, [Formula: see text] is the traveltime expected in the solid-phase material, and [Formula: see text] is the traveltime expected in the pore fluid. It follows from equation (1) that [Formula: see text]where ϕ is porosity, [Formula: see text] is the measured P-wave velocity, and [Formula: see text] and [Formula: see text] are the P-wave velocities in the solid and in the pore-fluid phases, respectively.