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:
where tP is the measured traveltime of a P-wave, τS is the traveltime expected in the solid-phase material, andτF is the traveltime expected in the pore fluid. It follows from equation (1) that
where ϕ is porosity, Vp is the measured P-wave velocity, and VpS and VpF are the P-wave velocities in the solid and in the pore-fluid phases, respectively.
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