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We carried out laboratory experiments under dry conditions on limestone core specimens of Sarvak formation obtained from an oil well in the southwest of Iran. Our objective was to study the effect of confining pressure on the compressional and shear wave velocities ([Formula: see text], [Formula: see text]), and on the dynamic to static Young’s modulus ratio ([Formula: see text]). Furthermore, we made attempts to predict [Formula: see text] and [Formula: see text] at atmospheric pressure based on the same velocities at various confining pressures. These analyses revealed that, below a critical pressure with an increase in confinement [Formula: see text] and [Formula: see text] increased exponentially, representing a poroelastic regime. Above a critical pressure, however, the trend was linear. Likewise, we observed that with an increase in confinement, [Formula: see text] initially decreased exponentially, followed by a linear decreasing trend above the critical pressure. This indicated that [Formula: see text] is more responsive than [Formula: see text]. Accordingly, these observations infer that it is possible to predict [Formula: see text] based on [Formula: see text] at different confining stresses. This is an important improvement for geomechanical modeling of hydrocarbon and geothermal reservoirs because static parameters are more realistic input parameters. Besides, we derived the coefficients of the velocity-pressure equation for Sarvak limestone using least square regression analysis. More interestingly, we predicted [Formula: see text] and [Formula: see text] at atmospheric pressure based on these coefficients. Good agreement was observed between measured and predicted velocities at atmospheric pressure. Analysis of similar published experiments on oceanic basalts strongly confirmed these observations.

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Laboratory measurement of P- and S-wave velocities ([Formula: see text] and [Formula: see text], respectively) under confining pressure indicates that with an increase in confining pressure, [Formula: see text] and [Formula: see text] will increase. The trend is exponential at low pressures, transitioning to linear above a critical pressure. However, the trend of the velocity-pressure curve for each rock specimen may be determined knowing the coefficients of this curve. We first studied how the coefficients of the velocity-pressure curve were expected to be functions of elastic moduli. Then, four empirical equations were used to estimate four coefficients of the velocity-pressure curve, using the rock density and [Formula: see text] and [Formula: see text] at atmospheric pressure (unconfined conditions). This analysis was carried out based on laboratory experiments on 285 rock specimens of different lithology from around the world, namely the United States, China, Germany, Iran, and deep-sea-drilling projects. For each rock specimen, [Formula: see text] and [Formula: see text] were measured at different confining stress levels, rendering more than 4000 data points. The accuracy of the estimated wave velocities was on the order of 2%–3% of the measured values on average. This methodology is especially valuable for prediction and analysis of the rock behavior at deep well conditions. This is applicable for predicting geophysical properties of the earth’s crust at depth, geomechanical study of hydrocarbon and geothermal reservoirs, wellbore stability analysis, and in situ stress determination.

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