Vp ∕ Vs ratio versus differential stress and rock consolidation — A comparison between rock models and time-lapse AVO data

Abstract

The compressional to shear wave velocity ratio [Formula: see text] is an important parameter in seismic amplitude versus offset (AVO) analysis, and this parameter plays a key role especially for lithology and fluid prediction methods. The P-wave velocity is a key parameter in traditional pressure prediction methods, because overpressure often results in a velocity reduction. However, for AVO-based pore pressure prediction methods, one expects that the [Formula: see text] ratio also is a key parameter. The Hertz-Mindlin geomechanical model predicts a constant [Formula: see text] ratio as the differential stress changes in a dry package of identical spheres. Ultrasonic core measurements show increased [Formula: see text] ratios as the differential stress decreases, especially for unconsolidated wet sands. Thus, one is likely to assume that the [Formula: see text] ratio is dependent on rock consolidation. By combining the Hertz-Mindlin model with the Gassmann model, we show how to obtain a sim-ple rock-physics framework including both the differential stress and the degree of rock consolidation. We use the number of grain-to-grain contacts (coordination number) to represent the rock consolidation. For two field examples, we calibrate this consolidation parameter to in-situ stress conditions, then compare the predicted [Formula: see text] ratios for the overpressured reservoir conditions with observed time-lapse AVO changes. The correspondence between modeled and AVO-estimated [Formula: see text] ratios is good within the assumed accuracy of the real time-lapse AVO changes. In both cases, we observe an increase in the [Formula: see text] ratio as the differential stress decreases. In the first case, a pore pressure increase of [Formula: see text] is measured, whereas the other case shows a pressure increase of approximately [Formula: see text]. The first reservoir represents a low-to-medium-consolidated sandstone reservoir of 33% porosity on average, whereas the second reservoir is a more consolidated sand with similar porosities (30%).