Summary

A method of calculating stress induced seismic velocity anisotropy is presented and studied. In a first step an effective stiffness tensor of a stressed rock is calculated using third order elasticity (TOE) theory. In a second step, anisotropic seismic P- and S-wave velocities are calculated from the effective stiffness tensor using Tsvankin’s notation, which is an extension of Thomsen’s weak anisotropy notation. This method is used to study anisotropic velocity changes due to changes in hydrostatic, uni-axial and tri-axial stress using stress-sensitivity (thirdorder) parameters given in the literature. The computations show, in agreement with experimental observations, that the strongest P-wave velocity increases are observed in the direction of the largest stress increase. For S-waves, the largest velocity increase is observed for S-waves polarized parallel to the direction of maximum stress-increase. Therefore, S-waves have the potential to be used as a tool to monitor horizontal stress changes.

Introduction

Knowledge of the subsurface stress-state is an important factor of oilfield management. Knowledge of stress conditions in the overburden and the reservoir can help to avoid drilling hazard and helps to manage reservoir production. Pressure drawdown during hydrocarbon production causes subsurface stress to change and seismic methods have the potential to monitor this change in stress state. In the last 5 years at least 15 fields were reported to show a stress-related time-lapse seismic response in the open literature (see Herwanger and Horne, 2009 for a table compiling the observations). Given that not all such observations are reported and that time-lapse seismic is not applied in all producing fields, the actual number of fields where time-lapse seismic stress monitoring can be used is far larger. The rock-physics relationship linking the observed velocity changes and the causative stress-changes is still an active area of research. The majority of reported field case studies assume that stress-induced velocity changes are isotropic. On the other hand, experimental evidence from laboratory measurements (Scott et al., 1993; Scott et al., 1998; Dillen et al., 1999) clearly shows that anisotropic velocity changes occur during non-hydrostatic stress changes. In this study, we examine the effect of elastic deformation of rock for hydrostatic, uni-axial and tri-axial compression on anisotropic seismic velocity. First, we present a method of computing stress induced changes in the elastic stiffness tensor based on third-order elasticity described by Prioul et al. (2004). Second, we then present anisotropy parameters and P-wave, S-wave velocities for orthorhombic media (Tsvankin, 1997). These methods are then used to study anisotropic velocity changes for each of three different scenarios and the resulting velocity changes are plotted. The vertical velocity is shown to be sensitive to stress path and depends on both vertical and horizontal strain. For the same amount of vertical strain, vertical velocity changes are by a factor of two larger for hydrostatic compression than for tri-axial stress changes following a stress-path typical for overburden stretching. The results predict that the percentage change in velocity anisotropy is far larger than the strain percentage change that is linked to tensor stress change.

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