Vertical velocity at hydrostatic and anisotropic stresses

Sonic and dipole wireline tools measure Vp and Vs along the vertical direction. The state of stress in the subsurface is predominantly anisotropic, while most laboratory experiments measuring the dynamic elastic properties are conducted under hydrostatic stress. The question we ask is whether such laboratory experiments provide the velocities that are close to those measured in the vertical wellbore where the stresses are anisotropic. To address this question, we conducted ultrasonic pulse transmission experiments on several room-dry rock samples. The comparison was made between the P- and S-wave velocities obtained at pure hydrostatic loading conditions and those at a smaller hydrostatic stress with added axial stress, so that the total stress along the axis of a cylindrical plug was the same as under pure hydrostatic loading. These differences were significant in the extreme case of only 1 MPa hydrostatic confining stress with the axial stress increasing up to 40 MPa. However, as the hydrostatic (confining) stress increased, the differences between the velocities along the axis of the sample became smaller and smaller. For example, at 1 MPa confining and 30 MPa axial stress, the relative difference in Vp was about 10%, while that in Vs was about 20%. However, at 10 MPa confining stress, these differences became about 3% and 6%, respectively, and further decreased as the confining stress increased. This means that even at strong in-situ contrasts between the vertical and horizontal stresses, the results of laboratory hydrostatic experiments can be used for in-situ velocity estimates. These results also appear to be consistent with a theoretical model that predicts the directional velocities at any triaxial stress conditions from those measured versus hydrostatic stress.