Determination of elastic anisotropy of rocks from P- and S-wave velocities: numerical modelling and lab measurements
Abstract
The most common type of waves used for probing anisotropy of rocks in laboratory is the direct P wave. Information potential of the measured P-wave velocity, however, is limited.
In rocks displaying weak triclinic anisotropy, the P-wave velocity depends just on 15 linear combinations of 21 elastic parameters, called the weak-anisotropy parameters. In strong triclinic anisotropy, the P-wave velocity depends on the whole set of 21 elastic parameters, but inversion for six of them is ill-conditioned and these parameters are retrieved with a low accuracy.
Therefore, in order to retrieve the complete elastic tensor accurately, velocities of S waves must also be measured and inverted. For this purpose, we developed a lab facility which allows the P-and S-wave ultrasonic sounding of spherical rock samples in 132 directions distributed regularly over the sphere.
The velocities are measured using a pair of P-wave sensors with the transmitter and receiver polarized along the radial direction and using two pairs of S-wave sensors with the transmitter and receiver polarized tangentially to the spherical sample in mutually perpendicular directions. We present inversion methods of phase and ray velocities for elastic parameters describing general triclinic anisotropy.
We demonstrate on synthetic tests that the inversion becomes more robust and stable if the S-wave velocities are included. This applies even to the case when the velocity of the S waves is measured in a limited number of directions and with a significantly lower accuracy than that of the P wave.
Finally, we analyse velocities measured on a rock sample from the Outokumpu deep drill hole, Finland. We present complete sets of elastic parameters of the sample including the error analysis for several levels of confining pressure ranging from 0.1 to 70 MPa.