Accounting for pressure-dependent ultrasonic beam skew in transversely isotropic rocks: combining modelling and measurement of anisotropic wave speeds

The intrinsic anisotropy of rock influences the paths of propagating seismic waves and indicates mineralogical texture and strains; and as such it is important that laboratory measurements of such properties be fully understood. Usually, when studying anisotropy, ultrasonic wave speeds are measured in a variety of strategic directions and, subsequently transformed to the dynamic elastic moduli using symmetry-appropriate formula. For transversely isotropic rocks the moduli are ideally found by measuring wave speeds in directions vertical, parallel and oblique to the foliation or bedding using finite-width ultrasonic transducers. An important, but ignored, complication is that at oblique angles the ultrasonic beam unavoidably deviates, or skews, away from the transmitter's normal axis making proper wave speed determinations difficult. The pressure dependence of the wave speeds further confounds finding a solution as skew angles, too, vary with confining pressure. We develop a new technique that incorporates dual ultrasonic receivers to account for and mitigate the effects of the pressure-dependent beam skew problem. Anisotropy measurements to 200 MPa hydrostatic confining pressure combined with recent beam modeling algorithms illustrate the errors obtained in the determined wave speeds that are subsequently magnified in calculating the full set of elastic stiffnesses. In materials with P-wave anisotropies near 30 per cent the error introduced by ignoring beam skew exceeds the transit time picking errors by more than a factor of three, these propagate to much larger errors in the stiffnesses particularly for C₁₃ and the dynamic elastic moduli referred to C₁₃. Meanwhile, shortening the sample or enlarging the transmitter size is not suggested to counter the beam skew issue because it reduces the beam skew effect but increases the diffraction effect.