Feasibility of theoretical formulas on the anisotropy of shale based on laboratory measurement and error analysis

This paper designs a total angle ultrasonic test method to measure the P-wave velocities (v(p)), vertically and horizontally polarized shear wave velocities (v(sv) and v(sh)) of all angles to the bedding plane on different kinds of strong anisotropic shale. Analysis has been made of the comparisons among the observations and corresponding calculated theoretical curves based on the varied vertical transversely isotropic (TI) medium theories, for which discussing the real similarity with the characterizations of the TI medium on the scope of dynamic behaviors, and further conclude a more accurate and precise theory from the varied theoretical formulas as well as its suitable range to characterize the strong anisotropy of shale. At a low phase angle (theta < 10 degrees), the three theoretical curves are consistent with the observations, and then tend to be distinct with the increase of the phase angle, especially for the Thomsen theoretical curves which tend toward serious deviation, while the Berryman expressions provide a relatively much better agreement with the measured data for v(p), v(sv) on shale. Also all of the three theories lead to more deviations in the approximation of the v(sv) than for the v(p) and v(sh). Furthermore, we created synthetic comparative ideal physical models (from coarse bakelite, cambric bakelite, and paper bakelite) as supplementary models to natural shale, which are used to model shale with different anisotropy, to research the effects of the anisotropic parameters upon the applicability of the former optimal TI theories, especially for the v(sv). We found the when the P-wave anisotropy, S-wave anisotropy epsilon, gamma > 0.25, the Berrryman curve will be the best fit for the v(p), v(sv) on shale.