Precise inversion of logged slownesses for elastic parameters in a gas shale formation

Dipole sonic log data recorded in a vertical pilot well and the associated production well are analyzed over a 200 × 1100-ft section of a North American gas shale formation. The combination of these two wells enables angular sampling in the vertical direction and over a range of inclination angles from 54° to 90°. Dipole sonic logs from these wells show that the formation’s average properties are, to a very good approximation, explained by a transversely isotropic medium with a vertical symmetry axis and with elastic parameters satisfying C13 1⁄4 C12, but inconsistent with the additional ANNIE relation (C13 1⁄4 C33 − 2C55). More importantly, these data clearly show that, at least for fast anisotropic formations such as this gas shale, sonic logs measure group slownesses for propagation with the group angle equal to the borehole inclination angle. Conversely, the data are inconsistent with an interpretation that they measure phase slownesses for propagation with the phase angle equal to the borehole inclination angle.