Estimation of rock anisotropic constants using sonic data from deviated wellbores

Seismic prospecting for hydrocarbons requires anisotropic velocity model that describes plane wave velocity propagation as a function of direction from the vertical symmetry axis of a transversely isotropic (TI) overburden shale. The anisotropic velocity model for a thick shale layer can be constructed in terms of five TI elastic constants. Generally, these elastic constants are estimated from borehole seismic data analysis. This paper describes a computationally efficient method to estimate all five TI constants using borehole sonic data acquired from boreholes with two different deviations from the vertical TI symmetry axis. A new technique for the estimation of all five TI elastic constants consists of measuring the compressional (qP), pure shear (SH) and quasi-shear (qSV) wave velocities along boreholes with two different deviations from the vertical. These velocities can be reliably estimated from a conventional processing of monopole and cross-dipole waveforms. The proposed algorithm is based on weak anisotropy approximation and it successfully inverts the qP, qSV, and SH wave velocities in the two depth intervals in the same lithology with different deviations for all five TI elastic constants. Two modified versions of this workflow can also invert the compressional and shear velocities from (1) a vertical wellbore parallel to the TI-symmetry axis and a deviated wellbore and (2) a horizontal wellbore in the TI-isotropic plane and a deviated wellbore, for all the five TI elastic constants. Explicit expressions for the compressional and shear velocities as a function of propagation direction from the TI-symmetry axis result in an efficient inversion of velocity data to obtain elastic constants of the propagating medium. Inverted elastic constants from these algorithms agree very well with the actual TI constants used to generate synthetic velocities for three different TI shale formations. Thus, we have validated the proposed algorithms using synthetic data for the estimation of all five TI elastic constants that do not require the use of Stoneley data and associated strong dependence on the borehole fluid compressional velocity in the estimation of Stoneley shear modulus.