Elastic waves in deviated boreholes in formations with triaxial stresses

A new 3D-finite-difference formulation of equations of motion for elastic waves in prestressed formations has been used to calculate synthetic waveforms at an array of receivers in a liquid-filled borehole. These equations describe the influence of borehole hydrostatic pressure as well as triaxial formation stresses on elastic waves produced by either a monopole or dipole transmitter placed on the borehole axis. The synthetic waveforms are processed by a slowness-time coherence (STC) and modified matrix pencil algorithms for isolating both non-dispersive and dispersive arrivals in the wavetrain. Computational results for the formation compressional, fast-shear, and slow-shear slownesses obtained from synthetic waveforms in a wellbore with deviations of 0°, 30°, and 60° from the vertical are consistent with the rotated stresses referred to the hole measurement axes. Compressional slowness changes are primarily affected by changes in the stress along the propagation direction. In contrast, shear slowness changes are equally affected by stress changes, either in the propagation or radial polarization direction.