Formation Stress Estimation Using Standard Acoustic Logging

Abstract

In situ formation stress directions and magnitudes are estimated by inverting the borehole flexural and Stoneley dispersions obtained from standard acoustic logging data (dipole and monopole logs). The underlying procedure consists of the following steps: first, we locate stressed zones in the formation by searching for crossovers in flexural dispersions. Second, the fast shear direction is estimated from the cross-dipole waveforms. It corresponds to the direction of the maximum horizontal stress (S[subscript H]). Finally, a multi-frequency inversion of both the Stoneley and flexural dispersions yields the maximum (S[subscript H]) and minimum (S[subscript h]) horizontal stress magnitudes together with the three formation nonlinear elastic constants, C[subscript 111], C[subscript 112] and C[subscript 113], defined about the selected reference (isotropic) state. The inversion method is based on equations that relate S[subscript H] and S[subscript h] with variations in phase velocities of the borehole flexural and Stoneley waves in the stressed state from those in the assumed reference state, the state that is hydrostatically loaded and isotropic. Phase velocities of the borehole flexural and Stoneley modes as a function of frequency can be obtained from processing the cross-dipole and monopole waveforms, respectively. The borehole flexural and Stoneley dispersions in the assumed reference (isotropic) state are obtained from the solution of a standard boundary-value problem. The sensitivity functions for the inversion model are obtained from the eigenfunctions of the boundary-value problem in the reference state. Results for the stress directions and magnitudes obtained from the inversion of the Stoneley and flexural dispersions over a selected bandwidth are consistent with focal mechanism and borehole breakout data present in the world map database (Zoback, 1992).