Mapping formation radial shear-wave velocity variation by a constrained inversion of borehole flexural-wave dispersion data

We have developed a novel constrained inversion method for estimating a radial shear-wave velocity profile away from the wellbore using dipole acoustic logging data and have analyzed the effect of the radial velocity changes on dipole-flexural-wave dispersion characteristics. The inversion of the dispersion data to estimate the radial changes is inherently a nonunique problem because changing the degree of variation or the radial size of the variation zone can produce similar wave-dispersion characteristics. Nonuniqueness can be solved by developing a constrained inversion method. This is done by constraining the high-frequency portion of the model dispersion curve with another curve calculated using the near-borehole velocity. The constraint condition is based on the physical principle that a high-frequency dipole wave has a shallow penetration depth and is therefore sensitive to the near-borehole shear-wave velocity. We have validated the result of the constrained inversion with synthetic data testing. Combining the new inversion method with four-component crossed-dipole anisotropy processing obtains shear radial profiles in fast and slow shear polarization directions. In a sandstone formation, the fast and slow shear-wave profiles show substantial differences caused by the near-borehole stress field, demonstrating the ability of the technique to obtain radial and azimuthal geomechanical property changes near the wellbore.