Summary Highly depleted reservoirs exhibit sharply lower pore pressures and horizontal stress magnitudes than does the overlying shaly formation. Drilling through such depleted reservoirs can cause severe fluid loss and drilling-induced wellbore instability. Accurate and reliable estimates of horizontal stresses can provide an early warning of impending drilling problems that may be mitigated by appropriate drilling fluid design and drilling practices. We have developed a new multifrequency inversion algorithm for the estimation of maximum and minimum horizontal stress magnitudes using cross-dipole dispersions. Borehole sonic data for the case study presented in this paper was acquired by a cross-dipole sonic tool in a deepwater well, offshore Louisiana in the Gulf of Mexico (GOM). The logged interval spans 1,000 ft below the casing shoe. In addition, the Modular Dynamic Tester (MDT) (©Schlumberger) minifrac tests were performed at three depths in shale, thus yielding two minimum horizontal stress magnitudes. The borehole sonic data were suitable for the inversion of crossdipole dispersions at three depths in shale, as well as at a depth in a highly depleted sand reservoir. There was one depth in shale above the depleted sand where we could estimate the minimum horizontal stress magnitude with both the MDT minifrac tests and inversion of borehole sonic data. The results of the two techniques are consistent, providing encouragement for further validation of the multifrequency inversion of cross-dipole dispersions to estimate horizontal stresses. Even though the overburden stress is expected to increase with depth, both the maximum (SHmax) and minimum (Shmin) horizontal stresses obtained from the inversion of borehole sonic data are significantly smaller in the depleted sand than in the overburden shale. However, both the horizontal stress magnitudes increase again in the shale below the depleted sand. Such rapid variations in horizontal stress magnitudes cause large fluctuations in the safe mud-weight window. This challenge in drilling through the depleted sand was successfully handled by using special drilling fluid to mitigate seepage losses and the differential sticking in the depleted sand and overlying shale. We have also performed dipole radial profiling (DRP) of formation shear slownesses using the measured cross-dipole dispersions at three depths in shale and one in highly depleted sand. Analysis of radial profiles in the two orthogonal directions indicates plastic yielding or stiffening of rock in the near-wellbore region. While plastic yielding increases the shear slowness, stiffening would reduce the shear slowness.