Elasticity of single-crystal San Carlos olivine has been derived from sound velocity and density measurements at simultaneous high pressure-temperature conditions up to 20 GPa and 900 K using in situ Brillouin spectroscopy and single-crystal X-ray diffraction in externally-heated diamond anvil cells. These experimental results are used to evaluate the combined effect of pressure and temperature on full elastic constants of single-crystal olivine to better understand its velocity profiles and anisotropies in the deep mantle. Analysis of the results shows that the shear moduli display strong concave behaviors as a function of pressure at a given high temperature, while the longitudinal modulus, C-11, and the off-diagonal moduli, C-12 and C-13, exhibit greater temperature dependence at higher pressures than at relatively lower pressures. Using a finite-strain theory and thermal equation of state modeling for a pyrolitic mantle composition along an expected mantle geotherm, our results show that the magnitude of the V-P and V-S jumps at the 410-km depth are 6% and 6.4%, respectively, which are greater than that found in seismic observations, suggesting a mantle olivine content of 40-50 vol%, which is less than what is expected for the pyrolite model. Our modeled velocity profiles for a metastable olivine wedge in the subduction slabs along a representative cold slab geotherm are 6% and 10% lower than those of wadsleyite and ringwoodite, respectively, at corresponding depths of the normal mantle. Our modeled results also show that metastable olivine in the cold slabs could have strong V-P and V-S anisotropies. The maximum V-P anisotropy is estimated to be 19-22% at transition zone depth, whereas the maximum V-S splitting is 13-23% and increases with depth. As a result, the presence of a metastable olivine wedge at the transition zone depth would exhibit a seismic signature of low velocity and strong seismic anisotropy which are consistent with recent seismic observations for various locations of the slabs and can be used as mineral physics constraints for future seismic detections of the metastable olivine wedges in the deep mantle. (C) 2015 Elsevier B.V. All rights reserved.