Many rocks in earth formations exhibit vertical transverse isotropy (VTI) (i.e., anisotropy with a vertical axis of symmetry). In such a case, a shear wave polarized in the horizontal plane has a different speed than a shear wave polarized in the vertical plane. For example, shale formations often exhibit VTI anisotropy on the order of 20 to 30%. VTI information plays an important role in seismic imaging of reservoirs; thus, it is desirable to obtain VTI information as a function of depth from acoustic logging tools. Typical acoustic logging tools generate acoustic modes (Stoneley, flexural, etc.) in the earth formation. The Stoneley mode is sensitive to the horizontal shear speed (or equivalently horizontal shear bulk modulus, c66). Conversely, the flexural mode is more sensitive to the vertical shear speed (or equivalently vertical shear bulk modulus, c44) (Tang and Cheng 2004). Therefore, these modes, and potentially others, can be used to invert for VTI anisotropy. However, the Stoneley mode dispersion curve is sensitive to mud speed, particularly in fast formations (Tang and Cheng 2004). Consequently, an accurate estimate of mud speed is important to any inversion scheme for estimating c66. The dispersion curves are also affected by noise. The flexural mode loses power near the cutoff frequency where it converges to the vertical shear speed. As a result, noise can increase the difficulty of estimating c44. This paper describes an algorithm that inverts for the Thomsen parameter, or normalized difference of the shear bulk moduli of the earth formation at a given depth. This is accomplished by jointly minimizing the weighted L2 norm of the difference between the frequency semblance dispersion curves of multiple modes derived from the data and theoretical dispersion curves parameterized by the formation and borehole properties. The depth-to-depth inversion uses an adaptive weighting scheme as a function of frequency to reduce the effect of noise, and a global optimization over multiple depths is used to improve the estimate of mud speed. The paper uses synthetic and field data to demonstrate the advantages of this new algorithm.