Acoustic logging systems and methods are provided with multi-mode inversion for at least vertical shear slowness and shear anisotropy. At least some method embodiments acquire waveforms for multiple acoustic wave modes as a function of tool position in a borehole, derive position-dependent mode dispersion curves from the waveforms, match the derived dispersion curves with parameterized dispersion curves to determine a vertical shear slowness and a shear anisotropy as a function of position, and displaying a borehole log that represents at least one of the vertical shear slowness and the shear anisotropy as a function of position. The objective function employed for the inversion is evaluated across multiple wave propagation modes and mud slownesses and may employ an adaptive, frequency-dependent weighting based on distance between the derived dispersion curves and the parameterized dispersion curves.