Surface-wave group-velocity tomography is an efficient way to obtain images of the group velocity over a test area. Because Rayleigh-wave group velocity depends on frequency, there are separate images for each frequency. Thus, at each point in these images the group velocities define a dispersion curve, a curve that relates group velocity to frequency. The objective of this study has been to find an accurate and efficient way to find the shear-wave structure from these dispersion curves.