Inclusion of amplitude data in reflection seismic tomography may help to resolve the ambiguity caused in the traveltime inversion by the trade-off between reflector position and velocity anomaly. To illustrate the uses of amplitude data we initially exclude all traveltime information from the inversion. In a previous paper (Wang & Houseman 1994) we have shown, using geologically relevant synthetic models, that the information contained in amplitude versus offset data suffices to accurately constrain the geometry of an arbitrary smooth 2-D reflector separating constant velocity layers, In this paper we investigate the implementation of the inversion for 2-D velocity variations using reflection seismic amplitude data.A stable method of ray tracing in a 3-D heterogeneous velocity medium is presented. The ray-geometric spreading which partly determines the ray amplitude is then calculated according to the propagator along the ray path. The ray-perturbation theory is used to trace the perturbed ray due to the model perturbation. We compare amplitude perturbations arising from slowness perturbations along the whole ray path with those arising from the slowness perturbation close to the interface, and see that in an inversion of reflection seismic amplitude data, the data residuals will have most effect on velocity anomalies near the interface. Synthetic models are used to demonstrate the efficacy of amplitude inversion for velocity variation, using the subspace inversion method, with a 2-D Fourier series parametrization of the slowness distribution. The efficiency of the inversion lies in a judicious partitioning of model parameters into subspaces. A stable strategy for the parameter partitioning is to separate parameters on the basis of the magnitude of rms values of the Frechet derivatives of ray amplitudes with respect to the model parameters, Numerical examples show that the amplitudes of reflected signals are sensitive to the location of the velocity anomalies. Inversions provide an approximate image of velocity variation, demonstrating that amplitude data contain information that can constrain unknown velocity variation.