Full-waveform inversion requires the accurate simulation of the dynamics and kinematics of wave propagation. This is difficult in practice because the amplitudes cannot be precisely reproduced for seismic waves in the earth. Wave-equation reflection traveltime tomography (WT) is proposed to avoid this problem by directly inverting the reflection-traveltime residuals without the use of the high-frequency approximation. We inverted synthetic traces and recorded seismic data for the velocity model by WT. Our results demonstrated that the wave-equation solution overcame the high-frequency approximation of ray-based tomography, was largely insensitive to the accurate modeling of amplitudes, and mitigated problems with ambiguous event identification. The synthetic examples illustrated the effectiveness of the WT method in providing a highly resolved estimate of the velocity model. A real data example from the Gulf of Mexico demonstrated these benefits of WT, but also found the limitations in traveltime residual estimation for complex models.