Sensitivity computation is an integral part of many waveform inversion algorithms. An accurate and efficient technique for sensitivity computation follows from the zero-order asymptotic solution to the elastodynamic equation of motion. Given the particular form of the asymptotic solution, we show that perturbations in high-frequency waveforms are primarily sensitive to perturbations in phase. The resulting expression for waveform sensitivity is the time derivative of the synthetic seismogram multiplied by the phase sensitivity. All of the necessary elements for a step in the waveform inversion algorithm result from a single forward simulation A comparison with sensitivities calculated using a purely numerical perturbation technique demonstrates that zero-order sensitivities are accurate. Based upon the methodology, we match 330 waveforms from a crosswell experiment at a bacterial transport site near Oyster, Virginia. Each iteration of the waveform inversion takes approximately 18 minutes of CPU time on a workstation, illustrating the efficiency of the approach.