A transmission + reflection wave-equation traveltime and waveform inversion method is presented that inverts the seismic data for the anisotropic parameters in a vertical transverse isotropic medium. The simultaneous inversion of anisotropic parameters v and ε is initially performed using transmission wave-equation traveltime inversion method. Transmission wave-equation traveltime only provides the low-intermediate wavenumbers for the shallow part of the anisotropic model; in contrast, reflection wave-equation traveltime estimates the anisotropic parameters in the deeper section of the model. By incorporating a layer-stripping method with reflection wave-equation traveltime, the ambiguity between the background-velocity model and the depths of reflectors can be greatly mitigated. In the final step, multi-scale full-waveform inversion is performed to recover the high-wavenumber component of the model. We use a synthetic model to illustrate the local minima problem of full-waveform inversion and how transmission and reflection wave-equation traveltime can mitigate this problem. We demonstrate the efficacy of our new method using field data from the Gulf of Mexico.