We have developed an adaptive mesh seismic tomography method based on tetrahedral and Voronoi diagrams to automatically match the inversion mesh to the data distribution. Two different irregular mesh interpolation methods, linear and natural neighbor, are evaluated. A synthetic test shows that the adaptive mesh seismic tomography method recovers the true synthetic model well in both the linear and natural neighbor interpolation cases. Use of more accurate differential data is helpful in removing artifacts in the model that result from the noisier absolute data. Application of the adaptive mesh scheme to Parkfield, California, results in much more uniform sampling of the model (as measured by the derivative weight sum) on the optimized irregular inversion mesh compared to a regular grid. The across-strike cross sections resulting from using either just the absolute data or both the absolute and differential data show a clear velocity contrast at the San Andreas fault in the linear and natural neighbor interpolation cases. The velocity model obtained using natural neighbor interpolation is smoother than that from linear interpolation. Including the differential data in the inversion yields more clustered event locations and removes a velocity reversal to the southwest of the fault, which is likely caused by noise in the absolute data.