We use the direct solution method (DSM) with optimally accurate numerical operators to calculate complete (including both body and surface waves) three-component synthetic seismograms for transversely isotropic (TI), spherically symmetric media, up to 2 Hz. We present examples of calculations for both deep (600 km) and shallow (5 km) sources. Such synthetics should be useful in forward and inverse studies of earth structure. In order to make these calculations accurately and efficiently the vertical grid spacing, maximum angular order, and cut-off depth must be carefully and systematically chosen.