Finite-difference approximations to the wave equation in spherical coordinates are used to calculate synthetic seismograms for global Earth models. High-order finite-difference (FD) schemes were employed to obtain accurate waveforms and arrival times. Application to SH-wave propagation in the mantel shows that multiple reflections from the core-mantle boundary (CMB), with travel times of about one hour, can be modeled successfully. FD techniques, which are applicable in generally heterogeneous media, can be used to determine realistic global earth structure. ¿ American Geophysical Union 1995