The tomographic inversion of group velocities of Rg waves is a viable technique for mapping lateral variations in the lithology of sedimentary basins. In order to determine a velocity structure, we first use the moving-window maximum entropy spectral analysis to measure the average Rg wave group travel times. Second, the group velocities within blocks (subregions) covering the area sampled by the Rg wave propagation paths are determined by tomographic inversion. Third, the vertical shear wave velocity profile within each block is determined from the inversion of group velocities for that block. Finally, a structural cross section is obtained by connecting blocks located along a profile. Rg waves recorded from mining explosions in Alabama were used in a test of the technique by modeling the Paleozoic sedimentary rocks in the Black Warrior Basin of northern Alabama. The high resolution of moving-window maximum entropy spectral analysis allows estimation of the Rg wave group velocities with a precision of better than 3%. The usable frequency range of 0.5 to 1.5 Hz allows determination of structures to depths of about 2.4 km with layers of 0.2 km thickness. Blocks of widths of 20 km or less could be resolved with appropriate data. Shear wave velocities in the Black Warrior Basin range from 1.6 to 4.0 km/s. The layering in the velocity structure corresponds to major geologic units. Within units, an increase in velocity to the northeast corresponds to observed facies changes. ¿ American Geophysical Union 1993