Aftershocks of three large earthquakes near Tennant Creek in the Northern Territory of Australia provide a unique opportunity to study regional seismic phases in the North Australian Craton. Three portable digital seismographs were operated near the source zone to provide control on earthquake locations, and seven recorders formed a line between Tennant Creek and the seismic array at Alice Springs, which is 430 km to the south. Eleven earthquakes of sufficient size for analysis were recorded during a one week deployment two months following the main shocks. The group velocity observed for Lg waves along this profile of 3.7 km / sec is at the high end of the normal range and appropriate for a stable continental interior. We estimate attenuation in discrete frequency bands by measuring the decay of amplitude as a function of distance from the source and assuming the common r−5/6 relationship for geometrical spreading. However, this assumption leads to frequency dependent Q values: Q = (230 ± 36) f(0.66 ± 0.12) that are abnormally low for a stable continental region. The apparent Q is also not consistent with other observations, such as the high Lg group velocity, the positive bias in ML estimates obtained for other parts of Australia using standard attenuation relations, the size of felt areas for large central Australian earthquakes, nor with the high frequency content of seismic reflection data collected near our profile. Some crustal models for northern Australia derived from seismic refraction work show a gradient zone between 30 and 55 km rather than a sharp Moho discontinuity. We therefore investigate the effect of gradient zones at the crust-mantle transition on the decay of Lg amplitudes using synthetic seismograms calculated with the wavenumber integral method. The modeling suggests that some of the S-wave energy that would be trapped in a crustal wave guide with a sharp lower boundary can leak out in the presence of a gradient and so enhance the attenuation. In addition, there are focusing effects due to the formation of caustics from the gradient zones which cannot be represented by a single analytic amplitude correction.