Temperature profiles from Mars Global Surveyor (MGS) radio occultation measurements reveal vertical wave structures assumed to be atmospheric gravity waves in Mars' lower atmosphere. For each vertical temperature profile derived from a radio occultation measurement, wave energy density is calculated, and results are locally averaged to derive a global distribution of gravity wave activity. Global distributions are determined for all values of solar longitude and for solar longitudes corresponding to northern summer and winter to show seasonality and for vertical wavelengths less than 10 km to remove the contribution from thermal tides, which dominate in the Martian tropics at larger vertical wavelengths. The global energy density patterns show significant wave activity over the tropics and the mountainous Tharsis region averaged over all seasons and enhanced activity in northern summer compared to winter. For the most part, the observed data does not correlate well with the orographic forcing schemes used to model gravity waves in general circulation models for Mars, suggesting that wave sources other than orography play an important role on Mars.