We report observations of Rayleigh waves that orbit around Mars up to three times following the S1222a marsquake. Averaging these signals, we find the largest amplitude signals at 30 s and 85 s central period, propagating with distinctly different group velocities of 2.9 km/s and 3.8 km/s, respectively. The group velocities constraining the average crustal thickness beneath the great circle path rule out the majority of previous crustal models of Mars that have a >200 kg/m3 density contrast across the dichotomy. We find that the thickness of the martian crust is 42-56 km on average, and thus thicker than the crusts of the Earth and Moon. Together with thermal evolution models, a thick martian crust suggests that the crust must contain 50-70% of the total heat production to explain present-day local melt zones in the interior of Mars.