The seismometer deployed by the InSight lander measured the seismic velocity of the Martian crust. We use a rock physics model to interpret those velocities and constrain hydrogeological properties. The seismic velocity of the upper ~10 km is too low to be ice-saturated. Hence there is no cryosphere that confines deeper aquifers. An increase in seismic velocity at depths of ~10 km could be explained by a few volume percent of mineral cement (1-5%) in the pores and may document the past or present depth of aquifers. Plain Language Summary Large amounts of water may be stored in the Martian crust and episodically released to flood the surface. Where this water exists, and even why, is uncertain. The seismometer on the InSight lander measured the speed of seismic waves in the Martian crust. The presence of ice and water affects seismic velocity. We argue that the measurements preclude a layer of ice-filled crust that confines liquid water in an aquifer. Key points • We interpret the seismic wave velocity of the Martian crust measured by InSight. • We quantity the effects of ice and water on seismic velocity using a rock physics model. • Measurements preclude a layer of ice-filled upper crust that confines liquid water in an aquifer. 1. Introduction Large volumes of water are hypothesized to have carved and passed through the Martian outflow channels (e.g., Baker, 2001). Because these channels originate from discrete sources, a groundwater origin is typically invoked (e.g., Head et al., 2003). Given the large discharges needed to create the observed landforms, in some cases a couple orders of magnitude greater than the largest catastrophic floods on Earth (Baker, 1982), large and permeable aquifers would be needed (e.g., Carr, 1979; Manga 2004). While most of the outflow channels are Hesperian (e.g., Tanaka, 1997), their formation continued through the Amazonian (e.g., Rodriguez et al., 2015). Some of the youngest channels originated from fissures in Eastern Elysium Planitia within the past 10s of millions of years (Burr et al., 2002; Voight and Hamilton, 2017). The subsurface of Mars thus appears to have hosted and episodically released large volumes of water over most of Martian history. Hence, detecting the presence and quantifying the volume of subsurface water and ice would help constrain the water budget and cycle from the Noachian to present (Clifford and Parker, 2001). To discharge water at the surface, aquifers must have sufficient pressure for water to reach the surface. One way to achieve hydraulic heads greater than hydrostatic and hence enable surface discharge is to confine aquifers beneath an overlying ice-saturated crust or cryosphere (e.g.