Fluid injection can cause extensive earthquake activity, sometimes at unexpectedly large distances. Appropriately mitigating associated seismic hazards requires a better understanding of the zone of influence of injection. We analyze spatial seismicity decay in a global dataset of 18 induced cases with clear association between isolated wells and earthquakes. We distinguish two populations. The first is characterized by near-well seismicity density plateaus and abrupt decay, dominated by square-root space-time migration and pressure diffusion. Injection at these sites occurs within the crystalline basement. The second population exhibits larger spatial footprints and magnitudes, as well as a power law-like, steady spatial decay over more than 10 kilometers, potentially caused by poroelastic effects. Far-reaching spatial effects during injection may increase event magnitudes and seismic hazard beyond expectations based on purely pressure-driven seismicity.