SUMMARY Since gravity changes propagate at the speed of light, gravity perturbations induced by earthquake deformation have the potential to enable faster alerts than the current earthquake early warning systems based on seismic waves. Additionally, for large earthquakes (Mw > 8), gravity signals may allow for a more reliable magnitude estimation than seismic-based methods. Prompt elastogravity signals induced by earthquakes of magnitude larger than 7.9 have been previously detected with seismic arrays and superconducting gravimeters. For smaller earthquakes, down to Mw ≃ 7, it has been proposed that detection should be based on measurements of the gradient of the gravitational field, in order to mitigate seismic vibration noise and to avoid the cancelling effect of the ground motions induced by gravity signals. Here we simulate the five independent components of the gravity gradient signals induced by earthquakes of different focal mechanisms. We study their spatial amplitude distribution to determine what kind of detectors is preferred (which components of the gravity gradient are more informative), how detectors should be arranged and how earthquake source parameters can be estimated. The results show that early earthquake detections, within 10 s of the rupture onset, using only the horizontal gravity strain components are achievable up to about 140 km distance from the epicentre. Depending on the earthquake focal mechanism and on the detector location, additional measurement of the vertical gravity strain components can enhance the detectable range by 10–20 km. These results are essential for the design of gravity-based earthquake early warning systems.