GEODETIC data, obtained by ground- or space-based techniques, can be used to infer the distribution of slip on a fault that has ruptured in an earthquake. Although most geodetic techniques require a surveyed network to be in place before the earthquake^1–3, satellite images, when collected at regular intervals, can capture co-seismic displacements without advance knowledge of the earthquake's location. Synthetic aperture radar (SAR) interferometry, first introduced⁴ in 1974 for topographic mapping^5–8 can also be used to detect changes in the ground surface, by removing the signal from the topography^9,10. Here we use SAR interferometry to capture the movements produced by the 1992 earthquake in Landers, California¹¹. We construct an interferogram by combining topographic information with SAR images obtained by the ERS-1 satellite before and after the earthquake. The observed changes in range from the ground surface to the satellite agree well with the slip measured in the field, with the displacements measured by surveying, and with the results of an elastic dislocation model. As a geodetic tool, the SAR interferogram provides a denser spatial sampling (100 m per pixel) than surveying methods^1–3 and a better precision (∼3 cm) than previous space imaging techniques^12,13.