We describe the direct measurement of ground displacement caused by the Hector Mine earthquake in southern California (Mw 7.1, October 16, 1999). We use a new method of instantaneous positioning, which estimates site coordinates from only a single epoch of Global Positioning System (GPS) data, to measure dynamic as well as static displacements at 24 stations of the Southern California Integrated GPS Network (SCIGN), with epicentral distances from 50 to 200 km. For sites outside the Los Angeles basin the observed displacements are well predicted by an elastic half-space model with a point shear dislocation; within the sedimentary basin we observe large displacements with amplitudes up to several centimeters that last as long as 3--4 min. Since we resolve the GPS phase ambiguities and determine site coordinates independently at each epoch, the GPS solution rate is the same as the receiver sampling rate. For the SCIGN data this is 0.033 Hz (once per 30 s), though sample rates up to 2 Hz are possible with the SCIGN receivers. Since the GPS phase data are largely uncorrelated at 1 s, a higher sampling rate would offer improved temporal resolution of ground displacement, so that in combination with inertial seismic data, instantaneous GPS positioning would in many cases significantly increase the observable frequency band for strong ground motions. ¿ 2001 American Geophysical Union