Summary We explore a recently developed procedure for kinematic inversion based on an elliptical subfault approximation. In this method, the slip is modelled by a small set of elliptical patches, each ellipse having a Gaussian distribution of slip. We invert near-field strong ground motion for the 2004 September 28 M w 6.0 Parkfield, California, earthquake. The data set consists of 10 digital three-component 18-s long displacement seismograms. The best model gives a moment of 1.21 × 1018 N m, with slip on two distinct ellipses, one with a high-slip amplitude of 0.91 m located 20 km northwest of the hypocentre. The average rupture speed of the rupture process is ∼2.7 km s−1. We find no slip in the top 5 km. At this depth, a lineation of small aftershocks marks the transition from creeping above to locked below, in the interseismic period. The high-slip patch coincides spatially with the hypocentre of the 1966 M w6.0 Parkfield, California, earthquake. The larger earthquakes prior to the 2004 Parkfield earthquake and the aftershocks of the 2004 earthquake (M w > 3) also lie around this high-slip patch, where our model images a sharp slip gradient. This observation suggests the presence of a permanent asperity that breaks during large earthquakes, and has important implications for the slip deficit observed on the Parkfield segment, which is necessary for reliable seismic hazard assessment.