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 Mw 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 Mw6.0 Parkfield, California, earthquake. The larger earthquakes prior to the 2004 Parkfield earthquake and the aftershocks of the 2004 earthquake (Mw > 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.