Our limited knowledge of the relationship between changes in the state of an aquifer or reservoir and the corresponding changes in the elastic moduli, that is the rock physics model, hampers the effective use of time-lapse seismic observations for estimating flow properties within the Earth. A central problem is the complicated dependence of the magnitude of time-lapse changes on the saturation, pressure, and temperature changes within an aquifer or reservoir. We describe an inversion methodology for reservoir characterization that uses onset times, the calendar time of the change in seismic attributes, rather than the magnitude of the changes. We find that onset times are much less sensitive than magnitudes to the rock physics model used to relate time-lapse observations to changes in saturation, temperature and fluid pressure. We apply the inversion scheme to observations from daily monitoring of enhanced oil recovery at the Peace River field in Canada. An array of 1492 buried hydrophones record seismic signals from 49 buried sources. Time-shifts for elastic waves traversing the reservoir are extracted from the daily time-lapse cubes. In our analysis 175 images of time-shifts are transformed into a single map of onset times, leading to a substantial reduction in the volume of data. These observations are used in conjunction with bottom hole pressure data to infer the initial conditions prior to the injection, and to update the reservoir permeability model. The combination of a global and local inversion scheme produces a collection of reservoir models that are best described by three clusters. The updated model leads to a nearly 70 percent reduction in seismic data misfit. The final set of solutions successfully predict the observed normalized pressure history during the soak and flow-back into the wells between 82 and 175 days into the cyclic steaming operation.