Most seismic studies of changes in traveltimes are of a qualitative nature and a major challenge in four dimensions is to use the information contained in time shifts to quantify the nature of velocity changes in the subsurface layers. We propose a 4D tomographic inversion method that uses time shifts from prestack seismic data to estimate parameters describing the 2D velocity field after changes have occurred. Prestack data allow for the usage of many offsets, thus increasing the information input for the inversion. The velocity changes are parameterized by a chosen number of Gaussian functions in two dimensions and weighted least-squares inversion is used to estimate the parameters describing these functions. We have found that the parameters describing the position and shape of the Gaussian velocity anomalies can be estimated with this method for simple synthetic cases. For more complex cases with overlapping Gaussian functions, resolution of the parameters can be difficult and in these cases our recommendation is to find the best fit for a simple smooth anomaly to a more complex real world. The method is tested on a real data set from a injection project above the Sleipner field in the North Sea, where quantification of changes is important for monitoring purposes. We have found that the noise levels in prestack traveltime data are on the high side for large-scale analysis; however, we estimate reasonable layer thickness and velocity compared to previous work in a nearby area.