In this study, we demonstrate the application of 3-D isotropic elastic full waveform inversion (FWI) to a field data set from the Sleipner area in the North sea. The field data set consists of a narrow azimuth marine towed streamer survey. The limited maximum offset of less than 2000 m poses strong challenges for the FWI technique, due to the lack of wide-angle wave phenomena, particularly for the deeper sediments. In addition, the lack of information about shear waves implies that only the P-wave velocities can be estimated with some confidence. In this work, the P-wave velocities are inverted using FWI, whereas the S-wave velocities and densities are coupled to the P-wave velocities using empirical relationships. To check the validity of this work flow, a synthetic sensitivity analysis inspired by a well log from the area is performed. In this analysis the difference between acoustic and elastic FWI is also compared. The conclusion from the sensitivity analysis is that, as long as the empirical relationships are not too far away from the true relationships, the elastic FWI is able to resolve the subsurface parameters within an acceptable error margin. Furthermore, the acoustic approximation fails due to the large differences between the elastic and acoustic reflection and transmission coefficients, meaning that elastic FWI is necessary for resolving the parameters satisfactorily. Acoustic and elastic FWI are performed for the field data. The results of the field data example show that elastic FWI produces an elastic model which accurately simulates the observed data, whereas the acoustic FWI produces an acoustic model that includes artefacts, particularly in the upper part close to the sea bottom. Elastic FWI is therefore favourable for short offset seismic streamer data. The estimated elastic P-wave velocity models were used to depth migrate the data. The depth migrated images show improved resolution and continuity compared to those migrated using a model derived from conventional seismic processing methods. At the same time, the P-wave velocities show strong correlations with the corresponding migrated seismic image, which increases the confidence on the inverted model.