Most of the easy oil and gas have now been discovered, and as the petroleum exploration moves towards more frontier areas, it is more important than ever before to combine different methods in order to find the remaining oil and gas. Therefore, this thesis investigates the feasibility of combining controlled-source electromagnetic (CSEM) inversion and acoustic seismic full waveform inversion (FWI) in a petrophysical joint inversion workflow to estimate reservoir properties (fluid saturation and porosity) in petroleum exploration. This is thought to be a candidate to the next generation of reservoir characterization. A Bayesian rock-physics inversion scheme is used in the joint inversion. Simple petrophysical relationships as Archie equation, Han's model and Gassmann equations are used in the forward model. The developed workflow of this thesis was first tested on synthetic models and afterwards tested on well log data and maps computed from 3D models of vertical resistivity and P-wave velocity from the Johan Castberg area in the Barents Sea. The developed method shows that the water saturation and porosity could be estimated with high accuracy from synthetic models and well log data. Taking density into account as a third geophysical parameter, improved the inversion results for well log data, especially for the porosity. On the other hand, the method worked for the maps, but the quality of the results are not as good as for the well log data. Bayesian inversion using a rock-physics inversion scheme shows reliable results for the synthetic models and well log data but the quality of the forward model and the input models of vertical resistivity and P-wave velocity, need to be improved before the results for the maps are reaching the quality of interest.