High-resolution velocity models of the subsurface in depth domain are increasingly obtained from seismic data by Full Waveform Inversion (FWI), which has become the leading-edge technology in this domain. FWI applications, however, often fail if severely band-limited seismic data lacks low-frequency information that determines the general trend of the subsurface velocity. The inversion then produces cycle skipping by adapting incompatible phases of the synthetic and measured data. In order to avoid this FWI failure, the general velocity trend may be obtained as starting models by alternative methods from severely band-limited seismic data. The Joint Migration Inversion (JMI) provides a better reconstruction of the velocity trend in the starting model, thus driving the FWI results much closer to the actual subsurface velocity. This is demonstrated for synthetic 2D seismic data from a realistic subsurface model obtained in marine gas-hydrate studies.