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Ocean-bottom seismic acquisition is attractive in the exploration of complex deep-water environments due to its source-receiver decoupling, which makes it possible to get a wide-azimuth coverage and long source-receiver distance to significantly improve the illumination at depth. However, such acquisition systems also provide information on the elastic properties of the subsurface by recording the displacement on the seabed with 3C geophones. This information is mostly overlooked up to now, while reconstructing jointly P-wave and S-wave velocity models would significantly improve the subsurface characterization. Achieving such a high-resolution multi-parameter reconstruction requires the design of an efficient 3D fluid-solid coupled inversion engine. The purpose of this study is to present such a tool, based on an acoustic-elastic coupled wave-equation system and a spectral-element discretization in space. The method is illustrated on a bilayered 2D model and a 3D extended Marmousi model, to show how P-wave and S-wave velocity models can be inferred from the data, and the resolution improvement obtained from the reconstruction of the S-wave velocity model.