Ocean data are crucial for ocean science and climate change research. While moored buoys and Argo floats can provide data on ocean temperature and salinity from the surface to the deep ocean, their spatial and temporal distribution is sparse and discontinuous. In recent years, satellite-based ocean observations have been widely used. These observations offer high spatial resolution and temporal continuity but are often limited to surface ocean quantities. In this study, we develop a novel algorithm to infer ocean subsurface temperature and salinity using satellite observations of ocean surface properties. Different from current prevalent machine learning methods, the algorithm proposed is efficient and interpretable. The resultant dataset has a global coverage with a high spatial resolution (0.25°x0.25°) and has been validated against in-situ observations with satisfactory accuracy.