Distributed acoustic sensing (DAS) leverages an ocean-bottom telecommunication fiber-optic cable into a densely sampled array of strain sensors. We demonstrate DAS applications to passive acoustic monitoring (PAM) through an experiment on a submarine fiber-optic cable in Longyearbyen, Svalbard, Norway. We show that DAS can measure many types of signals in the frequency range from 0.01 to 20 Hz generated by dynamics in the atmosphere, ocean, and solid earth. These include ocean-bottom loading pressure fluctuation of ocean surface waves generated by storms, winds and airflow turbulence, shear-wave resonances in low-velocity near-surface sediments, acoustic resonances in the water column, and propagating seismic waves. We show that DAS can record high-quality, low-frequency seismo-acoustic waves down to 0.01 Hz, which could be used for subsurface exploration. Using the shear-wave resonances recorded by DAS, we can determine the subsurface structure of near-surface sediments with low velocity. In addition, we can trace ocean swells back to their origins of distant storms as far as 13,000 km away from the cable. Because DAS is capable of seismo-acoustic monitoring with high spatial resolution of ~ 1 m over the cable of ~ 100 km long and with a broadband sensitivity down to 0.01 Hz on the low end, it can deliver great scientific value to ocean observation and geophysics community.