Seismic waves can be significantly amplified by soft sediment layers. Large dynamic strains can trigger a nonlinear response of shallow soils having low strength, which is characterized by a shift of the resonance frequencies, ground motion deamplification, and in some cases, soil liquefaction. We investigate the response of marine sediments during earthquake ground motions recorded along a fiber-optic cable offshore the Tohoku region, Japan, with Distributed Acoustic Sensing (DAS). We compute AutoCorrelation Functions (ACFs) of the ground motions from 103 earthquakes in different frequency bands. We detect time delays in the ACF waveforms that are converted to relative velocity changes (dv/v). dv/v drops, which are characteristic of soil nonlinearity, are observed during the strongest ground motions. Moreover, the dv/v values show a strong variability along the cable. This study demonstrates that DAS can be used to infer the dynamic properties of the shallow Earth with an unprecedented spatial resolution.