The principal motivation for the development of multicomponent ocean bottom seismometers (OBS's) was the hope that measurement of vector particle velocities would permit sharper interpretation of seismic data, since wave types (P and S) could be better indentified with this knowledge. The practical results of OBS use have not entirely borne out this expectation. Instead, the OBS-seafloor coupling system characteristically shows strong resonances, resulting in a ringy appearance of almost all OBS data. Previous attempts to deal with this problem have used seriously oversimplified one-dimensional analyses. In the present work we first consider an ideal model of an OBS as a Hamiltonian system with three spatial degrees of freedom. This is generalized to a linear system having a n degrees of freedom with three inputs and three outputs, and we find that the OBS site system is an all-pole minimum delay multichannel filter whose properties may be estimated from in situ seismic data. We apply the inverse of this filter to noise series obtained with a three-component OBS used in the Rivera Ocean Seismic Experiment. Resonance peaks in the noise power spectra are almost completely removed but at the cost of the gain obtained through resonant detection. The most significant implication of this work is that accurate ground motion can be recovered from almost any three-component OBS. Nevertheless, poor performance of OBS's will lead to degraded recovery of ground motion, so that design considerations which reduce the resonances in OBS-seafloor coupling remain important.