Apparatus and methods for acquiring seismic data using a seabed seismic data cable positioned on a seabed are described, including correcting for the effect of one or more sensor non-linear motions, which improves accuracy of seismic data. One or multiple non-linear movements of the sensor may be corrected for. It is emphasized that this abstract is provided to comply with the rules requiring an abstract, which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. 37 CFR 1.72(b).