Ambiguities in Direct Arrival Time Inversion for Ocean Bottom Nodes

We formulate an inverse problem to refine ocean bottom node locations, node clock drift, water velocity, and source positions. All quantities are sought simultaneously. For water velocity we seek a time dependent perturbation from a fixed background profile. Drift of a node’s clock is taken to be the sum of linear and quadratic terms. While source depths are assumed known, node depths on the seabed are not. Our objective is to investigate ambiguities in the solution to the problem when the only data available are arrival times of direct waves. For this purpose we generate data for a small synthetic node survey and solve using the singular value decomposition. We find, not surprisingly, that translation and rotation of all positions have no effect on the data. An additional, unanticipated, ambiguity is expansion or contraction of the survey geometry accompanied by increase or decrease in water velocity. We find also that determination of the individual drift terms is sensitive to noise, though total drift is more accurately obtained.