We have developed a comprehensive inversion scheme to analyze traveltime data collected through GPS-acoustic observations on a campaign basis. Our method uses a quantity called the “nadir total delay” (NTD), which is analogous to the zenith total delay in Global Navigation Satellite Systems analyses, to represent the time variation of the sound speed. The observation equation using the NTD is an approximated formulation. We examine its applicable scope using numerical experiments and demonstrate that the approximation holds well enough in practice. Traveltime data from all our observation campaigns were utilized together for inversion calculation to determine the following: (1) the positions of individual precision acoustic transponders at the time of a particular reference campaign, (2) the displacement from these positions of a rigid array at the time of each campaign, and (3) the time variation of the NTD during each campaign. We applied this method to actual data to fix the array geometry more precisely. Also, we have made a first step in detecting vertical motions as well as horizontal motions, though further enhancement of the accuracy will be required. In performing linear regression of array displacements obtained from the inversion, their error covariance has a significant effect on the resulting velocities. When the covariance is taken into account, nearly the same velocities are obtained no matter what campaign is taken as reference in the inversion.
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