Abstract: A high-order, polynomial regression curve is fitted to a global set of first-arrival pick times as a function of the nominal ranges between a plurality of acoustic sources having known geodetic coordinates and a plurality of acoustic detectors whose coordinates are imperfectly known. The polynomial is applied to the pick times to provide pick time distances with the vertical velocity gradient removed. The known source coordinates, the nominal detector coordinates and the pick time distances are combined to provide a quadratic surface to provide a common data block containing the coefficients for modeling the lateral velocity gradient. Using the so-determined coefficients, the imperfectly-known detector positions are iteratively updated using the Helmert blocking technique.

Abstract: A high-order polynomial regression curve is fitted to a global set of first arrival times as a function of the nominal ranges between a plurality of acoustic sources having known geodetic coordinates and a plurality of acoustic detectors whose coordinates are imperfectly known. The order of the polynomial is chosen to be that order that minimizes the variance of the parameters about the regression curve. The polynomial is used as a quasi-velocity function for iteratively optimizing the best estimate of the ranges between each detector and every source station. The best estimate of the detector position is derived by multi-lateration using the computed ranges.