Synthesis of point data and path data in estimating Sofar speed

Although an extensive body of data on the speed of sound in the ocean is available from hydrographic casts, considerably more precise measurements can be made of explosion travel times over long paths through the deep-ocean sound (Sofar) channel. A method is presented for analytically combining the two types of data to produce a functional description of the spatial variation of Sofar speed. This method is based on the fact that the integral, over a path, of a series representation of the reciprocal of speed yields a series representation of the travel time over that path, with the same set of coefficients entering linearly into both series. Both types of observations may then be combined in the same matrix equation for estimating the coefficients. An example is computed for the Pacific Ocean in the form of a spherical harmonic function of degree six. Hydrographic data consisted of values averaged for 4013 one-degree squares. Approximately 400 temporally independent travel-time measurements, over paths ranging in length from 17° to 110°, were used. The paths were concentrated in the northeast Pacific. The estimated variance of a single point observation of Sofar speed was 1.56 (m/sec)2, whereas the variance of a single observation of harmonic-mean Sofar speed was 0.016 (m/sec)2. These values were used, where appropriate, for weighting the data during least-squares estimation of the coefficients of the spherical harmonic function.