Collocation resolution of the oceanic geoid based on satellite altimetry

The approach presented is directed toward a specific adaptation of the least‐squares collocation with noise, yielding smooth predictions of geophysical quantities. The smoothing corresponds here to a truncated gravity field equivalent to an (n’, n') spherical‐harmonic expansion. This is reflected in the truncation, at the degree n‘, of the pertinent covariance and cross‐covariance functions in most (but not all) instances. The smooth predictions of geophysical quantities, made in an equilateral grid corresponding to the truncation degree n‘, serve in constructing contour maps after having been densified for the needs of a contour routine. Such a densification is carried out efficiently via errorless collocation with the degree truncation n‘ throughout. Consistent with this procedure, “residuals” at observation points (i.e., discrepancies between the contour map and the data) are computed using the same algorithm. The complete collocation approach is utilized for a 2° resolution of the earth's gravity field with emphasis on the oceanic geoid, based on the residuals from a global spherical‐harmonic adjustment of SEASAT altimetry. The presented results include contour maps of geoid undulations and gravity anomalies. They are compared to the results of a point‐mass adjustment, another technique based on the spherical‐harmonic adjustment. The agreement between these two techniques is found to be excellent.