Accuracy of Geoid Heights from Modified Stokes Kernels

Abstract

The dependence of the r.m.s. geoid height error on the degree of the first term in the zonal harmonics expansion of the kernel in Stokes's integration formula is examined. It is shown that kernels with the lower degree terms removed have some advantage over the conventional kernel when a significant error in the zeroth term of the gravity anomaly expansion is present. Numerical estimates of r.m.s. geoid height error vs integration cap size are obtained for several kernels.

Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications

“…The Wong and Gore (1969) method provides almost the same geoid models as the spectral combination method does, that is because at low degrees the ratio, (9) is close to 1. The Heck and Grüninger (1987) method does not show much more improvement than the Wong and Gore (1969) method, especially in higher degrees (i.e., L=360, and L=2160; see Figure 4. The available GPS leveling benchmarks in the target area.…”

“…If we push the modification degree into the limit (L=2160), the methods of Wong andGore (1969), spectral combination, andHeck andGrüninger (1987) still work normally, and the results do not have significant changes. The spectral combination method shows a marginal accuracy improvement than the methods of Wong and Gore (1969) and Heck and Grüninger (1987).…”

Deterministic, stochastic, hybrid and band-limited modifications of Hotine’s integral

“…(3). For Stokes's kernel, this approach is generally attributed to Wong and Gore (1969), though de Witte (1967) alluded to it. Vaníček et al (1992) and Sjöberg and Nord (1992) have applied this approach to Hotine's kernel, thus Eq.…”

“…3.1) are applied routinely because of the superior data now being provided by GRACE and/or GOCE EGMs, (2) the stochastic modifiers can be applied when the 'user' is confident with estimates of the error spectra of the data or wishes consider a stochastic interpretation of the gravity field, and (3) the deterministic modifiers can be applied when there is no reliable information of the error properties of the data or the 'user' does not wish to consider a stochastic interpretation of the gravity field. Ostach (1970);Meissl (1971) Set the spherical Stokes's kernel to zero at the truncation radius by subtraction Accelerate convergence of the truncation error Jekeli (1980aJekeli ( , 1981; Petrovskaya (1988); Wichiencharoen (1984); Smeets (1994); Featherstone and Olliver (1994); Šprlák (2010) Heck and Grüninger (1987) S e tt h eWong and Gore (1969) kernel to zero at the truncation radius by choice of degree of modification, subtraction, or both Vaníček and Kleusberg (1987); Vaníček and Sjöberg (1991) Minimise the L 2 norm of the truncation error for the Wong and Gore (1969) kernel…”

The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise

“…EGM2008, see Pavlis et al 2008, or EGG97, see Denker andTorge 1998) or the prediction of gravity data. A further error reduction is possible by a modification of the Stokes integral kernel, which is motivated by the early works of Molodensky et al (1962), Wong and Gore (1969) and Meissl (1971).…”