Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications
Various Stokes kernel modification methods have been developed over the years. The goal of this paper is to test the most commonly used Stokes kernel modifications numerically by using Alaska as a test area and EGM08 as a reference model. The tests show that some methods are more sensitive than others to the integration cap sizes. For instance, using the methods of Vaníček and Kleusberg or Featherstone et al. with kernel modification at degree 60, the geoid decreases by 30 cm (on average) when the cap size increases from 1° to 25°. The corresponding changes in the methods of Wong and Gore and Heck and Grüninger are only at the 1 cm level. At high modification degrees, above 360, the methods of Vaníček and Kleusberg and Featherstone et al become unstable because of numerical problems in the modification coefficients; similar conclusions have been reported by Featherstone (2003). In contrast, the methods of Wong and Gore, Heck and Grüninger and the least-squares spectral combination are stable at any modification degree, though they do not provide as good fit as the best case of the Molodenskii-type methods at the GPS/Leveling benchmarks. However, certain tests for choosing the cap size and modification degree have to be performed in advance to avoid abrupt mean geoid changes if the latter methods are applied.
A large systematic difference (ranging from −20 cm to +130 cm) was found between NAVD 88 (North AmericanVertical Datum of 1988) and the pure gravimetric geoid models. This difference not only makes it very difficult to augment the local geoid model by directly using the vast NAVD 88 network with state-of-the-art technologies recently developed in geodesy, but also limits the ability of researchers to effectively demonstrate the geoid model improvements on the NAVD 88 network. Here, both conventional regression analyses based on various predefined basis functions such as polynomials, B-splines, and Legendre functions and the Latent Variable Analysis (LVA) such as the Factor Analysis (FA) are used to analyze the systematic difference. Besides giving a mathematical model, the regression results do not reveal a great deal about the physical reasons that caused the large differences in NAVD 88, which may be of interest to various researchers. Furthermore, there is still a significant amount of no-Gaussian signals left in the residuals of the conventional regression models. On the other side, the FA method not only provides a better not of the data, but also offers possible explanations of the error sources. Without requiring extra hypothesis tests on the model coefficients, the results from FA are more efficient in terms of capturing the systematic difference. Furthermore, without using a covariance model, a novel interpolating method based on the relationship between the loading matrix and the factor scores is developed for predictive purposes. The prediction error analysis shows that about 3-7 cm precision is expected in NAVD 88 after removing the systematic difference.
Airborne gravimetry has been proved to be the primary technique to efficiently obtain middle to short wavelength signals of the Earth’s gravity field in regional geodetic applications. In particular, the LCR (LaCoste & Romberg) based scalar system (i.e., only measuring the vertical component of the gravity) is widely used or still in use for regional geoid improvements. In various aspects, many previous publications have shown positive contributions from the airborne gravity data obtained from such a system. However, the system equation used in these publications has several unnecessary or unclear approximations. By using the exact formulas and realistic data sets, the numerical analysis in this paper clearly shows that: 1) the higher order terms in the Eötvös correction neglected by Harlan (1968) are rather small (in μGal level), but are systematic mainly depending on latitude and height; 2) neglecting the roll and pitch angles can cause up to hundreds of mGal errors in the raw (unfiltered) gravity measurements if the lever-arm is not set up appropriately; 3) large (200s) smoothing windows have to be applied to reduce the lever-arm noise into sub-mGal level; 4) even under strong lever-arm setup conditions, i.e., no “horizontal offset” between the GPS antenna and the gravimeter, accurate (10 arc-minute ∼ 5 arc-minute) attitude angles from IMU (Inertial Measurement Units) are required to keep the lever-arm noise in sub-mGal level in the raw observables