Vertical control by GPS satellite surveying: Rapid methods and high-resolution local geoid computation. Applications to high-accuracy mapping and geophysical data acquisition

In many geoscientific studies, there is a need for good position control. Thus, the rapid (15 minutes to 1 second observation time) methods of the Global Positioning System (GPS) are important because of their accuracy and efficiency. However the height, sometimes required to within few centimeters (cm), is the most difficult component to determine: ellipsoidal (GPS) heights are more error prone than the horizontal, and a geoid correction is needed to obtain elevations above mean sea level, or orthometric heights. Several GPS and gravity studies were made in different areas for different objectives but also to investigate the best procedures for determining high accuracy vertical control. These studies include a pseudo-kinematic survey of 2700 gravity stations for gravel acquifer exploration in North Dakota, a rapid static survey of 1500 gravity stations for structural studies in Ecuador, airborne kinematic for photogrammetric tests in Florida, land kinematic in Minnesota to map the Red River Valley for flood control and rapid static and kinematic on sea ice in Alaska for gravity monitoring of hydrocarbon reservoirs. The geoid correction is approached through the computation of high resolution local models from Stokes' Integral and using the Fast Fourier Transform technique as implemented by Dennis Milbert. Three geographic regions with new gravity data are considered: topographically subdued North Dakota; topographically high and rugged Nevada (800 new stations); and southeast Ecuador on the east slope of the Andes and Amazon Basin (514 new stations). The effects of topographic variation and gravity data distribution on the recovery of the undulation of the geoid are analyzed in these areas. While the gravity data distribution was adequate for the selected areas in the US, it is very sparse for Ecuador. In North Dakota, no improvement was observed over previous models. In Nevada, the 1-minute local model has captured shorter wavelengths that were missing in the pre-existing 3-minute model and a maximum improvement of about 25 cm is made. Discrepancies of up to 3 meters were found between the 5-minute local geoid and the OSU91a global model for southeast Ecuador. This shows the relevance of local models in areas where the general gravity coverage is poor and proves that the combination of GPS heights and a geoid correction can efficiently produce high accuracy orthometric heights.