The optimal flight path for airborne gravimetry

The most important cost driver for any airborne gravimetry campaing is the flight time. Therefore, it is important to investigate the possiblies of designing a flight path that will minimize the needed time while at the same time ensuring that the research objectives are met. In our case, the objective is to derive the local geoid from observed gravity values. Unfortunately, only observations along the flight path can be made, leaving areas between the flight lines uncovered. When one tries to fit a surface function (such as spherical harmonics or a set of sines and cosines) to the observations, this function tends to produce spurious oscillations in these particular areas. The advantage of fitting spherical harmonics to gravity data is that once the Stokes coefficients are known, the geoid can be computed directly. To avoid the oscillation problem, one normally uses another approach called Least-Squares Collocation (LSC) to predict the most probable gravity values in the unobserved areas. Afterwards, the gravity values are converted into geoid undulations by applying the Stokes integral. A possible problem with this approach is that the spatial covariance function used could be incorrect for the surveyed area, producing an incorrect geoid. In practise, the accuracy of the obtained geoid is estimated by comparing the result at points where GPS and levelling values are available. Another validation approach is to use different programs to compute the geoid with the same observations and see if their results correspond. For both approaches (fitting of spatial functions to observations and the LSC/Stokes method) we will present a full propagation of errors that will help to predict the accuracy of the geoid before the observations have been made. Taking the Azores as a test case, we will use the instrumental noise observed during the AGMASCO campaign and state the required spacing between the flight paths.