| An analysis is made about the feasibility of using in-situ GRACE measurements for local gravity field determination as an alternative to global solution methods, which yield solutions in terms of spherical harmonic coefficients. The method investigated is based on integral inversion. The observables considered are potential differences (DT) and gravity disturbance differences (DGD). Both observables are affected by position, velocity and acceleration errors. With respect to position errors, the higher precision requirement is in relative position for DT, which requires about 1 cm. of absolute positional accuracy to produce 0.01 m2/s 2 error. For velocities, the higher precision requirement is in relative velocity for both DT and DGD. The observable DT requires the higher precision of 10-5 mgal in relative acceleration.;Data error requirements are very demanding for downward continuation of both DT and DGD. The solution errors obtained, from 0.01 m2/s2 measurement errors on DT, were about 3 m2/s2. It was found that model errors due to discrete and finite sampling cause large mean solution errors.;The system turns out to be ill-posed mainly due to gravity field attenuation at the operative altitude of the GRACE mission (300--500 km). Therefore regularization was required. The principal regularization methods employed were the Tikhonov, singular value decomposition, the conjugate gradient and the 1-D fast Fourier transform (FFT) method. Overall, the Tikhonov method performed better than the other methods.;In the search of the best regularization parameter (alpha), the L-curve method was analyzed and yielded good results when considering only random errors in the measurements. However, when considering model errors, the method did not produce satisfactory results. A geometry adaptive method was formulated to find a near optimum alpha.;Finally, the Tikhonov regularization combined with B-spline smoothing was applied. The method yielded smaller solution errors. The solution errors obtained were about 1.2 and 1.1 m2/s2 for 1°.2 resolution using DT and DGD, respectively. The corresponding relative error was about 10%. This could potentially produce about 10 cm geoid for about 150 km resolution. All simulations were made using the geopotential model EGM96. |
