A SIMULATION STUDY OF SMOOTHNESS METHODS IN RECOVERY OF REGIONAL GRAVITY FIELDS

Geophysical and geodetic inverse problems are often ill posed. They ar e smoothed to guarantee stable solutions. Geophysical and geodetic app lications of smoothness techniques like Tikhonov's regularization meth od seem to have been limited to one realization of sampling. However, smoothness (or ridge) parameters are data related but empirically chos en. It is expected that the ridge parameters and thus the resolutions of models will be different from one realization of sampling to anothe r. Therefore, the chief motivation of this paper is to investigate lar ge-sample properties of some smoothness (i.e. biased) estimators in te rms of mean-square error. Some potentially applicable biased estimator s are included in this simulation. The example is the recovery of loca l gravity fields from gradiometric observables. On the basis of 500 re alizations of sampling, we extensively investigate the mean-square err or and bias problems, the best and worst performances, and the statist ical properties of ridge parameters. All of the biased estimators inde ed improve the least-squares solution, but the sizes of improvement ar e quite different. If the iterative ridge estimator is employed, the a verage value of mean-square error roots of surface gravity anomalies i s much less than 5 mgal.