A Simulation Study of Smoothness Methods In Recovery of Regional Gravity Fields

Abstract

Geophysical and geodetic inverse problems are often ill posed. They are smoothed to guarantee stable solutions. Geophysical and geodetic applications of smoothness techniques like Tikhonov's regularization method seem to have been limited to one realization of sampling. However, smoothness (or ridge) parameters are data related but empirically chosen. It is expected that the ridge parameters and thus the resolutions of models will be different from one realization of sampling to another. Therefore, the chief motivation of this paper is to investigate large‐sample properties of some smoothness (i.e. biased) estimators in terms of mean‐square error. Some potentially applicable biased estimators are included in this simulation. the example is the recovery of local gravity fields from gradiometric observables. On the basis of 500 realizations of sampling, we extensively investigate the mean‐square error and bias problems, the best and worst performances, and the statistical properties of ridge parameters. All of the biased estimators indeed improve the least‐squares solution, but the sizes of improvement are quite different. If the iterative ridge estimator is employed, the average value of mean‐square error roots of surface gravity anomalies is much less than 5 mgal. Copyright © 1994, Wiley Blackwell. All rights reserved