GENERALIZED RIDGE-REGRESSION WITH APPLICATIONS IN DETERMINATION OF POTENTIAL FIELDS

Tikhonov's regularization techniques are widely applied to geophysical and geodetic inverse problems. A single regularization parameter is f requently adopted and needs to be properly chosen in order to obtain a stable solution. In this paper we generalize the ordinary regularizat ion method by introducing more than one regularization parameter, base d on consideration of the minimum mean square error of the estimator. It is shown that the new method results in a smaller mean square error of the estimate than the ordinary regularization method, if the regul arization parameters are properly selected. As one example of the most important applications of the proposed method, we discuss the problem of the determination of potential fields using satellite observations . As a result of the theory presented here we expect the following que stions can be answered in the positive: (1) Have the methods used conv entionally and based upon the use of empirical spectra of the potentia l coefficients, such as Kaula's rule or modified versions in determina tion of gravitational models, been adequate in stabilizing the solutio n in terms of minimum mean square error? (2) Can we solve the unstable problem of determination of potential fields from satellite-tracking data without use of empirical spectra of the potential coefficients? ( 3) Is it possible to further improve the recently produced potential m odels, if the proposed method is utilized? Numerical confirmation conc erning the size of the improvement will be left to a following contrib ution, which inevitably requires large scale simulations. The differen ces of interpreting a geophysical inverse problem between Bayesians an d frequentists are also detailed, and the practical implications are e specially stressed.