THEORY FOR INVERSION OF INTEGRAL-EQUATIONS WITH CONSTRAINTS - MATHEMATICAL RATIONALE AND SOME APPLICATIONS TO GEODETIC DATA

A mathematical rationale for inversion of integral equations with cons traints is presented in this paper. Solutions of a general inverse pro blem in geodynamics dealing with geodetic data are investigated. The n on-uniqueness of the inverse problem and the way of reducing the non-u niqueness of inverted results are discussed. Based on this work, a non linear method is proposed for inversion of geodetic data with a priori information. Several constraints for solving the general inverse prob lem with geodetic data are given. To demonstrate applications of the p roposed method, two examples are presented. In the first example we es timate the seismic source parameters of the 1976 Tangshan earthquake i n China by the inversion of observed horizontal displacements with a p riori information of the earthquake fault. The inverted results show t hat the non-uniqueness has been improved by using the proposed method, and the estimated seismic source parameters are consistent with those from the inversion of seismic waves. In the second example we estimat e the lithosphere thickness from the inversion of observed gravity cha nge rates in Fennoscandia. We propose a method for inversion of change rates of segments between the gravity points to estimate the lithosph ere thickness. Inverted results from the change rates of segments on t he 63 degrees gravity line indicate an estimate of 62 +/- 10 km of the thickness of the Fennoscandian lithosphere, which fits well to the ob servations, as proved by a statistical test.