Abstract
Three types of inverse problem are proposed and defined in solid mechanics, and their solutions and properties are investigated. The solutions of the inverse problems are transformed into those of an optimization problem, and the solutions are obtained by a non-linear programming method. Based on this work, the parameter optimization method for inversion of a structural stress field is presented, and a method for evaluating solutions of the non-linear inverse problem is discussed. The feasibility of these methods is demonstrated by numerical tests. Finally, by using the proposed method and geodetic data, the non-uniform rupture pattern of the Tangshan earthquake fault is analysed. It is shown that the parameter optimization method for inversion of the tectonophysical model will improve the present methods used in the studies of structural stress fields.
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