INVERSION OF GEODETIC DATA

PART I. MATHEMATICAL FORMULATION

Abstract

A reasonable and practical method of finding an optimal fault-plane solution and evaluating the degree of its non-uniqueness from a set of inaccurate geodetic data is developed by using the inversion technique.
The static deformation fields are modelled by a multiple-fault system in an elastic half-space, which consists of several dimensional faults with various variables, such as the magnitude and direction of a slip, the length, width, depth and location of a fault, the dip-angle and strike direction. Analytical expressions for the elements of the coefficient matrix which relates a set of model parameters to a set of data parameters are given in section 3 for a case of surface displacement.
In section 2, Jackson's formula on the discrete general linear inversion is followed and extended to a non-linear case in a systematic fashion by introducing a criterion for the convergence of the solution. As a measure of the reliability of the resulting solution, the "effective data number" is also introduced, which is defined as the number of effective data contributing to the determination of a model parameter.