The geophysical gravity method is described and the corresponding inverse problem stated as an integral equation. A survey of previous work associated with gravity data inversion is given followed by an account of the inherent difficulties associated with gravity inversion; this is done by a discussion of the integral equation already given, the inversion of which constitutes an ill-posed problem. The integral equation gives rise to an ill-conditioned system of linear equations; existing

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... for the solutions of such systems are reviewed. Then follows an account of the previous use of quadratic programming techniques in the solution of illposed problems. A new approach to the inverse gravity problem is described, via formulation as a problem in quadratic programming. This quadratic programming problem is stabilised (a well-posed problem is created from the previously ill-posed problem) by the use of both linear constraints and damping. Two examples of the method, one with field data and one with synthetic data, are presented, the. solutions being effected via an existing quadratic programming algorithm. This algorithm, however, is unable to handle certain kinds of a priori information associated with the gravity problem and a new algorithm, based on the existing one, is developed to handle the additional constraints. The new algorithm is then run on the two sets of gravity data, having first been tested on a range of other