A new approach to determine a multi-point deformation of the earth's surface or objects upon it, represented by point fields measured in two epochs, is presented. The problem of determining, which points have been deformed, is not approached by testing point-by-point, but by formulating alternative hypotheses that test if one, two or more subsets of points have been deformed, each subset in its own way. The method is based on the least squares connection adjustment, defines alternative hypotheses and searches the best one by testing a large amount of them. If the best hypothesis is found, a least squares estimation of the deformations is provided. The test results of the presented method are invariant under changes of the S-systems in which the point coordinates are defined. The results of a numerical test of the method applied to a simulated network are given. In designing a geodetic deformation network minimal detectable deformations can be computed, belonging to likely deformation patterns. The proposed method leads to a reconsideration of the duality of reference and object points. A comparison with the method of testing confidence ellipsoids is made. The relevance of the difference between geometric and physical interpretations of deformations and the consequences of the presented method for future developments are discussed.

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In geodetic deformation analysis observations are used to identify form and size changes of a geodetic network, representing objects on the earth’s surface. The network points are monitored, often continuously, because of suspected deformations. A deformation may affect many points during many epochs. The problem is that the best description of the deformation is, in general, unknown. To find it, different hypothesised deformation models have to be tested systematically for agreement with the observations. The tests have to be capable of stating with a certain probability the size of detectable deformations, and to be datum invariant. A statistical criterion is needed to find the best deformation model. Existing methods do not fulfil these requirements. Here we propose a method that formulates the different hypotheses as sets of constraints on the parameters of a least-squares adjustment model. The constraints can relate to subsets of epochs and to subsets of points, thus combining time series analysis and congruence model analysis. The constraints are formulated as nonstochastic observations in an adjustment model of observation equations. This gives an easy way to test the constraints and to get a quality description. The proposed method aims at providing a good discriminating method to find the best description of a deformation. The method is expected to improve the quality of geodetic deformation analysis. We demonstrate the method with an elaborate example.