abstract

Frank's method of obtaining shear strains γ1 and γ2 from a repeated observation of the angles of a triangle has been generalized to deal with any collection of angles and an arbitrary number of surveys of each angle. This modification makes it possible to increase the signal-to-noise ratio and thus detect smaller magnitude strain fields. Under the assumption that the strain rate is constant over the space time covered by the survey data, the shear strain components γ1 and γ2 are replaced by their rates γ˙1 and γ˙2, and a least-squares adjustment of the observations is used in determining most probable values of γ˙1 and γ˙2. The nonzero correlation between observations of adjacent angles that have been observed by the method of rounds is taken into consideration in making the adjustment by using the full variance-covariance matrix at each station. Statistical testing of the method indicates that it correctly estimates the dispersion of γ˙1 and γ˙2.

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