‘Strain probe’: Best-fitting a homogeneous strain to the motions of scattered points

Abstract

In laboratory experiments, or, e.g., in studies of glacier motion, one sometime wants to estimate a finite strain from images or surveys of scattered marker points taken at successive times. Similarly, crustal geodetic strain can be estimated by measuring velocities of geodetic stations. The ‘strain probe’ presented here is a simple formula that calculates a best-fit strain from the motions of n marker points distributed over an area or a volume and monitored in a Cartesian reference frame. Specifically, it is the product of two 2 × 2 (or 3 × 3 in 3-D) symmetric matrices whose components are populated from the known positions and the measured displacements of the markers.Two examples – implemented in Excel workbooks – illustrate how to combine the strain probe with the processing of the data and of its results. Speck motions in a ‘Means-Urai’ see-through experiment are an example of a finite strain calculation. Published geodetic site velocities – 120 stations in Central Anatolia – are an example of infinitesimal strain.