Tectonophysics, 42 (1977) T7-T16 o Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands zyxwvutsrqponm Letter Section T7 Determination of geologic strain using randomly oriented strain markers of any shape PIERRE-YVES F. ROBIN Department of Geology and Erindale College, University of Toronto, Missiseauga, Ont. L5L 1 C6 (Canada) (Submitted February 10,1977;revised version accepted May 29,1977) ABSTRACT Robin, P-Y.F., 1977. Determination of geologic strain using randomly oriented strain markers of any shape. Tectonophysics, 42: T7-T16. Strain markers are geologic bodies within a rock which, during the deformation of that rock, have retained their identity but did not differ from their surrounding material in their mechanical behaviour. In sections they appear as closed contours. If it can be assumed that there was no preferred orientation of the markers, the axial-strain ratio in a planar section can be determined. TXO lines are drawn through the centre of each marker, parallel respectively to the two axes of the sectional strain ellipse. If aj and ej are the segments defined by the intersection of these two lines with the contour of a marker j, then the axial-strain ratio is the logarithmic average of all ej/Cj. As shown in an example, this method can also be used if the markers are ellipsoids. A statistical test of initial isotropy is proposed for this special case. INTRODUCTION A major concern of the geologist trying to unravel geologic deformations is the discovery, assessment and use of natural strain gauges. The ideal strain gauge is of course an originally spherical body having the same competence as the host, because its fin&,.&ape is then that pf the strain ellipsoid itself. This determines the state of strain except for a possible volume change. The deformed oijids analyzed in Cloos’ (1947) classical study came very close zyxwvutsrqp to this ideal. Departures from this ideal case are of two kinds. (1) There may be a competency contrast between gauges and host rock. Other methods have been developed for this case (eg. see Ramsay, 1967, Section 5--X3) which require different assumptions. (2) There is no competency contrast but the deformed markers are not spherical. Two situations may be distin~i~~: (a) The initial shape of the markers is known, as in the case of deformed fossils; bilaterally symm&ric fossils are particularly useful in this regard.