Journal of StructuralGeology, Vol. 5, No. 6, pp. 603 to 609, 1983 0191-8141/83 $03.00 + 0.00 Printed in Great Britain © 1983 Pergamon Press Ltd. Estimation of viscosity contrast and finite strain from deformed elliptical inclusions R. J. LISLE Department of Structural Geology, Institute of Earth Sciences, Budapestlaan 4, Utrecht, The Netherlands H. E. RONDEEL, D. DOORN, J. BRUGGE and P. VAN DE GAAG Department of Structural Geology, Geological Institute, Nieuwe Prinsengracht 130, Amsterdam, The Nether- lands (Received 4 January 1983; accepted in revised form 8 July 1983) Abstract--A method of strain analysis is described which takes into account a possible competence difference between the strain markers and the rest of the rock. Using data consisting of the sectional shapes and orientations of groups of inclusions from conglomerate-like rocks, limits are placed on the possible effective viscosity contrast between the inclusions and the rock as a whole as well as on the bulk finite strain suffered by the rock. These results are calculated using a computer program, based on the theory for the deformation of elliptical cylinders. The method can be considered an extension of the Rf/d) method, but provides more information and involves less restrictive assumptions. INTRODUCTION THE SHAPES of pebbles and other sedimentary clasts have been widely used as indicators of tectonic strain. The calculation of the strain has usually been based on the assumption that the internal strain within the inclu- sion is identical to that of the host rock implying that the inclusions have been transformed in a passive fashion along with the matrix. Although geologists have long been aware of the likely existence of competence differ- ences between inclusion and matrix in such rocks, taking account of this additional variable alters the strain analysis from a problem of purely geometrical character to a physical one of considerable complexity. In pioneer- ing work towards the solution of this problem, Gay (1968a) considered both inclusion and matrix as viscous fluids of differing viscosity. For specific deformation histories Gay derived equations relating the strain of the inclusion to that of the whole rock (the bulk strain) assuming widely spaced pebbles of negligible volume compared with that of the matrix. A finite concentration of particles like that present in conglomerates, Gay suggested, would reduce the influence of the particle/ matrix viscosity ratio in the equations describing the relative deformation of the inclusion and the system. He suggested how the 'effective viscosity contrast' of such systems can be calculated from the true viscosity ratio and noted that it decreases rapidly with increase in particle concentration. For conglomerates composed of pebbles of one type, Gay (1968b) and Gay et al. (1976) described a practical method whereby the bulk strain can be estimated from pebble shapes. According to his method the viscosity ratio of matrix and pebbles required for the calculation is not determined in situ. Instead a value is taken from compiled viscosity ratios determined from previous anal_yses of deformed polymict conglomerates where pebbles, corresponding in lithology to that of the matrix and to the pebbles concerned, were present. Assigning a viscosity ratio in this way to a pair of rock-types could be a significant source of error in the analysis of bulk strain. Some recent analyses of conglomerates (e.g. Evans et al. 1980, Lisle & Savage 1983) indicate that the competence variations between different pebbles is sometimes more closely related to textural characteristics such as grain size than to compositional variables. These studies suggest that viscosity contrasts between pebbles of two lithological types could vary considerably depending on the deformation mechanisms, metamorphic conditions prevailing at the time of deformation, and so on. This paper describes how shape and orientation data from inclusions within deformed conglomerates and similar rocks can be used to estimate the viscosity ratio and the finite strain suffered by the conglomerate, obviating the need to assign a viscosity contrast on the basis of previous analyses elsewhere. We begin with a description of the proposed method developed by one of us (R.J.L.) and proceed by describing its application to field examples including conglomerates studied by the other authors in the Swedish Grythyttan area. THE THEORETICAL BASIS OF THE METHOD The method described below can be considered as an extension of the Rf/cb technique for the analysis of tectonic strain from elliptical markers. The axial ratios (R f) and orientations (~b)of deformed elliptical markers as seen on planar sections show variations which can be attributed to variations in pre-tectonic shape and orien- tation. Ramsay (1967) and Dunnet (1969) decribe how the pattern of the plotted markers on an Rf/ck diagram, assuming the absence of initial preferred orientations, 603