An empirical test of sample size and precision of Robin's method of strain analysis

Using Robin's method of strain analysis, we attempted to determine empirically how many inclusions must be measured to obtain principal strain ratios that are reproducible within ± 10%. Six large specimens of deformed leuco-granite with strained lenticular quartz aggregates were studied from a crescentic pluton in the Grenville Province of southeastern Ontario.Between 63 and 177 inclusions were measured per specimen face, and principal strain ratios calculated on that basis. Using sets of 100 measurements, ten separate strain ratios were calculated for each sample size of 10, 15, 20, … 45 inclusions drawn at random from each data set. Only about 35 inclusions need to be measured per specimen face to obtain strain ratios within ± 10%.     

Granulite-Facies Metamorphism, Granite Falls-Montevideo Area, Minnesota

In the Granite Falls-Montevideo area, Minnesota, granulite faciesmineral assemblages were collected from three major lithologicunits—hornblende-pyroxene gneiss, garnet-biotite gneiss,and granitic gneiss. Mineral assemblages most commonly observedare: plagioclase-hornblende-orthopyroxene-clinopyroxene-magnetite-ilmenite-(biotite-quartz);quartz-plagioclase-biotite-garnet-orthopyroxene-(orthoclase);quartz-plagioclase-biotite-garnet-(orthoclase); quartz-plagioclase-microcline-(garnet-hematite);and quartz-plagio-clase-microcline-biotite-(garnet-hematite-rutile).Partial analyses of isomorphous phases from the hornblende-pyroxenegneiss and the garnet-biotite gneiss were determined with anelectron microprobe. Negligible compositional variation within single grains andof a particular mineral within a given specimen, regular distributionof Fe and Mg between coexisting hornblende, ortho-pyroxene,and clinopyroxene, obedience of the mineral assemblages to theGibbs Phase Rule, and lack of empirically determined incompatiblephases indicate a close approach to chemical equilibrium duringmetamorphism. Plots of coexisting biotite, garnet, and orthopyroxeneon an appropriate phase diagram result in some crossing tielines which cannot be adequately explained by temperature orpressure differences, but suggest that H₂O and/or O₂ were notperfectly mobile components during metamorphism. This is alsoindicated by interlayering of hornblende assemblages with pyroxeneassemblages and by different iron oxide phases in essentiallythe same mineral assemblage. Textural and chemical relationships of retrograde metamorphicassemblages suggest that some retrograde reactions are a resultof cooling following the granulite-facies metamorphism, butthat others may have resulted from recrystallization duringa stage of thermal metamorphism that is reflected in the potassium-argonand rubidium-strontium biotite ages of the metamorphic rocks.     

Strain distribution within arcuate diapiric ridges of silicone putty

Twenty crescent-shaped diapiric models of silicone putty were made in two high-capacity centrifuges. The strain distribution within the models was studied by means of coloured rectangular elements, a method which led to large errors at random locations. Most elements affected by large errors could be identified in repeated experiments.The deformation pattern within the central segment of the diapiric ridges is dominated by two large regions of contrasting principal strain normal to the radial symmetry plane (axial plane of the crescents). This principal strain is tensile near the concave boundary of a ridge and compressive near the convex boundary of a ridge.Within the radial symmetry plane, the orientation pattern of long axes of the total-strain ellipses resembles an open fan which diverges toward the crest of the diapiric ridge. In the high-amplitude models, there is a narrow crestal region in which the long axes are subhorizontal. A similar region has been noted in comparable models of cylindrical diapiric ridges.In one of our models (WMS 20), the arcuate hinge line has pronounced culminations at both ends of the diapiric ridge. This results in a strong crestal depression at the radial symmetry plane where the strain analysis was performed. Accordingly, the characteristic region of tensile normal strain occupies most of the radial section.     

Distortion and dilatation in paleostrain analysis

Little is known about the magnitudes of natural volume change in ductile rocks during tectonism. In making analyses of paleostrain, geologists have found it convenient to assume that the dilatation is zero. Rather than introducing errors of unknown magnitude, this assumption restricts analysis to the state of distortion. Many parameters of finite strain are unaffected by the assumption of no volume change, although the individual principal strains can be markedly different from the corresponding values of principal distortion. Only in certain types of symmetric structures is it possible to determine the values of principal strain.