Strain determination from the measurement of pebble shapes

Cross-sections of pebbles or other near-ellipsoidal bodies in rocks can be measured in three planes, conveniently chosen orthogonal to each other, but otherwise oriented arbitrarily. The three sets of measurements, referred to a single Cartesian coordinate system, can in principle be used to calculate the average pebble shape. Some of these measurements, however, are necessarily redundant and, generally, not compatible without adjustments for the distribution of an error. The calculation of the average ellipsoid is developed, as is that of the strain which transforms an original sphere into such an ellipsoid. This calculation involves the distribution by a weighted least-squares method of the error due to redundancy and leads to the assignment of an estimated error to each of the second-rank tensor components of the strain. The assumption is made that, after being referred to the common coordinate system, the measured values for each tensor component have a normal distribution. This assumption may not always be correct but could be tested before this method is used.     

Internal morphology, habit and U-Th-Pb microanalysis of amphibolite-to-granulite facies zircons: geochronology of the Ivrea Zone (Southern Alps)

Several types of growth morphologies and alteration mechanisms of zircon crystals in the high-grade metamorphic Ivrea Zone (IZ) are distinguished and attributed to magmatic, metamorphic and fluid-related events. Anatexis of pelitic metasediments in the IZ produced prograde zircon overgrowths on detrital cores in the restites and new crystallization of magmatic zircons in the associated leucosomes. The primary morphology and Th-U chemistry of the zircon overgrowth in the restites show a systematic variation apparently corresponding to the metamorphic grade: prismatic (prism-blocked) low-Th/U types in the upper amphibolite facies, stubby (fir-tree zoned) medium-Th/U types in the transitional facies and isometric (roundly zoned) high-Th/U types in the granulite facies. The primary crystallization ages of prograde zircons in the restites and magmatic zircons in the leucosomes cannot be resolved from each other, indicating that anatexis in large parts of the IZ was a single and short lived event at 299 ± 5 Ma (95% c. l.). Identical U/Pb ages of magmatic zircons from a metagabbro (293 ± 6 Ma) and a metaperidotite (300 ± 6 Ma) from the Mafic Formation confirm the genetic context of magmatic underplating and granulite facies anatexis in the IZ. The U-Pb age of 299 ± 5 Ma from prograde zircon overgrowths in the metasediments also shows that high-grade metamorphic (anatectic) conditions in the IZ did not start earlier than 20 Ma after the Variscan amphibolite facies metamorphism in the adjacent Strona–Ceneri Zone (SCZ). This makes it clear that the SCZ cannot represent the middle to upper crustal continuation of the IZ. Most parts of zircon crystals that have grown during the granulite facies metamorphism became affected by alteration and Pb-loss. Two types of alteration and Pb-loss mechanisms can be distinguished by cathodoluminescence imaging: zoning-controlled alteration (ZCA) and surface-controlled alteration (SCA). The ZCA is attributed to thermal and/or decompression pulses during extensional unroofing in the Permian, at or earlier than 249 ± 7 Ma. The SCA is attributed to the ingression of fluids at 210 ± 12 Ma, related to hydrothermal activity during the breakup of the Pangaea supercontinent in the Upper Triassic/Lower Jurassic. Received: 7 July 1998 / Accepted: 4 November 1998     

Construction of three-phase data to model multiphase flow in porous media: Comparing an optimization approach to the finite element approach

Multiphase flow modelling is a major issue in the assessment of groundwater pollution. Three-phase flows are commonly governed by mathematical models that associate a pressure equation with two saturation equations. These equations involve a number of secondary variables that reflect the fluid behaviour in a porous medium. To improve the computational efficiency of multiphase flow simulators, several simplified reformulations of three-phase flow equations have been proposed. However, they require the construction of new secondary variables adapted to the reformulated flow equations. In this article, two different approaches are compared to quantify these variables. A numerical example is given for a typical fine sand.     

Synthesis and thermal stability of 2 \frac{1}{2}-octahedral sodium mica,NaMg2.5 (OH)2∫i4O10]

A new 2 \(\frac{1}{2}\) -octahedral sheet silicate, NaMg_2.5 Si₄O₁₀ (OH)₂, has been synthesized from oxide mixtures in the temperature range 500–600°C at pressures between 1 and 5 kb. The lattice parameters are a ₀ = 5.298 Å, b ₀ = 9.047 Å, c ₀ = 9.479 Å and ß=99.55°. X-ray data are given in the text. At temperatures above 605° C/1 kb and 630° C/5 kb, it decomposes to magnesiorichterite plus quartz.