The Significance of Multiple Saturation Points in the Context of Polybaric Near-fractional Melting

Experimental petrologists have successfully located basalticliquid compositions parental to mid-ocean ridge basalt thatare, within experimental resolution, multiply saturated withthree-phase harzburgite or four-phase lherzolite assemblageson their liquidus at some elevated pressure. Such an experimentalresult is a necessary consequence of any paradigm in which eruptedbasalts derive from single-batch primary liquids that equilibratewith a mantle residue and undergo no subsequent magma mixingbefore differentiation and eruption. Here we investigate whether,conversely, such evidence of multiple saturation is sufficientto exclude dynamic melting models wherein increments of meltare mixed after segregation from residues, during melt transportor in magma chambers. Using two independent models of crystal–liquidequilibria to simulate polybaric near-fractional peridotitemelting, we find that aggregate liquids from such melting processescan display near-intersections of liquidus surfaces too closeto distinguish experimentally from exact multiple saturationpoints. Given uncertainties in glass compositions, fractionationcorrections, experimental temperature and pressure conditions,and achievement of equilibrium, these results suggest that polybaricmixtures can in fact masquerade as mantle-equilibrated single-batchprimary liquids. Multiple saturation points on the liquidussurfaces of primitive basalts do, however, preserve informationabout the average pressure of extraction of their constituentincrements of liquid. KEY WORDS: mantle melting; basaltic volcanism; experimental igneous petrology; thermodynamic modelling; inverse method     

Grain coarsening in contact metamorphic carbonates: effects of second-phase particles, fluid flow and thermal perturbations

Under contact metamorphic conditions, carbonate rocks in the direct vicinity of the Adamello pluton reflect a temperature‐induced grain coarsening. Despite this large‐scale trend, a considerable grain size scatter occurs on the outcrop‐scale indicating local influence of second‐order effects such as thermal perturbations, fluid flow and second‐phase particles. Second‐phase particles, whose sizes range from nano‐ to the micron‐scale, induce the most pronounced data scatter resulting in grain sizes too small by up to a factor of 10, compared with theoretical grain growth in a pure system. Such values are restricted to relatively impure samples consisting of up to 10 vol.% micron‐scale second‐phase particles, or to samples containing a large number of nano‐scale particles. The obtained data set suggests that the second phases induce a temperature‐controlled reduction on calcite grain growth. The mean calcite grain size can therefore be expressed in the form D = C₂ e^Q*/RT(d_p/f_p)^m*, where C₂ is a constant, Q* is an activation energy, T the temperature and m* the exponent of the ratio d_p/f_p, i.e. of the average size of the second phases divided by their volume fraction. However, more data are needed to obtain reliable values for C₂ and Q*. Besides variations in the average grain size, the presence of second‐phase particles generates crystal size distribution (CSD) shapes characterized by lognormal distributions, which differ from the Gaussian‐type distributions of the pure samples. In contrast, fluid‐enhanced grain growth does not change the shape of the CSDs, but due to enhanced transport properties, the average grain sizes increase by a factor of 2 and the variance of the distribution increases. Stable δ¹⁸O and δ¹³C isotope ratios in fluid‐affected zones only deviate slightly from the host rock values, suggesting low fluid/rock ratios. Grain growth modelling indicates that the fluid‐induced grain size variations can develop within several ka. As inferred from a combination of thermal and grain growth modelling, dykes with widths of up to 1 m have only a restricted influence on grain size deviations smaller than a factor of 1.1. To summarize, considerable grain size variations of up to one order of magnitude can locally result from second‐order effects. Such effects require special attention when comparing experimentally derived grain growth kinetics with field studies.     

Analysis of geomagnetic field along seismic profile P4 of the International Project POLONAISE'97

This paper presents relative secular variations of the total intensity of the geomagnetic field against a background of results of magnetic anomaly interpretation along seismic profile P4. Profile P4 crosses a Variscan folding zone in the Paleozoic Platform (PLZ), the Trans-European Suture Zone (TESZ), and the Polish part of the East European Craton (EEC). Secular geomagnetic field variations measured in 1966–2000 along a line adjacent to seismic profile P4 were analysed. The study of secular variations, reduced to the base recordings at the Belsk Magnetic Observatory, showed that the growth of geomagnetic field at the East European Craton was slower than in the Trans-European Suture Zone and the Paleozoic Platform.A 2D crustal magnetic model was interpreted as a result of magnetic modelling, in which seismic, geological and geothermal data were also used. The modelling showed that there were significant differences in the magnetic model for geotectonic units, which had been earlier determined based on deep seismic survey data. It should be noted that a fundamental change of trend of the relative secular variations was observed at the slope of the Precambrian Platform. After analysing the geomagnetic field observed along profile P4, the hypothesis that the contact between Phanerozoic and Precambrian Europe lies in Poland's territory can be proven.     

Centrifuge modelling of the influence of crustal fabrics on the development of transfer zones: insights into the mechanics of continental rifting architecture

Centrifuge analogue experiments are used to model the reactivation of pre-existing crustal fabrics during extension. The models reproduced a weakness zone in the lower crust whose geometry was varied in order to investigate its role in controlling the architecture of rift segments and related transfer zones. The typical rift system geometry was characterised by two offset rift segments connected by a major transfer zone in which boundary faults were oblique to the extension vector and displayed a significant transcurrent component of movement. The transfer zone was also characterised by cross-basin faults with both trend and strike-slip component of movement opposite to that displayed by the master faults. Typically, different structural patterns were obtained by changing the offset angle φ between the rift segments, supporting that the structural pattern at transfer zones is strongly influenced by the orientation of pre-existing discontinuities with respect to the stretching vector. In the models, the aspect ratio (ratio of length vs. width) of the transfer zone shows a positive correlation with the offset angle (i.e., the more the inherited fabric is parallel to the extension direction, the longer and narrower the transfer zones). In case of staircase offset of the rift segments (φ=90°), the structural pattern was characterised by two isolated rift depressions linked by a narrow transfer zone in which border faults with alternating polarity overlapped. Prominent rise of the ductile lower crust was also observed at the transfer zone. Many of these geometrical features display striking similarities with natural rift systems. The results of the current experiments provide useful insights into the mechanics of continental rift architecture, supporting that rift propagation, width and along-axis segmentation may be strongly controlled by the reactivation of pre-existing pervasive crustal fabrics.     

Transformation of Residuals to Avoid Artifacts in Geostatistical Modelling with a Trend

Trend modelling is an important part of natural resource characterization. A common approach to account for a variable with a trend is to decompose it into a relatively smoothly varying trend and a more variable residual component. Then, the residuals are stochastically modelled independent of the trend. This decomposition can result in values outside the plausible range of variability, such as grades below zero or ratios that exceed 1.0. We transform the residuals conditional to the trend component to explicitly remove these complex features prior to geostatistical modelling. Back transformation of the modelled residual values allows the complex relations to be reproduced. A petroleum-related application shows the robustness of the proposed transformation. Furthermore, a mining application shows that when this conditional transformation is applied to the original variable, instead of the residual, simulated values are assured to be nonnegative.     

Émergence de la complexité dans un modèle simple de comportement mécanique des roches

We propose a mechanical model for the behaviour of rocks based on progressive damage at the elementary scale and elastic interaction. It allows us to simulate several experimental observations: mechanical behaviour ranging from brittle to ductile, fractal structure of the damage, power-law distribution of the damage avalanches. These macroscopic properties are not incorporated at the elementary scale, but are the results of the interaction between elements. This emerging complexity permits us to consider the strain rock process as a complex system characterized by non-linear dynamics. To cite this article: D. Amitrano, C. R. Geoscience 336 (2004).     

Three-dimensional forward and backward modelling of diapirism: numerical approach and its applicability to the evolution of salt structures in the Pricaspian basin

Numerical studies of ductile deformations induced by salt movements have, until now, been restricted to two-dimensional (2D) modelling of diapirism. This paper suggests a numerical approach to model the evolution of three-dimensional (3D) salt structures toward increasing maturity. This approach is also used here to restore the evolution of salt structures through successive earlier stages. The numerical methodology is applied to study several model examples. We analyse a model of salt diapirs that develop from an initial random perturbation of the interface between salt and its overburden and restore the evolved salt diapirs to their initial stages. We show that the average restoration errors are less than 1%. An evolutionary model of a 2D salt wall loaded by a 2D pile of sediments predicts a decomposition of the salt wall into 3D diapiric structures when the overburden of salt is supplied by 3D synkinematic wedge of sediments. We model salt extrusion feeding a gravity current over the depositional surface and estimate an average rate of extrusion and horizontal velocity of salt spreading. Faulting of the overburden to salt overhangs initiates new secondary diapirs, and we analyse the growth of these secondary diapirs. We also study how lateral flow effects the evolution of salt diapirs. The shape of a salt diapir can be very different if the rate of horizontal flow is much greater than the initial rate of diapiric growth solely due to gravity. We discuss the applicability of the results of the models to the evolution of Late Permian salt structures in the Pricaspian basin (Russia and Kazakhstan). These structures are distinguishable into a variety of styles representing different stages of growth: salt pillows, diapirs, giant salt massifs, 2D diapiric walls and 3D stocks complicated by large overhangs. The different sizes, shapes and maturities of salt structures in different parts of the Pricaspian basin reflect areal differences in salt thickness and loading history. Our results suggest that the numerical methodology can be employed to analyse the evolution of all salt structures that have upbuilt through younger ductile overburdens.