Stresses and velocities in orogenic wedges with power-law rheology and linearly varying longitudinal strain rate

A two-dimensional analytical solution for stress, strain rate, and velocity is obtained for parallel-sided and wedge-shaped blocks with generalized viscous rheology (linearly viscous and power-law) deforming in plane strain. The main assumptions used in the derivation of the solution are that the material is incompressible, the longitudinal gradient in shear stress is much less than the vertical gradient of vertical normal stress, and the longitudinal strain rate varies linearly in the horizontal direction. Velocity boundary conditions are specified at the top of the block, and shear stress boundary conditions at the base of the block. In the one-dimensional case (where stress and strain rate do not vary in the longitudinal direction), the solution reduces to a well-known solution for the deformation of parallel-sided ice sheets [Nye, J. F. (1957) The distribution of stress and velocity in glaciers and ice sheets. Proceedings of the Royal Society of London A-239, 113–133]. The stress equilibrium for tapered wedges [Platt, J. P. (1986) Dynamics of orogenic wedges and the uplift of high-pressure metamorphic rocks. Geological Society of America Bulletin 97, 1037–1053] is a special case of the present stress solution. Implementation of the solution requires the subdivision of the wedge into vertical segments, and yields the tectonic normal and shear stresses that must be applied to the rear of a block with specified rheology in order to maintain a given longitudinal strain rate. The solution makes it possible to model deformation patterns analytically with longitudinally varying strain rate (including coeval compression and extension) and with vertical components of velocity reflecting the effects of underplating.     

Transfer functions under no-analog conditions: Experiments with Indian Ocean planktonic Foraminifera

This paper documents and investigates an important source of inaccuracy when paleoecological equations calibrated on modern biological data are applied downcore: fossil assemblages for which there are no modern analogs. Algebraic experiments with five calibration techniques are used to evaluate the sensitivity of the methods with respect to no-analog conditions. The five techniques are: species regression; principal-components regression [e.g., Imbrie, J., and Kipp, N. G. (1971). In “The Late Cenozoic Ages,” 71–181]; distance-index regression [Hecht, A. D. (1973). Micropaleontology19, 68–77]; diversity-index regression (Williams, D. F., and Johnson, W. C. (1975). Quaternary Research5, 237–250]; weighted-average method [Jones, J. I. (1964). Unpublished Ph. D. Thesis, Univ. of Wisconsin]. The experiments indicate that the four regression techniques extrapolate under no-analog conditions, yielding erroneous estimates. The weighted-average technique, however, does not extrapolate under no-analog conditions and consequently is more accurate than the other techniques. Methods for recognizing no-analog conditions downcore are discussed, and ways to minimize inaccuracy are suggested. Using several equations based on different calibration techniques is recommended. Divergent estimates suggest that no-analog conditions occur and that estimates are unreliable. The value determined by the weighted-average technique, however, may well be the most accurate.     

Isostasie flexurale et érosion différentielle : modélisation numérique appliquée au seuil du PoitouFlexural isostasy and differential erosion: numerical modelling applied at the ‘Seuil du Poitou’

One uses the principle of flexural isostasy to represent the uplift of the ‘Seuil du Poitou’ in response to erosion. The model indicates that a different uplift of on the last five millions years resulted from an erosion paradoxically stronger in the crystalline basement than in the limestones bedrock. To cite this article: J.-C. Maurin, K. Renaud, C. R. Geoscience 334 (2002) 1149–1155.     

Compressional- and transpressional-stress pattern for Pliocene and Quaternary brittle deformation in fore arc and intra-arc zones (Andes of Central and Southern Chile)

Kinematic analysis of fault slip data for stress determination was carried out on Late Miocene to Quaternary rocks from the fore arc and intra-arc regions of the Chilean Andes, between 33° and 46° south latitudes. Studies of Neogene and Quaternary infilling (the Central Depression), as well as plutonic rocks of the North Patagonian Batholith along the Liquiñe–Ofqui Fault Zone, have revealed various compressional and/or transpressional states of stress. In the Pliocene, the maximum compressional stress (σ₁) was generally oriented east–west. During the Quaternary, the deformation was partitioned into two coeval distinctive states of stress. In the fore arc zone, the state of stress was compressional, with σ₁ oriented in a N–S to NNE–SSW direction. In the intra-arc zone the state of stress was transpressional with σ₁ striking NE–SW. Along the coast, in one site (37°30′S) the Quaternary strain deformation is extensional, with an E–W direction, which can be explained by a co-seismic crustal bending readjustment.     

The Variance-Based Cross-Variogram: You Can Add Apples and Oranges

The variance-based cross-variogram between two spatial processes, Z₁ (·) and Z₂ (·), is var (Z₁ ( u ) – Z₂ ( v )), expressed generally as a bivariate function of spatial locations uandv. It characterizes the cross-spatial dependence between Z₁ (·) and Z₂ (·) and can be used to obtain optimal multivariable predictors (cokriging). It has also been called the pseudo cross-variogram; here we compare its properties to that of the traditional (covariance-based) cross-variogram, cov (Z₁ ( u ) – Z₁ ( v ), Z₂ ( u ) – Z₂ ( v )). One concern with the variance-based cross-variogram has been that Z₁ (·) and Z₂ (·) might be measured in different units (apples and oranges). In this note, we show that the cokriging predictor based on variance-based cross-variograms can handle any units used for Z₁ (·) and Z₂ (·); recommendations are given for an appropriate choice of units. We review the differences between the variance-based cross-variogram and the covariance-based cross-variogram and conclude that the former is more appropriate for cokriging. In practice, one often assumes that variograms and cross-variograms are functions of uandv only through the difference u – v. This restricts the types of models that might be fitted to measures of cross-spatial dependence.     

Le passage Ordovicien–Silurien et la partie inférieure du Silurien (Sud-Est du Massif armoricain, France)The Ordovician–Silurian transition and the lower part of the Silurian (southeastern Armorican Massif, France)

A new section in the Silurian graptolitic ‘phtanites’ (black cherts) of Les Fresnaies at Chalonnes-sur-Loire (SE Armorican Massif) shows for the first time that these rocks (1) succeed conformably to Uppermost Ordovician (Hirnantian) glaciomarine deposits and (2) contain successive graptolite assemblages that characterise the base of the Silurian, the whole Rhuddanian and Aeronian stages and the lower part of the Telychian. To cite this article: J.M. Piçarra et al., C. R. Geoscience 334 (2002) 1177–1183.     

Datation Ar/Ar des leucogranites sous couverture du complexe plutonique de Charroux–Civray (Vienne)Ar/Ar dating of leucogranites in the sediment-covered Charroux–Civray complex (Vienne)

⁴⁰Ar/³⁹Ar dating on muscovites, performed on leucogranitic intrusions of Charroux–Civray plutonic complex, points out the existence of two peraluminous magmatic activities, whose equivalents are known in the Limousin: (1) garnet-bearing leucogranitic veins at ca. 340 Ma; (2) a specialised leucogranite associated with W ± Sn deposits at ca 310 Ma. However, available ⁴⁰Ar/³⁹Ar data do not allow us to provide further data concerning the age and the geometry at depth of a large leucogranitic body identified by geophysics. To cite this article: P. Alexandre et al., C. R. Geoscience 334 (2002) 1141–1148.     

Crustal assimilation in basalt and jotunite: Constraints from layered intrusions

To constrain the amount and rate of crustal contamination that is possible in basaltic and jotunitic magma, and to gain an insight into the physical and thermal processes of assimilation in crustal magma chambers, we have modelled published Sr and Nd isotopic data from three layered intrusions. Well-exposed sequences of cumulates with no evidence of magma recharge provide direct records of concurrent assimilation and fractional crystallization (AFC). The key to the modelling is that F, the mass fraction of magma remaining in the chamber, can be estimated from the thicknesses of the studied cumulate sequences. This allows AFC model curves to be fitted to the isotopic data by varying r, the ratio of the rate of mass assimilated to the rate of mass crystallized. The results of modelling show that r is nearly constant in 800 to 2000 m thick sequences of cumulates displaying up-section decreases in anorthite content of plagioclase, increases in whole-rock Sr₀ (initial ⁸⁷Sr/⁸⁶Sr) and decreases in whole-rock εNd₀ (initial εNd). The r-values of the layered sequences range from 0.12 in the Fongen–Hyllingen Intrusion, over 0.20 in the Bjerkreim–Sokndal Intrusion, to 0.27 in the Hasvik Intrusion. The total amount of assimilation, the bulk crust/magma ratio, reaches values of 0.08, 0.19 and 0.28 at the level of the most contaminated samples after 60% to 80% crystallisation, whereas the instantaneous crust/magma ratio of the most contaminated magmas were respectively 0.14, 0.46, and 0.70, for the three intrusions.Innumerable country rock xenoliths occur in the three layered intrusions and played a crucial role in the assimilation process. The xenoliths spalled off the roofs of the magma chambers during magma emplacement and their initial temperature and composition relate to r in the intrusions. In the Hasvik Intrusion (r = 0.27), the initial temperature of the country rocks was 450 °C and the xenoliths were fusible metasediments and therefore produced a high fraction of partial melt that could be assimilated. In the Bjerkreim–Sokndal Intrusion (r = 0.20), the country rocks were initially at temperatures of 640–880 °C but included both refractory massif-type anorthosite and fusible gneisses. In the Fongen–Hyllingen Intrusion (r = 0.12), the country rocks were cooler (300 °C) and the xenoliths include refractory metabasalt (dominant) and fusible metapelite. We argue that the refractory metabasalt and anorthosite xenoliths acted mainly as heat sinks, resulting in reduced r-values in Fongen–Hyllingen and Bjerkreim–Sokndal Intrusions.Heating of refractory and fusible xenoliths, and melting of fusible xenoliths absorbed sensible and latent heat of the magma. Energy-balanced modelling shows that up to 75% of the heat available was absorbed by xenoliths within the magma chambers, promoting higher rates of cooling and crystallisation than would have resulted from loss of heat to the envelope of country rocks alone. The high r-values reflect the amount of heat absorbed by heating and melting country rock within the magma chambers themselves, and their constancy reflects the ready availability of fusible xenoliths.     

Rb-Sr-und K-Ar-Evidenz für eine intensive alpidische Beeinflussung der Paragesteine in Kor-und Saualpe,SE-Ostalpen, Österreich

Zusammenfassung Von den Paragesteinen der Kor-und Saualpe werden 30 Gesamtgesteins-Analysen, 21 Rb–Sr-Glimmer-Analysen und 27 K–Ar-Glimmer-Analysen mitgeteilt. Die Rb–Sr-Altersdaten (Biotit und Hellglimmer) geben ausnahmslos frühalpidische Abkühlalter an: 14 Biotite: 72–84 M.J., 7 Hellglimmer: 82–115 M.J.Die K–Ar-Bestimmungen geben einen deutlichen Hinweis auf Ar-Überschuß bei den 14 Biotiten mit Altersdaten von 76–122 M.J., während, dies bei den Hellglimmern mit 80–95 M.J. nicht so deutlich ist.Gesamtgesteins-Isochronen an drei verschiedenen Gesteinen der Decke (Pilger undWeissenbach, 1965) zeigen eine alpidische Öffnung des Rb–Sr-Systems für die Gesteine an. Die Gesteine aus dem Klieningfenster und die aus dem Wolfsberger-Fenster (Morauf, 1980) zeigen keine alpidische Öffnung an. Damit wird der Befund vonPilger undWeissenbach (1965), daß die Decke höher metamorph ist als das Liegende, voll bestätigt, sowie transportierte Metamorphose (Pilger undWeissenbach, 1971) nachgewiesen.Mit 3 Abbildungen     

New observational information on the precursory accelerating and decelerating strain energy release

Recent reliable data are used to study the behavior of seismic activity before 46 strong shallow earthquakes (M ≥ 6.0), which correspond to five complete samples of mainshocks. These samples include 6 mainshocks (M = 6.0–7.1) that occurred in western Mediterranean since 1980, 17 mainshocks (M = 6.0–7.2) which occurred in the Aegean (Greece and surrounding area) since 1980, 5 mainshocks (M = 6.4–7.5) that occurred in Anatolia since 1980, 12 mainshocks (M = 6.0–7.3) that occurred in California since 1980 and 6 mainshocks (M = 7.0–8.3) that occurred in Japan since 1990. In all 46 cases, a similar precursory seismicity pattern is observed. Specifically, it is observed that accelerating Benioff strain (square root of seismic energy) release caused by preshocks occurs in a broad circular region (critical region), with a radius about eight times larger than the fault length of the mainshock, in agreement with results obtained by various research groups during the last two decades. However, in a much smaller circular region (seismogenic region), with a radius about four times the fault length, the corresponding preshock strain decelerates with the time to the mainshock. The time variation of the strain follows in both cases a power law but the exponent power is smaller than unit (m ¯ = 0.3) in the case of the accelerating preshock strain and larger than unit (m ¯ = 3.0) in the case of the decelerating preshock strain. Predictive properties of this “Decelerating In–Accelerating Out Strain” model are expressed by empirical relations. The possibility of using this model for intermediate-term earthquake prediction is discussed and the relative model uncertainties are estimated.     

Neotectonic evolution of the Central Betic Cordilleras (Southern Spain)

Paleostress orientations were calculated from fault-slip data of 36 sites located along a traverse through the Central Betic Cordilleras (southern Spain). Heterogeneous fault sets, which are frequent in the area, have been divided into homogeneous subsets by cross-cutting relationships observed in the field and by a paleostress stratigraphy approach applied on each individual fault population. The state of stress was sorted according to main tectonic events and a new chronology is presented of the Miocene to Recent deformation in the central part of the Betic Cordilleras. The deviatoric stress tensors fall into four distinct groups that are regionally consistent and correlate with three Late Oligocene–Aquitanian to Recent major tectonic events in the Betic Cordilleras. The new chronology of the neotectonic evolution includes, from oldest to youngest, the following main tectonic phases:

(1) Late Oligocene–Aquitanian to Early Tortonian: σ₁ subhorizontal N–S, partly E–W directed, σ₃ subvertical; compressional structures (thrusting of nappes, large-scale folding) and strike-slip faulting in the Alborán Domain and the External Zone of the Betic Cordilleras;

(2) Early Tortonian to Pliocene–Pleistocene: σ₁ subvertical, σ₃ subhorizontal NW–SE, partly N–S directed or E–W-directed (radial extension); large-scale normal faulting in the Central Betic Cordilleras and in the oldest Neogene formations of the Granada Basin related to the gravitational collapse of the Betic Cordilleras and the exhumation of the intensely metamorphosed rock series of the Internal Zones, at the same time formation of the Alborán Basin and intramontane basins such as the Granada Basin;

(3) Pleistocene to Recent: (3a) σ₁ subvertical, σ₃ subhorizontal NE–SW with prominent normal faulting, but coevally; (3b) σ₁ subhorizontal NW directed, σ₃ NE–SW subhorizontal with strike-slip faulting. Extensional structures and strike-slip faulting are related to the ongoing convergence of the Eurasian and African Plates and coeval uplift of the Betic Cordilleras. Reactivation of pre-existing fractures and faults was frequently observed. Phase 3 is interpreted as periodic strike-slip and normal faulting events due to a permutation of the principal stress axes, mainly σ₁ and σ₂.

The “El Pilote” fluorite skarn: A crucial deposit in the understanding and interpretation of the origin and mobilization of F from northern Mexico deposits

Fluorite deposits are widespread in northern Mexico and those deposits have traditionally been categorized as exclusively hydrothermal–magmatic in origin. Recently, two different fluorite-bearing type models have been proposed for the Northern Mexican deposits: (1) MVT-like deposits formed from basinal brines mobilized during the Laramide Orogeny (La Encantada deposit, Gonzalez-Partida et al., [Gonzalez-Partida, E., Carrillo-Chavez, A., Grimmer, J.O.W., Pironon, J., 2002. Petroleum-rich fluid inclusions in fluorite, Purisima mine, Coahuila, Mexico. International Geological Review 44 (8), 751–763.]; Tritlla et al., [Tritlla, J., Gonzalez-Partida, E., Levresse, G., Banks, D., Pironon, J., 2004. Fluorite deposits at Encantada-Buenavista, Mexico: products of Mississippi Valley type processes — a reply. Ore Geology Reviews 25, 329–332.]); and (2) fluorite-bearing skarns in close contact with rhyolite intrusives (Levinson, [Levinson, A.A., 1962. Beryllium–fluorine mineralization at Aguachile Mountain, Coahuila, Mexico. American Mineralogist 47, 67–75.]). The El Pilote fluorite deposit falls into the second category, and is the only known example of a magmatic-related fluorite deposit in the area. The fluorite trace-element patterns from both the El Pilote skarn and La Encantada MVT deposits display comparable and very low relative abundances as well as comparable chondrite-normalized REE patterns; this would suggest that the skarn F-source comes from the remobilization of a MVT fluorite manto.     

Enregistrement de phénomènes de resédimentation au cours du Maastrichtien supérieur et du Paléocène supérieur (J. Serj, Tunisie atlasique) : apport micropaléontologique et signature tectono-eustatique

Sedimentological and biostratigraphic analysis of Campanian–Maastrichtian reduced series of the J. Serj permitted to characterize two episodes of submarine erosion. The first is pre-Upper Maastrichtian (Rosita contusa zone), the second is pre-Upper Palaeocene (Morozovella velascoensis zone). Thus, two type-1 boundary surfaces are distinguished. These surfaces limit three stratigraphic intervals in apparent continuity. Syn-sedimentary tectonic activity is attested by gravity deposits or processes (conglomerates, slumps). To cite this article: A. Amri et al., C. R. Geoscience 337 (2005).     

Microstructure mechanism map of dynamically recrystallized marble

The relative nucleus density (RND) model of dynamically recrystallized grain size [Sakai, T., Jonas, J.J. 1984. Dynamic recrystallization: mechanical and microctructutal consideration. Acta metallurgica, 32, 198–209] was applied to experimentally and to naturally deformed marbles that have undergone dynamic recrystallization. The model shows that a relationship between initial grain size (D₀) and stable dynamically recrystallized grain size (D_S) for a given value of temperature-corrected strain-rate (Z) controls grain size evolution during dynamic recrystallization. New microstructural mechanism maps (MM-maps) for experimentally and naturally deformed marbles (based on previously published data) were defined in log grain size–log Z space and show two distinct regions of grain reduction and grain coarsening. The boundary between these two regions corresponds to an equation relating dynamically recrystallized grain size and temperature corrected strain rate, as proposed in this work. The new MM-map was used to trace semi-quantitatively microstructural and grain size evolution in naturally deformed marbles that underwent dynamic recrystallization at different thermal conditions. The boundary between grain coarsening and grain reduction does not necessarily coincide with the boundary between rotation and migration recrystallization mechanisms. Assessment of available natural data shows that the boundary condition D₀ = 2D_S between grain-coarsening and grain-reduction introduced by Sakai and Jonas [Sakai, T., Jonas, J.J. 1984. Dynamic recrystallization: mechanical and microctructutal consideration. Acta metallurgica, 32, 198–209] is not required for naturally deformed marble.     

Structural setting and tectonic evolution of the Apennine Units of northern Calabria

A new structural–stratigraphic synthesis of the Apennine units of northern Calabria is presented. The Meso-Cenozoic successions are grouped into two tectonic units, named Pollino–Ciagola Unit (PCU) and Lungro–Verbicaro Unit (LVU), comprising terrains formerly attributed to five different tectonic units. FeMg carpholite and blue amphibole record HP–LT metamorphism in the LVU, followed by progressive decompression leading to final greenschist facies re-equilibration during dominantly extensional deformation. Final tectonic emplacement of the LVU over the PCU post-dated the metamorphism of the LVU and was accompanied by intense ductile deformation along zones of strain localisation in footwall rocks. All of the units were later affected by folding and minor thrusting during subsequent Apennine tectonics. To cite this article: A. Iannace et al., C. R. Geoscience 337 (2005).     

HP–LT Variscan metamorphism in the Cubito-Moura schists (Ossa-Morena Zone, southern Iberia)

Multi-equilibrium thermobarometry shows that low-grade metapelites (Cubito-Moura schists) from the Ossa–Morena Zone underwent HP–LT metamorphism from 340–370 °C at 1.0–0.9 GPa to 400–450 °C at 0.8–0.7 GPa. These HP–LT equilibriums were reached by parageneses including white K mica, chlorite and chloritoid, which define the earliest schistosity (S₁) in these rocks. The main foliation in the schists is a crenulation cleavage (S₂), which developed during decompression from 0.8–0.7 to 0.4–0.3 GPa at increasing temperatures from 400–450 °C to 440–465 °C. Fe³⁺ in chlorite decreased greatly during prograde metamorphism from molar fractions of 0.4 determined in syn-S₁ chlorites down to 0.1 in syn-S₂ chlorites. These new data add to previous findings of eclogites in the Moura schists indicating that a pile of allochtonous rocks situated next to the Beja-Acebuches oceanic amphibolites underwent HP–LT metamorphism during the Variscan orogeny. To cite this article: G. Booth-Rea et al., C. R. Geoscience 338 (2006).     

Spatial correlation of deformation and mineral reaction in experimentally deformed plagioclase–olivine aggregates

Shear deformation of hot pressed plagioclase–olivine aggregates was studied in the presence and absence of mineral reaction. Experiments were performed at 900 °C, 1500 MPa, and a constant shear strain rate of 5×10⁻⁵ s⁻¹ in a solid medium apparatus. Whether the mineral reaction between plagioclase and olivine takes place or not is controlled by choosing the appropriate plagioclase composition; labradorite (An₆₀) does not react, anorthite (An₉₂) does. Labradorite–olivine aggregates deformed without reaction are very strong and show strain hardening throughout the experiment. Syndeformational reaction between olivine and anorthite causes a pronounced strain weakening. The reaction produces fine-grained opx–cpx–spinel aggregates, which accommodate a large fraction of the finite strain. Deformation and reaction are localised within a 0.5-mm-wide sample. Three representative samples were analysed for their fabric anisotropy R* and shape-preferred orientation α* (fabric angle with the shear plane) using the autocorrelation function (ACF). Fabric anisotropy can be calibrated to quantify strain variations across the sheared samples. In the deformed and reacted anorthite–olivine aggregate, there is a strong correlation between reaction progress and strain; regions of large shear strain correspond to regions of maximum reaction progress. Within the sample, the derived strain rate variations range up to almost one order of magnitude.