Some limitations of the Rfφ technique of strain analysis — Reply

The analysis presented in the discussion is statistically invalid.     

A statistical analysis applied to the Rf/φ method

A statistical analysis for the R_f/φ method is developed in the paper. The technique provides estimates of R_s, R_i and θ according to R_f and φ. Moreover, we can restore the pattern of initial orientations of marker objects by means of their frequency histogram, provided the strain is homogeneous. It is unnecessary to postulate random initial orientations if the principal directions of strain ellipsoid are known.     

Some limitations of the Rf/φ technique of strain analysis

Finite strain determined from R_f/φ analysis of deformed ellipse distributions cannot be separated into compactional and tectonic parts on the basis of population asymmetry about the orientational mean, as was originally suggested. Furthermore, where there is a ductility contrast between objects and matrix, R_f/φ analysis yields an invalid estimate of the strain suffered by the objects.     

Magnitude of σ1, σ2, and σ3 at mid-crustal levels in an orogenic belt: Microboudin method applied to an impure metachert from Turkey

We revised an equation for estimating palaeostress magnitude using the microboudin technique by incorporating the influence of time on the fracture strength of minerals. The equation was used to estimate triaxial palaeostresses from a rare sample of metachert from Turkey that contains microboudinaged, columnar tourmaline grains in a wide range of orientations within the foliation plane. The estimated principal palaeostresses are σ₁ = 605 MPa, σ₂ = 598 MPa, and σ₃ = 597 MPa. As the microboudinage is considered to have occurred immediately before the rock encountered the brittle-plastic transition during exhumation, these stress values correspond to conditions at approximately 18 km depth and 300 °C within a Cretaceous orogenic belt.     

Seismic lateral earth pressure coefficients for c–φ soils by slip line method

In this paper, the author proposes a rotation of axes in the solution of slip line equations for determination of lateral earth pressure with the presence of seismic loading under general conditions. A general c–φ soil system under a general condition can be considered so that K_pγ, K_pc, K_pq, K_aγ, K_ac and K_aq can all be determined. For passive pressure, K_pc is found to be much greater than K_pγ and the effect of seismic coefficient on passive pressure is relatively small as compared with the corresponding situation for active pressure. The use of iterative analysis is found to be useful for passive pressure determination but unimportant for active pressure determination.     

Molecular isotopic heterogeneity of fossil organic matter: implications for δCbiomass and δCpalaeoatmosphere proxies

The degree of isotopic variation in fossil organic matter renders bulk δ¹³C signatures strongly influenced by molecular isotopic heterogeneity. For example, in fossil wood the relative abundance of less depleted ¹³C moieties, i.e. preserved ¹³C enriched polysaccharides versus the relatively ¹³C depleted lignin moieties, can be seen to significantly bias δ¹³C_{fossil wood} values. Moreover the variation in δ¹³C values of specific compounds within fossil material are themselves highly variable and reflect the heterogeneity in isotopic values of different carbon atoms within individual compounds. For studies using δ¹³C values of fossil plant material as proxies (e.g., for δ¹³C_{palaeoatmosphere}, δ¹³C_biomass) it is recommended that the biases introduced through molecular heterogeneity, preservation type and taxonomic status of the fossil material are determined initially. Biases inherent in the bulk signature can then be reduced, rendering this value more robust. Alternatively, compound specific stable carbon isotope measurements of individual moieties preserved through geological time might prove to be an alternative proxy for monitoring changes in the bulk δ¹³C value of the plant and might reveal atmospherically induced trends.     

The importance of the effective intermediate principal stress (σ′2) to fault slip patterns

In normal faulting regimes, the magnitudes and orientations of the maximum and minimum principal compressive stresses may be known with some confidence. However, the magnitude of the intermediate principal compressive stress is generally much more difficult to constrain and is often not considered to be an important factor. In this paper, we show that the slip characteristics of faults and fractures with complex or nonoptimal geometry are highly sensitive to variation or uncertainty in the ambient effective intermediate principal stress (σ′₂). Optimally oriented faults and fractures may be less sensitive to such variations or uncertainties. Slip tendency (T_s) analysis provides a basis for quantifying the effects of uncertainty in the magnitudes and orientations of all principal stresses and in any stress regime, thereby focusing efforts on the most important components of the system. We also show, for a normal faulting stress regime, that the proportion of potential surfaces experiencing high slip tendency (e.g., T_s ≥ 0.6) decreases from a maximum of about 38% where σ′₂ = σ′₃, to a minimum of approximately 14% where σ′₂ is halfway between σ′₃ and σ′₁, and increases to another high of approximately 29% where σ′₂ = σ′₁. This analysis illustrates the influence of the magnitude of σ′₂ on rock mass strength, an observation previously documented by experimental rock deformation studies. Because of the link between fault and fracture slip characteristics and transmissivity in critically stressed rock, this analysis can provide new insights into stress-controlled fault transmissivity.     

K-H3OFe3(SO4)2(OH)6铁矾的XRD研究

根据X射线衍射(XRD)分析发现: A Fe₃(SO₄)₂(OH)₆(A=K⁺、H₃O⁺)系列铁钒的XRD数据十分相近,难以用XRD区别,需通过能谱(EDS)辅助分析,才能区分此类铁矾。另外,此类铁矾的003和107面网间距d随K⁺含量增大而增大,且呈一元三次方程的关系;而033和220面网间距d随K⁺含量增大而减小,呈一元二次方程的关系。对该现象从铁矾晶体结构方面进行解释:K⁺、H₃O⁺离子位于较大空隙中,且沿着Z轴方向排列,当K⁺、H₃O⁺离子之间相互替换时,会导致该铁矾晶体结构在Z轴方向有较明显的变化。     

Solubility of Fe-ettringite (Ca6[Fe(OH)6]2(SO4)3 · 26H2O)

The solubility of Fe-ettringite (Ca₆[Fe(OH)₆]₂(SO₄)₃ · 26H₂O) was measured in a series of precipitation and dissolution experiments at 20 °C and at pH-values between 11.0 and 14.0 using synthesised material. A time-series study showed that equilibrium was reached within 180 days of ageing. After equilibrating, the solid phases were analysed by XRD and TGA while the aqueous solutions were analysed by ICP-OES (calcium, sulphur) and ICP-MS (iron). Fe-ettringite was found to be stable up to pH 13.0. At higher pH-values Fe-monosulphate (Ca₄[Fe(OH)₆]₂(SO₄) · 6H₂O) and Fe-monocarbonate (Ca₄[Fe(OH)₆]₂(CO₃) · 6H₂O) are formed. The solubilities of these hydrates at 25 °C are:      

The bearing of the system CaMgSi2O6CaAl2SiO6CaFeAlSiO6 on fassaitic pyroxene

The system CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ has been studied in air at 1 atm. The phase assemblage at subsolidus temperatures in the CaMgSi₂O₆-rich portion is Cpx + An + Mel and that in the CaMgSi₂O₆-poor portion Cpx + An + Mel + Sp. At subsolidus temperatures the sigle-phase field of clinopyroxene increases with an increase in the CaFeAlSiO₆ component of the system. The Al₂O₃ content of clinopyroxene, however, continues to increase beyond the single-phase field and attains at least 16.04 wt.% Al₂O₃ with 3.9 wt.% Fe₂O₃. The stability field of fassaite in the system over a range of pressures and oxygen fugacities has been estimated from data in the literature as well as the present data. The CaFeAlSiO₆ content of fassaite is dependent on oxygen fugacity, but is not influenced by pressure. The stability field is strongly influenced by oxygen fugacity at low and high pressure, and decreases with decreasing oxygen fugacity. Clinopyroxenes in both volcanic and metamorphic rocks from various localities, when plotted on the CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ triangle, show that there is no compositional gap between diopside and fassaitic pyroxene in metamorphic rocks, and that the fassaitic pyroxene in alkalic rocks becomes richer in both CaAl₂SiO₆ and CaFeAlSiO₅ components as crystallization proceeds. These results agree with those obtained in the experimental study.     

The dynamics of central Main Ethiopian Rift waters: Evidence from δD, δO and Sr/Sr ratios

Water samples from cold and geothermal boreholes, hot springs, lakes and rivers were analyzed for δD, δ¹⁸O and ⁸⁷Sr/⁸⁶Sr compositions in order to investigate lake water–groundwater mixing processes, water–rock interactions, and to evaluate groundwater flow paths in the central Main Ethiopian Rift (MER) of the Ziway–Shala basin. Different ranges of isotopic values were recorded for different water types: hot springs show δ¹⁸O −3.36 to +3.69 and δD −15.85 to +24.23, deep Aluto-Langano geothermal wells show δ¹⁸O −4.65 to −1.24 and δD −12.39 to −9.31, groundwater wells show δ¹⁸O −3.99 to +5.14 and δD −19.69 to +32.27, whereas the lakes show δ¹⁸O and δD in the range +3.98 to +7.92 and +26.19 to +45.71, respectively. The intersection of the Local Meteoric Water Line (LMWL: δD = 7 δ¹⁸O + 11.2, R² = 0.94, n = 42) and the Local Evaporation Line (LEL: δD = 5.63δ¹⁸O + 8, n = 14, R² = 0.82) was used to estimate the average isotopic composition of recharge water into the basin (δD = −5.15 and δ¹⁸O = −2.34). These values are depleted if compared with the modern-day average precipitation, presumably indicating paleo-groundwater components recharged during previous humid climatic phases. The measured stable isotope values indicate that the geothermal wells, some of the hot springs and groundwater wells mainly consist of meteoric water. The Sr isotopic signatures in all waters are within the range of the Sr isotopic composition of the rift basalts and rhyolites. The variability of Sr isotopic data also pinpoints complex water–rock interaction and mixing processes in groundwater and surface water. The ⁸⁷Sr/⁸⁶Sr ratio ranges from 0.70445 to 0.70756 in the hot springs, from 0.70426 to 0.70537 in two deep geothermal wells, and from 0.70673 to 0.70721 in the rift lakes Ziway, Langano, Shala and Awasa. The radiogenic composition recorded by the lakes indicates that the input water was predominantly affected by progressive interaction with rhyolitic volcanics and lacustrine sediments.     

A nuclear method for the analysis of light elements (Z </ 11) in geological samples

A nuclear method of measurement of major as well as trace light elements in silicates is presented. This method is particularly applied to the determination of Li content in micas in order to optimize some experimental conditions. The other elements that can be reached with a good sensitivity ( 10 ppm) are Be, B, F and Na. The particles which provoke the nuclear reactions are single-charged -particles provided by a Van de Graaf accelerator. The possibility of obtaining a well-focused -beam and the good accuracy of the method permit us to consider this method as a valuable complement of the electron microprobe.     

The role of “excess” CO2 in the formation of trona deposits

The prevailing theory for the formation of trona [Na₃(CO₃)(HCO₃) · 2(H₂O)] relies on evaporative concentration of water produced by silicate hydrolysis of volcanic rock or volcaniclastic sediments. Given the abundance of closed drainage basins dominated by volcanics, it is puzzling that there are so few trona deposits and present-day lakes that would yield dominantly Na–CO₃ minerals upon evaporation. Groundwater in the San Bernardino Basin (southeastern Arizona, USA and northeastern Sonora, Mexico) would yield mainly Na–CO₃ minerals upon evaporation, but waters in the surrounding basins would not. Analysis of the chemical evolution of this groundwater shows that the critical difference from the surrounding basins is not lithology, but the injection of magmatic CO₂. Many major deposits of trona and Na–CO₃-type lakes appear to have had “excess” CO₂ input, either from magmatic sources or from the decay of organic matter. It is proposed that, along with the presence of volcanics, addition of “excess” CO₂ is an important pre-condition for the formation of trona deposits.     

Some thermodynamic properties of the Berman and Brown model for CaO-Al2O3-SiO2

The and (1984) excess free energy model (B&B) is extremely convenient to use in modelling multicomponent solutions. However, spinodal calculations reveal that their calibration of this model for CaO-Al₂O₃-SiO₂ produces liquation tielines that do not appear to be in agreement with experimental work. In addition, their calibration contains some strongly negative excess entropy parameters and these permit a most unusual inverted liquation field to start at approximately >2115°C, wt% (SiO₂, Al₂O₃, CaO) = (70, 16, 14). This inverted field expands rapidly to cover most of the ternary for T> 2300°C and continues to expand at all higher temperatures. The Berman and Brown calibration for this system carries these negative excess entropies of mixing because the solution model is very strongly asymmetric as a result of the use of normal oxide mole weights in modelling the configurational entropy of mixing. A suggestion is made for a fairly natural restriction on the relative sizes of empirical models for excess versus configurational entropy.

Expressions are presented for the general consolute condition (all solution models) and for the second and third partials of the B&B G^x model.     

Mechanisms of sulfur introduction chemically controlled: δS imprint

Organic sulfur in marine sediment is ³⁴S enriched relative to the co-existing pyrite. This phenomenon is still enigmatic. Timing of the sulfur incorporation, immobilization and different sulfur species involved are part of the explanations. The reduced sulfur species incorporation into organic matter (OM) is generally assumed to have negligible δ³⁴S fractionation. This assumption has never been confirmed by laboratory experimental data. The present study measures the δ³⁴S changes resulting from reduced sulfur species (sulfides and polysulfide anions) incorporation into organic model compounds in an aquatic and low temperature (25 °C) system that simulates diagenetic marine environment. In addition, we also investigate the δ³⁴S fractionation and the isotope chemical mixing in the formation of polysulfide anions produced from elemental sulfur and sulfide anions. The results showed total isotope mixing between the two species in the formation of polysulfides. Acidification of the polysulfides solution caused δ³⁴S fractionation between the released elemental sulfur and H₂S. The incorporation of polysulfides and sulfides into carbonyl groups, caused ³⁴S enrichment relative to the starting polysulfides and sulfide of 4–5‰. The ³⁴S enrichment of the sulfurized carbonyl groups showed a minimal effect by temperature (0–70 °C) and is not affected by salinity, polysulfides composition, reaction time or solubility in water. The incorporation of polysulfides and sulfides into brominated organic compounds was negligibly ³⁴S enriched. The chemical mechanisms controlling the polysulfides incorporation into OM depend mostly on the functional groups and determine the ³⁴S enrichment of the sulfurized OM. The results presented in this study can explain part of the difference between pyrite δ³⁴S and sulfurized OM δ³⁴S in natural marine sediments.     

Occurrence and origin of keilite, (Fe>0.5,Mg<0.5)S, in enstatite chondrite impact-melt rocks and impact-melt breccias

Keilite (Fe_>0.5,Mg_<0.5)S, the iron-dominant cubic analog of niningerite, (Mg_>0.5,Fe_<0.5)S, occurs in enstatite chondrites [Shimizu, M., Yoshida, H., Mandarino, J.A., 2002. The new mineral species keilite, (Fe,Mg)S, the iron-dominant analog of niningerite. Can. Mineral. 40, 1687–1692]. I find that keilite occurs only in enstatite chondrite impact-melt rocks and impact-melt breccias. Based on the phase relations in the system MgS–MnS–CaS–FeS [Skinner, B.J., Luce, F.D., 1971. Solid solutions of the type (Ca,Mg,Mn,Fe)S and their use as geothermometers for the enstatite chondrites. Am. Mineral. 56, 1269–1296], I conclude that keilite formed from niningerite or alabandite (Mn_>0.5,Fe_<0.5)S by reaction with troilite (FeS) at elevated temperatures of well above 500 °C (the lowest equilibration temperature of keilite), but it is likely that the maximum temperatures during melting experienced by keilite-bearing impact-melt rocks and impact-melt breccias were considerably higher, perhaps >1500 °C, as indicted by the occurrence of euhedral enstatite that formed from a melt [McCoy, T.J., Dickinson, T.L., Lofgren, G.E., 1999. Partial melting of the Indarch (EH4) meteorite: a textural, chemical, and phase relations view of melting and melt migration. Meteorit. Planet. Sci. 34, 735–746]. Based on the classifications of the keilite-bearing meteorites as impact-melt rocks and impact-melt breccias and my own textural observations, I conclude that this elevated temperature was reached as a result of impact and not internal heating and melting, followed by fast cooling, thus, quenching in keilite. Enstatite chondrite impact-melt rocks and impact-melt breccias that do not contain keilite may have been more deeply buried after impact and, hence, cooled slowly and were annealed so that FeS exsolved from keilite, concomitant with the formation of niningerite, alabandite or various (Mn,Mg,Fe) mixed sulfides.     

Calcite–dolomite geothermometry in the system CaCO3–MgCO3–FeCO3: an experimental study

Abstract An experimental study of the system CaCO₃–MgCO₃–FeCO₃ was undertaken in order to calibrate the iron correction to the calcite–dolomite geothermometer, which is based on the solubility of magnesium in calcite in the assemblage calcite + dolomite. The experiments, at 450°C and lower temperatures, resulted in products with a very small grain size and incomplete equilibration. However, application of a carefully-devised automatic data processing algorithm to analyses of the phases in experimental charges, combined with a thermodynamic analysis, results in geothermometer diagrams which should be preferred to previous theoretical predictions.