A Note on Extension Variances in IR2

Matheron (1971) proposed an approximation of the extension variance in IR. We propose in this note an extension of this formula in IR ² , based on a MacLaurin formula. Its application is shown in an example, the estimation of the maximum depressional storage of a soil surface.     

Variation of Φ (logMi,L) in relation with geochemistry of oil-field waters and its applications

Samples of oil-field waters taken from more than fifty oil-fields in ten major oil-gasbearing basins of China have been studied in special reference to various bond parameters. It is found that the concentrations of Na⁺, Ca²⁺ and Mg²⁺ (ppm) show a logarithmic correlation with the bond parameters. This correlation is treated with the quantitative formula logMi=a+bL for Φ (logMi, L). Additionally, the relations between the variation of Φ (logMi, L) and the origin of oil-field waters and between that and the nature of crude oil are explored. For the convenience of solution of the formula, nomogaphy is recommended in this paper.     

Suspended sediment load prediction of river systems: GEP approach

This study presents gene expression programming (GEP), an extension of genetic programming, as an alternative approach to modeling the suspended sediment load relationship for the three Malaysian rivers. In this study, adaptive neuro-fuzzy inference system (ANFIS), regression model, and GEP approaches were developed to predict suspended load in three Malaysian rivers: Muda River, Langat River, and Kurau River [ANFIS (R ²?=?0.93, root mean square error (RMSE)?=?3.19, and average error (AE)?=?1.12) and regression model (R ²?=?0.63, RMSE?=?13.96, and AE?=?12.69)]. Additionally, the explicit formulations of the developed GEP models are presented (R ²?=?0.88, RMSE?=?5.19, and AE?=?6.5). The performance of the GEP model was found to be acceptable compare to ANFIS and better than the conventional models.     

Hydrodynamic study of karstic and intergranular aquifers using isotope geochemistry in Basara basin, Sulaimani, North-Eastern Iraq

The study area is located in the border of the high and low folded zone having a semi-arid climate area. This study initiated in 2009–2010, deals essentially with the investigation of the stable isotope (¹⁸O and deuterium ²H) as well as radioactive isotope represented by tritium ³H in rain, carbonate springs, intergranular aquifer, and surface water in order to investigate the source and relative ages of the groundwater and to show the influence of the altitude variations of the isotope composition. In this study and for the first time in the area, a local meteoric water line have been drawn with an empirical formula δ ²H?=?7.7δ ¹⁸O?+?14.4. The δ ¹⁸O–altitude effect was determined using isotopic data for several samples taken from groundwater and surface water; it was approximated at ?0.79?‰/100 m for the entire area of the study. The output of the tritium concentrations in the springs and water well samples revealed to the conclusion that the values closely resembles to the present time tritium concentration in precipitation.     

Deviation of the arrival-time delay of pulses for the Crab pulsar from a quadratic frequency region

Our measurements of the arrival-time delays of radio pulses from the Crab pulsar, PSR B0531+21, at low frequencies 111, 63, and 44 MHz revealed additional delays compared to the usual quadratic frequency relation, Δt(v) ∝ v ^?2. These additional delays are 65 ms between 63 MHz and 111 MHz—i.e., a factor of two longer than the pulsar’s period, i.e., a factor of five longer than the pulsar period—and cannot be explained by the “twisting” of the magnetic-field lines by the rotation of the pulsar. We suggest the model in which a previously unknown high-density plasma layer with a high electron concentration is present along the line of sight in the Crab nebula, causing an additional frequency-dependent delay of the observed radio pulses at low frequencies due to the contribution of the n _e ² v ^?4 term in the dispersion-delay formula. The parameters of this inferred layer have been derived: emission measure EM ? 4 × 10⁶ pc/cm⁶, electron density n _e ? 10⁶ cm^?3, depth along the line of sight d ? 4 × 10^?6 pc, and electron temperature T _e ≥ 2 × 10⁶ K.     

Extensional deformation along the southern boundary of the Gyeonggi Massif,South Korea: structural characteristics,age constraints,and tectonic implications

The Permo–Triassic collision of the North and South China blocks caused the development of the Dabie–Sulu Orogen in China and Songrim Orogen in the Korean Peninsula. Extension after this collision is known from the Dabie–Sulu Orogen, but post-orogenic extension is not well defined in the Korean Peninsula. Extensional deformation along the southern boundary of the Gyeonggi Massif in Korea is characterized by top–down-to-the-south ductile shearing and subsequent brittle normal faulting, and was predated by regional metamorphism and north-vergent contractional deformation. Extension occurred between ~220 and 185 Ma based on the ages of pre-extensional regional metamorphism and post-extensional pluton emplacement. ⁴⁰Ar/³⁹Ar dating of syn-extensional muscovite in quartz–mica mylonite yields an age of 187.8 ± 5.6 (2σ) Ma, in agreement with constraints from structural relationships. Together with the extensional deformation identified along the northern boundary of the Gyeonggi Massif (~226 Ma), the extension along the southern boundary is probably related to the exhumation of the massif during late-orogenic or post-orogenic extension associated with the Songrim Orogeny of the Korean Peninsula and forms an important event in the Phanerozoic crustal evolution of East Asia.     

Late Mesozoic magmatism in the East Qinling Orogen,China and its tectonic implications

The Qinling Orogen in Central China records the history of a complex geological evolution and tectonic transition from compression to extension during the Late Mesozoic,with concomitant voluminous granitoids formation.In this study,we present results from petrological,geochemical,zircon U-Pb-Lu-Hf isotopic studies on the Lengshui felsic dykes from Luanchuan region in the East Qinling Orogen.We also compile published geochronological,geochemical,and Hf isotopic data from Luanchuan region and present zircon Hf isotopic contour maps.The newly obtained age data yield two group of ages at～145 Ma and 140 Ma for two granite porphyries from the Lengshui felsic dykes,with the ～145 Ma interpreted as response to the peak of magmatism in the region,and the ～140 Ma as the timing of formation of the felsic dykes.The corresponding Hf isotopic data of the granite porphyries display negativeeHit)values of-16.67 to-4.61,and Hf crustal model ages(T_(DM~C_)of 2255-1490 Ma,indicating magma sourced from the melting of Paleo-to Mesoproterozoic crustal materials.The compiled age data display two major magmatic pulses at 160-130 Ma and 111-108 Ma with magmatic quiescence in between,and the zircon Hf isotopic data display/ε_(Hf)(t)values ranging from-41.9 to 2.1 and T_(DM)~c values of3387-1033 Ma,suggesting mixed crustal and mantle-derived components in the magma source,and correspond to multiple tectonic events during the Late Mesozoic.The Luanchuan granitoids are identified as 1-type granites and most of these are highly fractionated granites,involving magma mixing and mingling and crystal fractionation.The tectonic setting in the region transformed from the Late Jurassic syn-collision setting to Early Cretaceous within-plate setting,with E-W extension in the Early Cretaceous.This extension is correlated with the N-S trending post-collisional extension between the North China Craton and Yangtze Craton as well as the E-W trending back-arc extension triggered by the westward Paleo-Pacific Plate subduction,eventually leading to lithospheric thinning,asthenospheric upwelling,mafic magma underplating,and crustal melting in the East Qinling Orogen.     

Computation of surface energies in an electrostatic point charge model: I. Theory

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and Ψ(x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy (γ ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy γ is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Solubility of gold in arsenian pyrite

Although Au and As can be enriched up to the weight percent level in arsenian pyrite, there is little knowledge of their limiting concentrations and nature of incorporation. This study reports SIMS and EMPA analyses showing that As and Au contents of arsenian pyrites plot in a wedge-shaped zone with an upper compositional limit defined by the line

CAu=0.02⋅CAs+4×10⁻⁵     

Secular decrease of the radio flux density of Cassiopeia A determined from long-term observations. Observations at 38, 81.5, and 151.5 MHz

Long-term measurements of the radio flux density of the young supernova remnant Cassiopeia A relative to the radio galaxy Cygnus A have been carried out at 38 MHz (1987–2004) and 151.5 MHz (1980–2004). Using other data from the literature, we find a secular decrease of the radio flux density of Cassiopeia A at the rates d(38 MHz) = ?0.79 ± 0.14% yr^?1 (for 1956–2004) and d(151.5 MHz) = ?0.83 ± 0.04% yr^?1 (for 1966–2004). Based on measurements made in 1997 and 1998 and data from the literature, this secular decrease at 81.5 MHz is d(81.5 MHz) = ?0.86 ± 0.14% yr^?1 (for 1966–1998). Absolute flux densities of Cassiopeia A at 38 and 151.5 MHz for epoch 2005.5 are calculated based on the relative flux density of Cassiopeia A and the spectrum of Cyg A, which is approximated using an empirical formula at meter and decameter wavelengths.     

The crystal structure of sudburyite

Sudburyite is known to occur in many copper and nickel sulfide deposits in China. Its ideal formula is PdSb. The three-dimensional parameters as determined by an automatic single crystal X-ray diffractometer PW 1100 are:a ₀=4.083,c ₀=5.602 Å,Z=2. Space groupD _6h ⁴ -P6³/mmc. It is isostructural with niccolite, with parametes Pd 000,00 1/2; Sb 2/3 1/3 ¼, 1/3 2/3 ¾ andR=0.11.     

Reconstruction of seasonal temperature variability in the tropical Pacific Ocean from the shell of the scallop, Comptopallium radula

We investigated the oxygen isotope composition (δ¹⁸O) of shell striae from juvenile Comptopallium radula (Mollusca; Pectinidae) specimens collected live in New Caledonia. Bottom-water temperature and salinity were monitored in-situ throughout the study period. External shell striae form with a 2-day periodicity in this scallop, making it possible to estimate the date of precipitation for each calcite sample collected along a growth transect. The oxygen isotope composition of shell calcite (δ¹⁸O_{shell calcite}) measured at almost weekly resolution on calcite accreted between August 2002 and July 2003 accurately tracks bottom-water temperatures. A new empirical paleotemperature equation for this scallop species relates temperature and δ¹⁸O_{shell calcite}:

t(°C)=20.00(±0.61)-3.66(±0.39)×(δ¹⁸O_{shell calcite VPDB}-δ¹⁸O_{water VSMOW})     

Equilibrium mass-dependent fractionation relationships for triple oxygen isotopes

With a growing interest in small ¹⁷O-anomaly, there is a pressing need for the precise ratio, ln¹⁷α/ln¹⁸α, for a particular mass-dependent fractionation process (MDFP) (e.g., for an equilibrium isotope exchange reaction). This ratio (also denoted as “θ”) can be determined experimentally, however, such efforts suffer from the demand of well-defined process or a set of processes in addition to high precision analytical capabilities. Here, we present a theoretical approach from which high-precision ratios for MDFPs can be obtained. This approach will complement and serve as a benchmark for experimental studies. We use oxygen isotope exchanges in equilibrium processes as an example.We propose that the ratio at equilibrium, θ^E ≡ ln¹⁷α/ln¹⁸α, can be calculated through the equation below:

     

A new Cu-rich variety of lyonsite from fumarolic sublimates of the Tolbachik volcano (Kamchatka, Russia) and its crystal structure

A new Cu-rich variety of lyonsite has been found from fumarolic sublimates of the Tolbachik volcano (Kamchatka, Russia). The empirical formula is Cu_4.33Fe _2.37 ³⁺ Ti_0.26Al_0.26Zn_0.07(V_5.85As_0.07Mo_0.07P_0.01S_0.01)O₂₄. The crystal structure was studied on single crystal using synchrotron radiation, R = 0.0514. The mineral is orthorhombic, Pnma, a = 5.1736(7), b =10.8929(12), c = 18.220(2) Å, V = 1026.8(2) ų, and Z = 2. The structural formula is (Cu_0.6Ti_0.3Al_0.3Fe _0.2 ³⁺ □_0.6)_Σ2Cu₂(Fe _2.2 ³⁺ Cu_1.8)_Σ4(V_5.8As_0.1Mo_0.1)_Σ6O₂₄. It is proposed to recast the simplified formula of lyonsite as Cu_3+x (Fe _4?2x ³⁺ Cu_2x )(VO₄)₆, where 0 ≤ x ≤ 1.     

Fe-rich Li-bearing magnesionigerite-6N6S from Xianghualing tin-polymetallic orefield, Hunan Province, P.R. China

The Fe-rich Li-bearing magnesionigerite-6N6S occurs in the Xianghualing tin-polymetallic ore field, Linwu County, Hunan Province, Peoples Republic of China. It was found near the outer contact zone of the Laizhiling granite body and in the Middle-Upper Devonian carbonate rocks of Qiziqiao Formation. The mineral formed during the skarn stage. Its empirical formula is Sn_1.81Li_0.67(Fe_1.43Zn_1.19 Mn_0.41)_Σ3.03(Al_14.89Mg_1.46 Ti_0.11Si_0.01)_Σ16.47O₃₀(OH)₂. The structure for magnesionigerite-6N6S was solved and refined in space group R-3?m, with a?=?5.7144(8), c?=?55.446(11) Å, V?=?1568.0(4) ų, to R1?=?0.0528. Based on the structural refinement of single crystal diffraction data the formula of magnesionigerite-6N6S is Sn_1.80Li_0.97(Fe_1.89Zn_0.91) _Σ2.80 (Al_14.60Mg_1.63 Ti_0.20)_Σ16.43O₃₀(OH)₂ with Z?=?3. Fe-rich Li-bearing magnesionigerite-6N6S contains 0.74 wt.% Li₂O. The idealized charge-balanced composition of magnesionigerite-6N6S may be expressed by bivalent and trivalent cations: (Mg²⁺)₄(Al³⁺)₁₈O₃₀(OH)₂. The simplified general formula for the 6N6S polysomes in the nigerite and högbomite groups can be given as A _x B_18-x O₃₀(OH)₂, x?=?~4, where A?=?Mg²⁺, Fe²⁺, Zn²⁺; B?=?Al³⁺, Sn⁴⁺, Ti⁴⁺, Li⁺, □.     

Mantle heat drives hydrothermal fluids responsible for carbonate-hosted base metal deposits: evidence from 3He/4He of ore fluids in the Irish Pb-Zn ore district

There is little consensus on whether carbonate-hosted base metal deposits, such as the world-class Irish Zn + Pb ore field, formed in collisional or extensional tectonic settings. Helium isotopes have been analysed in ore fluids trapped in sulphides samples from the major base metal deposits of the Irish Zn-Pb ore field in order to quantify the involvement of mantle-derived volatiles that require melting to be realised, as well as test prevailing models for the genesis of the ore fields. ³He/⁴He ratios range up to 0.2 R _a, indicating that a small but clear mantle helium contribution is present in the mineralising fluids trapped in galena and marcasite. Sulphides from ore deposits with the highest fluid inclusion temperatures (~200 °C) also have the highest ³He/⁴He (>0.15 R _a). Similar ³He/⁴He are recorded in fluids from modern continental regions that are undergoing active extension. By analogy, we consider that the hydrothermal fluids responsible for the carbonate-hosted Irish base metal mineralization circulated in thinned continental crust undergoing extension and demonstrate that enhanced mantle heat flow is ultimately responsible for driving fluid convection.     

Numerical tools for geoscience computations: Semiautomatic differentiation—SD

This paper presents a differentiation method [referred to here as semiautomatic differentiation (SD)] based on generalization and extension of the Squire and Trapp formula for complex differentiation of real-valued functions. The performance of the generalized formulas for first-order derivatives is tested and compared with manual, automatic (AD), and finite difference (FD) techniques. My results show that, in terms of accuracy, the SD technique is competitive with AD, and in terms of implementation simplicity, it is identical to the FD method with the added advantage of being step-size insensitive and, hence, free from the step-size dilemma that plagues FD. Using central differencing in the complex plane, I extend the SD method to second-order derivatives, thus enabling approximation of the Hessians. Performance of the extension formulas is evaluated and compared with AD and FD methods. The results indicate that the differencing operation reduces the accuracy of the extension formulas by four to five orders of magnitude below that of the original Squire and Trapp formula. Nonetheless, compared to FD schemes, the SD method is six to seven orders of magnitude more accurate in all tests conducted. In addition, the extension formulas exhibit step-size (h) insensitive behavior over the entire h-range of the tests (1–10⁻³⁰), indicating high numerical stability of the schemes. I show by examples that SD provides a complete differentiation system that is computationally stable, efficient, highly accurate, and easy to implement.     

Optimal methods for estimating kinetic isotope effects from different forms of the Rayleigh distillation equation

The interpretation of stable isotope values hinges on precise, accurate estimates of kinetic isotope effects (α), which are equal to ¹k/²k, where ¹k and ²k are the reaction rate constants for the two isotopes. Kinetic isotope effects are commonly determined by monitoring the reactant concentration (C) and isotope ratio (R) relative to their initial values (C₁ and R₁, respectively). Values of α are estimated from the C and R values by using the Rayleigh distillation equation (RDE).

(A)     

Stable carbon and oxygen isotope fractionation in bivalve (Placopecten magellanicus) larval aragonite

The relationship between stable isotope composition (δ¹³C and δ¹⁸O) in seawater and in larval shell aragonite of the sea scallop, Placopecten magellanicus, was investigated in a controlled experiment to determine whether isotopes in larval shell aragonite can be used as a reliable proxy for environmental conditions. The linear relationship between δ¹³C_DIC and δ¹³C_aragonite (r² = 0.97, p < 0.0001, RMSE = 0.18) was:

δ¹³C_DIC=1.15(±0.05)∗δ¹³C_aragonite-0.85(±0.04)     

Apparent solubilities of schwertmannite and ferrihydrite in natural stream waters polluted by mine drainage

The apparent solubilities of schwertmannite and ferrihydrite were estimated from the H⁺, OH⁻, Fe³⁺, and SO₄²⁻ activities of the natural stream waters in Korea and mine drainage in Ohio, USA. Both chemical composition of the stream waters and the mineralogy of the precipitates were determined for samples from two streams polluted by coal mine drainage. This study combines these new results with previous data from Ohio, USA to redetermine solubilities. The activities of the dissolved species necessary for the solubility determinations were calculated from the chemical compositions of the waters with the WATEQ4F computer code.Laboratory analyses of precipitates indicated that the main minerals present in Imgok and Osheep creek were schwertmannite and ferrihydrite, respectively. The schwertmannite from Imgok creek had a variable chemical formula of Fe₈O₈(OH)_8−2x(SO₄)_x· nH₂O, where 1.74 ≤ x ≤ 1.86 and 8.17 ≤ n ≤ 8.62. The chemical formula of ferrihydrite was Fe₂O₃· 1.6H₂O. With known mineralogy of the precipitates from each stream, the activities of H⁺, OH⁻, Fe³⁺, and SO₄²⁻ in the waters were plotted on logarithmic activity-activity diagrams to determine apparent solubilities of schwertmannite and ferrihydrite. The best estimate for the logarithm of the solubility product of schwertmannite, logK_s, was 10.5 ± 2.5 around 15°C. This value of logK_s constrains the logarithm of the solubility product of ferrihydrite, logK_f, to be 4.3 ± 0.5 to maintain the stability boundary with schwertmannite observed in natural waters.