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1.
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. 相似文献
2.
Abdulwahab A. Abokhodair 《Computational Geosciences》2007,11(4):283-296
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. 相似文献
3.
Michele Zema Mark D. Welch Roberta Oberti 《Contributions to Mineralogy and Petrology》2012,163(5):923-937
The thermoelastic behaviour of a natural gedrite having the crystal-chemical formula ANa0.47
B(Na0.03 Mg1.05 Fe0.862+ Mn0.02 Ca0.04) C(Mg3.44 Fe0.362+ Al1.15 Ti0.054+) T(Si6.31 Al1.69)O22
W(OH)2 has been studied by single-crystal X-ray diffraction to 973 K (Stage 1). After data collection at 973 K, the crystal was heated to 1,173 K to induce dehydrogenation, which was registered by significant
changes in unit-cell parameters, M1–O3 and M3–O3 bond lengths and refined site-scattering values of M1 and M4 sites. These changes and the crystal-chemical formula calculated from structure refinement show that all Fe2+ originally at M4 migrates into the ribbon of octahedrally coordinated sites, where most of it oxidises to Fe3+, and there is a corresponding exchange of Mg from the ribbon into M4. The resulting composition is that of an oxo-gedrite with an inferred crystal-chemical formula ANa0.47
B(Na0.03 Mg1.93 Ca0.04) C(Mg2.56 Mn0.022+ Fe0.102+ Fe1.223+ Al1.15 Ti0.054+) T(Si6.31 Al1.69) O22
W[O1.122− (OH)0.88]. This marked redistribution of Mg and Fe is interpreted as being driven by rapid dehydrogenation at the H3A and H3B sites, such that all available Fe in the structure orders at M1 and M3 sites and is oxidised to Fe3+. Thermoelastic data are reported for gedrite and oxo-gedrite; the latter was measured during cooling from 1,173 to 298 K
(Stage 2) and checked after further heating to 1,273 K (Stage 3). The thermoelastic properties of gedrite and oxo-gedrite are compared with each other and those of anthophyllite. 相似文献
4.
H. B. Poorooshasb 《Computers and Geotechnics》1985,1(3):195-205
A simple numerical procedure for the solution of the non-linear differential equation is presented. Such an equation with the appropriate boundary conditions is often encountered in the analysis of piles subjected to lateral loads and bending moments. The method is suitable for application using a microcomputer of limited memory capacity and the extension of the procedure to cover the solution to the equation 4+f(u, y) = 0 which governs the mode of deformation of slab-on-grades is possible and straight-forward. 相似文献
5.
The paper studies the propagation of Rayleigh waves in an incompressible layer with general variation of rigidity as μ=μ0(1+bz)m resting over a homogeneous incompressible elastic half-space. Instead of using the Whittaker function, the expansion formula proposed by Newlands has been used for better results at shallow depths. As a particular case for m=1, the results have been shown to coincide with those obtained by Newlands. The velocities have been computed for different values of m and the results are presented in graphs. 相似文献
6.
Hornblende Ar/Ar geochronology across terrane boundaries in the Sveconorwegian Province of S. Norway
Bernard Bingen Ariel Boven Lea Punzalan Jan R. Wijbrans Daniel Demaiffe 《Precambrian Research》1998,90(3-4)
Hornblende incremental heating 40Ar/39Ar data were obtained from augen gneiss and amphibolite of the Sveconorwegian Province of S. Norway. In the Rogaland-Vest Agder and Telemark terranes, four pyroxene-rich samples, located close (≤ 10 km) to the anorthosite-charnockite Rogaland Igneous Complex, define an age group at 916 + 12/ − 14 Ma and six samples distributed in the two terranes yield another group at 871 + 8/ − 10 Ma. The first age group is close to the reported zircon U---Pb intrusion age of the igneous complex (931 ± 2 Ma) and the regional titanite U---Pb age (918 ± 2 Ma), whereas the second group overlaps reported regional mineral Rb---Sr ages (895-853 Ma) as well as biotite K---Ar ages (878-853 Ma). In the first group, the comparatively dry parageneses of low-P thermal metamorphism (M2) associated with the intrusion of the igneous complex are well developed, and hornblende 40Ar/39Ar ages probably record a drop in temperature shortly after this phase. In other hornblende + biotite-rich samples, with presumably a higher fluid content, the hornblende ages are probably a response to hornblende-fluid interaction during a late Sveconorwegian metamorphic or hydrothermal event. A ca 220 m.y. diachronism in hornblende 40Ar/39Ar ages is documented between S. Telemark (ca 870 Ma) and Bamble (ca 1090 Ma). Differential uplift between these terranes was mostly accommodated by shearing along the Kristiansand-Porsgrunn shear zone. The final stage of extension along this zone occurred after intrusion of the Herefoss post-kinematic granite at 926 ± 8 Ma. On the contrary, the southern part of the Rogaland-Vest Agder and Telemark terranes share a common cooling evolution as mineral ages are similar on both sides of the Mandal-Ustaoset Line the tectonic zone between them. The succession within 20 m.y. of a voluminous pulse of post-tectonic magmatism at 0.93 Ga, a phase of high-T-low-P metamorphism at 0.93-0.92 Ga, and fast cooling at a regional scale ca 0.92 Ga, suggests that the southern parts of Rogaland-Vest Agder and Telemark were affected by an event of post-thickening extension collapse at that time. This event is not recorded in Bamble. 相似文献
7.
8.
基于相机摄影测量的冰面反照率反演方法研究 总被引：1，自引：1，他引：0
雪冰反照率是冰川与积雪能量平衡计算的关键参数,也是观测的难点. 为测量冰面反照率,试验采用相机摄影测量技术,在祁连山十一冰川开展了自动拍摄、并利用共线方程进行冰川正射制图,在此基础上于2012年7月28日-8月18日在冰川表面开展了不同海拔梯度的反照率观测. 通过统计分析晴天与阴天观测反照率与对应点相机拍摄获取的RGB归一化指数之间的关系,对十一冰川进行冰面反照率参数化方法研究. 结果表明：晴天冰面反照率与RGB归一化指数存在明显的指数关系,拟合R2达到0.79;而阴天的统计关系较差,线性拟合R2仅为0.52. 据此尝试利用晴天的拟合公式对整个冰面进行反照率参数化,计算表明：在晴天冰川表面地形阴影区的反照率存在低估现象,而无阴影区的反照率估算结果可信度较高. 利用2013年的反照率观测数据进行了参数化方案的验证,结果表明：观测值与模拟值平均误差仅为0.037,表明利用RGB影像对反照率参数化具有一定的可用性和可靠性. 相似文献
9.
C. F. Woensdregt 《Physics and Chemistry of Minerals》1992,19(1):59-69
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 (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 (
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 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. 相似文献
10.
ABSTRACT Active and remnant back-arc regions do not follow a typical conductive lithosphere cooling model, but instead have an apparent two-stage cooling, defined by a high heat flow back-arc region during subduction and a second post-subduction heating event that extends elevated heat flow for several 10s million years. Numerical one-stage cooling models have not reproduced observed heat flow anomalies in active subduction zones using physically realistic parameters and require a secondary post-subduction heating mechanism. Here, an extension driven-volcanism model is developed to examine extension driven heating and volcanism as a mechanism to produce a prolonged thermal anomaly within back-arc lithosphere. This model is tested using the recorded thermal evolution of the Northern Cordillera Volcanic Province (NCVP), a Neogene-Quaternary alkaline volcanic province located in the remnant back-arc region of the Pacific-North American subduction zone in British Columbia, Canada. A single steady-state lithosphere geotherm does not intersect all previously published temperature estimates, suggesting previous data record the thermal evolution of the NCVP. Calculated geotherms at equilibrium with the minimum and maximum MELTS temperatures predict an increase in reduced mantle heat flow (Qm ) from 43 to 72 mW/m2 and lithosphere thinning from a depth of 87 to 48 km. The newly developed extension-volcanism model reproduced the calculated pre- and post-volcanism thermal regimes for the NCVP and supports that extension within the remnant back-arc could produce the present heat flow anomaly and volcanism. The model most readily produces volcanism when Qm is ~45–65 mW/m2, a typical range for back-arcs. Back-arc regions are prime locations for limited volcanism because their warmer thermal regime minimizes tectonic stress requirements to produce volcanism. Additionally, two-stage cooling of back-arcs can be explained with a time-dependent extension-volcanism thermal feedback mechanism that is possible because of the subduction driven pre-heating of back-arc regions. 相似文献
11.
This paper is an extension of the earlier one dealing with kyanite in which the best fitting value of the oxygen ligand distance for Cr3+ is adopted to study the spectroscopic properties of Cr3+ ions doped at the two possible Al sites in the other two polymorphs of the aluminosilicate group (Al2O3 · SiO2), namely, andalusite and sillimanite. The superposition model and the crystal field analysis package recently developed for 3d ions doped at arbitrary low symmetry sites in crystals are used to predict energy levels and statevectors within the whole 3d
3 configuration. Then the values of the ground state zerofield splitting for Cr3+ ions at each Al sites in the two crystals are obtained. The splittings of the lower excited states 2
E and 4
T
2 as well as the admixture of 4
T
2 into 2
E have also been predicted. Comparison of our results with the available experimental data enable us to correlate the optical and EPR Spectroscopic properties with the substitutional Cr3+ sites. The conclusion is that in andalusite and sillimanite only the Al sites with nearly-octahedral six-fold coordination seem to be occupied by Cr3+ ions. 相似文献
12.
Tourmaline with the general formula XY3Z6(BO3)3Si6O18(OH,O)3(OH,F) and the trigonal space group R3m (C3v5) is known as a gemstone with great variety of colors. Some color centers are related to transition metal ions, and others to electron or hole traps. In this paper we report on a combined study using electron paramagnetic resonance (EPR), electron nuclear double resonance (ENDOR), and the optical detection of EPR (ODEPR) on a yellow color center produced by -irradiation in colorless Li-bearing elbaite tourmaline from Brazil. The color center is an O– hole trap center, which is stabilized within the plane spanned by three Y sites, and is located in the structural channels formed by Si6O18. We suggest that two of the Y sites are substituted by 27Al and the other by 6,7Li. During the irradiation process atomic hydrogen H0 is also produced, which shows the same thermal stability as the hole center (250 °C). Therefore, we assign H0 to be the local charge compensator for the hole trap. From the ODEPR measurements we conclude that the yellow color is caused by the O– hole center. The large negative isotropic Al superhyperfine interaction of the O– hole trap center is consistent with a calculation of the transferred hyperfine interactions by exchange polarization supporting the proposed defect model of an O– at the O1 sites, whereby the O– is relaxed into the plane formed by three Y ions. 相似文献
13.
Kyle P. Larson Dawn A. Kellett John M. Cottle Alfredo Camacho Alex D. Brubacher 《地学学报》2020,32(2):151-158
The Tibetan plateau is host to numerous ~N‐S striking graben that have accommodated E‐W directed extension. The development of these structures has been interpreted to reflect a variety of different geological processes including plateau collapse, oroclinal bending or mid‐to‐lower crustal flow. New 40Ar/39Ar thermochronology and quartz c‐axis data from the Thakkhola graben of west‐central Nepal show that E‐W extension was ongoing at least locally by the early Miocene (ca. 17 Ma). Our new, and previously published chronologic information on the initiation of graben across the orogen shows that they typically developed immediately after cessation of the South Tibetan detachment system, a structural network that facilitated differential southward movement of the upper and middle crust. We interpret this fundamental switch in orogen kinematics to reflect recoupling of the middle and upper Himalayan crust such that the subsequent widespread flow of the mid‐to‐lower crust out of the system to the east forced brittle accommodation in the upper crust. 相似文献
14.
It was not possible to carry out a complete analyses of crystal, as the experiment by Ding and Shi et al.. It's analysis precision R=0.25 or more big than this, which value are not satisfied for single crystal study, but we through many test and found the best: [R(int)=14.5%]. The final fullmatix least-squares refinement on F2 converged to R1=0.0791 and wR2=0.1864 for 704 observed reflections [I 3 2s(I)]. Daomanite is orthorhombic system, space group Cmc21, a=3.7520(8))?, b=15.844(4) ?, c=5.8516(12) ?, α=β=γ=90°. V=347.86(14)?3, Z=4. Daomanite chemical formula is Cu Pt AsS 2. Idealized composition Me+M2+M2+S2=CuS ·PtA s S. There is no other similar mineral in the world. 相似文献
15.
Accuracy of predicting pile capacities by pile driving formulas have been investigated. Five test piles were driven up to
a depth of about 9 m of clay deposit and the penetrations due to final blows were recorded. The pile bearing capacity of each
pile was predicted using 6 different pile driving formulas and the predicted pile capacity was compared with measured pile
capacity from the pull up tests. Hiley formula, Modified Engineering News Record (ENR) formula, Janbu formula, Dutch formula,
Danish formula, and Gates formula were used. The performance and accuracy of each formula was evaluated and the correlation
coefficient of each pile driving formula was determined for a more accurate pile capacity prediction. Methods used to evaluate
the performance of each formula were; (1) the best fit line for Q
p versus Q
m (2) cumulative probability for Q
p/Q
m and (3) the arithmetic mean and standard deviation for Q
p/Q
m. From the study, it was found that using Dutch formula provided the most accurate pile capacity estimate compared to the
other formulas with an average of 7% deviation from value obtained from the field pull up test. It was followed by the Danish
formula, Janbu formula, Hiley formula, Modified ENR formula, and Gates formula. The ability to predict the accuracy of estimating
pile capacity using an appropriate method is very important and valuable to contractors, developers, geotechnical engineers,
and manufacturers. 相似文献
16.
I. E. Paukov N. K. Moroz Yu. A. Kovalevskaya I. A. Belitsky 《Physics and Chemistry of Minerals》2002,29(4):300-306
The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured
in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented
with the formula (Na1.90K0.22Ca0.06)[Al2.24Si2.76O10]·nH2O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function)
have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K−1 mol−1 for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K−1 mol−1 for tetranatrolite.
Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework
cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two
extraframework cations per formula yields: C
p
(298.15)=359.1 J K−1 mol−1, S(298.15) −S(0)=362.8 J K−1 mol−1. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral
atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated
zeolite may become unstable at temperatures above 200 K.
Received: 30 July 2001 / Accepted: 15 November 2001 相似文献
17.
Based on the theory of thermal conductivity, in this paper we derived a formula to estimate the prolongation period （AtL） of cooling-crystallization process of a granitic melt caused by latent heat of crystallization as follows：△tL=QL×△tcol/（TM-TC）×CP where TM is initial temperature of the granite melt, Tc crystallization temperature of the granite melt, Cp specific heat, △tcol cooling period of a granite melt from its initial temperature （TM） to its crystallization temperature （Tc）, QL latent heat of the granite melt.
The cooling period of the melt for the Fanshan granodiorite from its initial temperature （900℃） to crystallization temperature （600℃） could be estimated -210,000 years if latent heat was not considered. Calculation for the Fanshan melt using the above formula yields a AtL value of -190,000 years, which implies that the actual cooling period within the temperature range of 900°-600℃ should be 400,000 years. This demonstrates that the latent heat produced from crystallization of the granitic melt is a key factor influencing the cooling-crystallization process of a granitic melt, prolongating the period of crystallization and resulting in the large emplacement-crystallization time difference （ECTD） in granite batholith. 相似文献
The cooling period of the melt for the Fanshan granodiorite from its initial temperature （900℃） to crystallization temperature （600℃） could be estimated -210,000 years if latent heat was not considered. Calculation for the Fanshan melt using the above formula yields a AtL value of -190,000 years, which implies that the actual cooling period within the temperature range of 900°-600℃ should be 400,000 years. This demonstrates that the latent heat produced from crystallization of the granitic melt is a key factor influencing the cooling-crystallization process of a granitic melt, prolongating the period of crystallization and resulting in the large emplacement-crystallization time difference （ECTD） in granite batholith. 相似文献
18.
The Jiashan Syenite in northern Hebei: A record of lithospheric thinning in the Yanshan Intracontinental Orogenic Belt 总被引：1，自引：0，他引：1
Fu-quan Yang Hai Wu Franco Pirajno Bo-yong Ma Hao-dong Xia Hui-juan Deng Xiao-wen Liu Gang Xu Yue Zhao 《Journal of Asian Earth Sciences》2007,29(5-6):619-636
The Early Cretaceous Jiashan Syenite is located in a region of late Jurassic crustal thickening. The Jiashan Syenite can be divided into three concentrically arranged units, the Jiangjiawan, Longtangou and Longtannangou units, which were intruded sequentially. Geochemically, the Jiashan Syenite has a high Ga/Al ratio (>3), is enriched in silica, alkalis, Fe, REE, Th, Ga, Nb, Zr and Hf, is depleted in Mg, Ba, Sr and Ti and in transition elements such as Cr, Co, Ni and V. The three units of the Jiashan Syenite have Ce/Pb ratios ranging from 6.12 to 13.41 and are enriched in light REE (LREE) with a moderate Eu negative anomaly. The 87Sr/86Sr initial ratios range from 0.701409 to 0.707405, with a mean of 0.70379. The εNd (t) values of −2.27 to −5.58 indicate that the magma was probably derived from enriched mantle. The Jiashan Syenite is a post-orogenic intrusion, and can be considered to be an A-type granite. It was emplaced in an environment of lithospheric extension during asthenospheric mantle upwelling. This suggests that the regional compressional shortening and crustal thickening tectonic regime in the Yanshan Orogenic Belt during the Late Jurassic (ca. 135 Ma) changed to lithospheric extension and thinning in the Early Cretaceous. 相似文献
19.
R. AUGIER P. AGARD P. MONIÉ L. JOLIVET C. ROBIN G. BOOTH-REA 《Journal of Metamorphic Geology》2005,23(5):357-381
The combination of metamorphic petrology tools and in situ laser 40Ar/39Ar dating on phengite (linking time of growth, compositions and P–T conditions) enables us to identify a detailed P–T–d–t path for the still debated tectonometamorphic evolution of the Nevado‐Filabride complex and infer new geodynamic‐scale constraints. Our data show an isothermal decompression (at 550 °C) from 20 kbar for the Bédar‐Macael unit and 14 kbar for the Calar Alto unit down to c. 3–4 kbar for both units at 2.8 mm year?1. At 22–18 Ma, this first part of the exhumation is followed by a final exhumation at 0.6 mm year?1 along a high‐temperature low‐pressure (HTLP) gradient of c. 60 °C km?1. The age of the peak of pressure is not precisely known but it is shown that it is around 30 Ma and possibly older, which is at variance with recent models suggesting a younger age for high‐pressure (HP) metamorphism. Most of the exhumation is related to late‐orogenic extension from c. 30 to 22–18 Ma. Thus the formation of the main ductile extensional shear zone, the Filabres Shear Zone (FSZ), occurred at 22–18 Ma and is clearly associated with a top‐to‐the‐west shear sense once the FSZ is well localized. The transition from ductile to brittle then occurred at c. 14 Ma. The final exhumation, accommodated by brittle deformation, occurred from c. 14 to 9 Ma and was accompanied, from 12 to 8 Ma, by the formation of nearby extensional basins. The duration of the extensional process is c. 20 Myr which argues in favour of a progressive slab retreat from c. 30 to 9 Ma. The change in the shape of the P–T path at 22–18 Ma together with strain localization along the main top‐to‐the‐west shear zone suggests that this date corresponds to a change in the direction of slab retreat from southwards to westwards. 相似文献
20.
Many folds of both deformation phases on Söröy exhibit a prominent lineation brought out by elongate micas or spindleform-quartz grains. This lineation displays a variety of patterns, depending on ils orientation relative to the fold axis. This dependence confirms the primary nature of the axial noncy lindrism.The lineation is a product of layer-parallel extension and represents the long axis of the sectional strain ellipse (X1), for the particular attitude of the layering. The formation of the lineation is confined to those layer orientations which cut the extension field of the strain ellipsoid. If the noncylindrical fold axes curve from normal into parallelism with the lineation, the patterns of lineation orientation developed will reveal the attitude of the major extension axis (X) and indicate the nature of the strain.The lineation developed in the earlier stages of fold growth and became a passive marker in later fold modification.The regional pattern of the lineation is similar to that for minor fold axes, and together they are held to identify the XY-plane of the bulk finite strain-field. 相似文献