绿洲防护林系统的最优控制模式及其应用研究   总被引：3，自引：0，他引：3  

李自珍  程国栋  惠苍 《地球科学进展》2002,17(1):27-32

以河西地区绿洲防护林系统为研究对象，分析了防护林资源分布的时空特征及建群种的增长动态，运用生物控制理论，构建了防护林区生物资源管理的最大持续产量模型、生态经济意义下的最优控制模型及多资源种群控制模型。根据有关模型和试验观测结果，确定了防护林建群种的资源保护指标、生态经济意义下的最优种群水平和人工调控措施。该防护林主要建群种二白杨胸径的保护指标为 k/2＝18．22cm，在不同成本与价格比下计算了主要建群种二白杨胸径指标的个最优控制量。估算了防护林系统的生态需水量，其中农田生态需水量为 1 796 m³/hm²，固沙林和阻沙防护林生态需水量为57 100m³/hm²，并提出了相应的持续发展对策。  相似文献   

Behaviors of trace elements and relationships between the compositions of solid phase and melt during fractional crystallization     

Zhu Zhenhua 《中国地球化学学报》1988,7(4):336-347

Given r_i =f _i(F) andK _i = g_i(F), wherer _i is the mineral mass fraction in an instantaneous solid phase,K _i the partition coefficient, andf _i(F) andg _i(F) respectively the continuous, sectionally smooth functions of solidification degreeF, we have: $$C^1 = \frac{{C_0 }}{{1 - F}} \cdot \exp \left( { - \int_0^F {\frac{{\Sigma fi(F) \cdot g_i (F)}}{{1 - F}} \cdot dF} } \right)and \bar C^s = \frac{{C_o }}{F}\left[ {1 - (1 - F) \cdot \frac{{C^1 }}{{C^0 }}} \right]$$ Also presented in this paper are other equations describing the compositional changes of solid and liquid phases in magmatic processes (partial melting). The following understanding is attained based on the application of these equations to the Hushan pluton of Mt. Taishan in the west of Shandong Province. 1) For granitoids changes in rock-forming minerals may not be taken into consideration in theoretical modelling of REE distribution, but accessory minerals rich in REE, especially those highly rich in some REE must be taken into account. 2) In the case of well differentiated granitoids, it can be assumed thatFε [0,1] may exert only little influence on the calculations. 3) In practice the (La / Sm)-La diagram should be applied with care.  相似文献   

遥感与GIS技术支持下的湖北省生态环境综合分析   总被引：30，自引：0，他引：30  

王思远  张增祥  赵晓丽  周全斌 《地球科学进展》2002,17(3):426-431

在遥感与地理信息系统技术支持下，应用主成分分析法对湖北省全省生态环境质量状况进行了综合评价，得出了湖北省全省生态环境质量状况分级图。在定义生态环境背景指数和土地资源利用程度指数的基础上，通过生成生态环境背景图和土地利用程度图，分析了生态环境背景与土地利用程度的关系，通过相关分析证明土地资源利用程度与生态环境背景有着明显的相关关系，生态环境的好坏决定了土地资源利用程度的高低。同时，对湖北省生态环境演变机制及其驱动因子进行了一些探讨。  相似文献   

An Empirical Failure Criterion for Intact Rocks   总被引：1，自引：1，他引：0  

Jun Peng  Guan Rong  Ming Cai  Xiaojiang Wang  Chuangbing Zhou 《Rock Mechanics and Rock Engineering》2014,47(2):347-356

The parameter m _i is an important rock property parameter required for use of the Hoek–Brown failure criterion. The conventional method for determining m _i is to fit a series of triaxial compression test data. In the absence of laboratory test data, guideline charts have been provided by Hoek to estimate the m _i value. In the conventional Hoek–Brown failure criterion, the m _i value is a constant for a given rock. It is observed that using a constant m _i may not fit the triaxial compression test data well for some rocks. In this paper, a negative exponent empirical model is proposed to express m _i as a function of confinement, and this exercise leads us to a new empirical failure criterion for intact rocks. Triaxial compression test data of various rocks are used to fit parameters of this model. It is seen that the new empirical failure criterion fits the test data better than the conventional Hoek–Brown failure criterion for intact rocks. The conventional Hoek–Brown criterion fits the test data well in the high-confinement region but fails to match data well in the low-confinement and tension regions. In particular, it overestimates the uniaxial compressive strength (UCS) and the uniaxial tensile strength of rocks. On the other hand, curves fitted by the proposed empirical failure criterion match test data very well, and the estimated UCS and tensile strength agree well with test data.  相似文献   

Extension of the empirical Alyavdin equation for representing batch grinding data     

L.G Austin  K Shoji  V.K Bhatia  F.F Aplan 《International Journal of Mineral Processing》1974,1(2):107-123

The Alyavdin equation for batch grinding data is: where P(χ,t) is the weight fraction less than size χ after grinding time t, c (χ) is constant with t and p is a constant close to one. It is shown that this equation is illogical (except for a single size of feed) unless c (χ) varies with P(χ,0), which makes the equation of little utility. A new empirical equation is developed for finite size intervals: which reduces to the Alyavdin equation for a single size of feed, and which gives consistent computations for any feed size distribution. Techniques are given for determining K_i, γ values from sets of batch grinding data. The values are then used to predict size distributions for other times and other feed size distributions. The equation was quite successful in predicting size distributions in batch milling: (a) providing the feed size distribution was not un-natural, that is, not truncated or (b) if a truncated feed was used, the values of K_i and γ are determined from size distributions of grinding of the same type of feed. Thus, K_i, γ are not, unfortunately, completely independent of the starting feed size distribution.  相似文献   

Amorphous silica solubilities V. Predictions of solubility behavior in aqueous mixed electrolyte solutions to 300°C     

William L Marshall  Chen-Tung A Chen 《Geochimica et cosmochimica acta》1982,46(2):289-291

Solubilities of amorphous silica in several aqueous electrolyte solutions up to 300°C (Marshall, 1980a; Chen and Marshall, 1982) fitted the Setchénow equation, $\text{log(}\text{s}{}^0\text{s}\text{) = D·m}$ as described earlier (Marshall, 1980b) where s⁰ and s are molal solubilities of silica in pure water and salt solution, respectively, m is the molality of salt, and D is a proportionality constant related to the particular salt and temperature. It is now shown that, to a first approximation, the D parameters for various salts at the same temperature are additive. For instance, D(NaCl) ? D(KCl) = D(NaNO₃) ? D(KNO₃) or D(MgSO₄) = D(MgCl₂) + D(Na₂S0₄) ? 2D(NaCl). It also follows that $\text{(}\text{s}{}_0\text{s}\text{) =}\text{∑}\text{i}\text{(D}{}_{\mathrm{i}}\text{m}{}_{\mathrm{i}}\text{)}$.This additivity principle was used to estimate amorphous silica solubilities in mixed NaCl-Na₂SO₄, NaCl-MgCl₂, NaCl-MgSO₄, Na₂SO₄-MgCl₂, Na₂SO₄-MgSO₄, and MgCl₂-MgSO₄ aqueous solutions up to 300°C. The method produces results that agree reasonably well with experimental values and would be useful for predicting silica solubilities, for example, in seawater and its hydrothermal concentrates and in geothermal energy applications.  相似文献   

Pyroxene-melt equilibria: an updated model     

Roger L. Nielsen  Paula M. Davidson  Timothy L. Grove 《Contributions to Mineralogy and Petrology》1988,100(3):361-373

An updated model for pyroxene-melt equilibria at 1 atm has been developed and calibrated using new and existing experimental data in order to refine calculations of liquid lines of descent, which simulate the effect of igneous differentiation processes. We combine the Davidson and Lindsley (1985) model for activities of components in clinopyroxene and orthopyroxene solid solutions, a _i ^p , where i represents a quadrilateral endmember, with the Nielsen and Drake (1979) expressions for component activities in the melt, a _i ^L (two-lattice melt model). The chemical potential differences for pyroxene-melt equilibria are expressed in the form: $$\Delta \mu _{\iota } = 0 = In \left( {{{a_i^p } \mathord{\left/{\vphantom {{a_i^p } {a_i^L }}} \right.\kern-\nulldelimiterspace} {a_i^L }}} \right) + A_i + {{B_i } \mathord{\left/{\vphantom {{B_i } T}} \right.\kern-\nulldelimiterspace} T}$$ Pyroxene compositions were projected to quadrilateral compositions with the method of Lindsley and Anderson (1983). The regression constants A _i and B _i were calculated from experimental data that consists of 282 pyroxene-melt pairs, including 83 orthopyroxene-melt pairs. These experiments were all performed at 1 atm and represent compositions ranging from basalts (alkali to lunar) to dacites (42–66 wt% SiO₂). The model is calibrated for 1000相似文献   

The solubility of noble gases in water and in NaCl brine     

S.P. Smith  B.M. Kennedy 《Geochimica et cosmochimica acta》1983,47(3):503-515

A direct-sampling, mass-spectrometric technique has been used to measure simultaneously the solubilities of He, Ne, Ar, Kr, and Xe in fresh water and NaCl brine (0 to 5.2 molar) from 0° to 65 °C, and at 1 atm total pressure of moist air. The argon solubility in the most concentrated brines is 4 to 7 times less than in fresh water at 65 °C and 0°C, respectively. The salt effect is parameterized using the Setschenow equation. where M is NaCl moiarity, βⁱ_o(T) and βⁱ(T) the Bunsen solubility coefficients for gas i in fresh water and brine, and Kⁱ_M(T) the empirical salting coefficient. Values of Kⁱ_M(T) are calculated using volumetric concentration units for noble gas and NaCl content and are independent of NaCl molarity. Below about 40°C, temperature coefficients of all Kⁱ_M are negative. The value of K^He_M is a minimum at 40°C. K^Ar_M decreases from about 0.40 at 0°C to 0.28 at 65 °C. The absolute magnitudes of the differences in salting coefficients (relative to K^Ar_M) decrease from 0° to 65°C. Over the range of conditions studied, all noble gases are salted out, and K^He_M ? K^Ne_M < K^Ar_M < K^Kr_M < K^Xe_M.From the solubility data, we calculated $\text{Δ}\text{G}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{H}{}^0{}_{\mathrm{tr}}$ and $\text{Δ}\text{C}{}^{\mathrm{O}}{}_{\mathrm{p,tr}}$ for the transfer of noble gases from fresh water to 1 molar NaCl solutions. At low temperatures $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, is positive, but decreases and becomes negative at temperatures ranging from about 25°C for He to 45°C for Xe. At low temperatures, the dissolved electrolyte apparently interferes with the formation of a cage of solvent molecules about the noble gas atom. At higher temperatures, the local environment of the gas atom in the brine appears to be slightly more ordered than in pure water, possibly reflecting the longer effective range of the ionic fields at higher temperature.The measured solubilities can be used to model noble gas partitioning in two-phase geothermal systems at low temperatures. The data can also be used to estimate the temperature and concentration dependence of the salt effect for other alkali halides. Extrapolation of the measured data is not possible due to the incompletely-characterized minima in the temperature dependence of the salting coefficients. The regularities in the data observed at low temperatures suggest relatively few high-temperature data will be required to model the behavior of noble gases in high-temperature geothermal brines.  相似文献   

Dilution and removal of dissolved metals from acid mine drainage along Imgok Creek,Korea     

《Applied Geochemistry》2001,16(9-10):1041-1053

The dilution factors (D_i) and removal fractions (R_i) of pollutants from acid mine drainage (AMD) were quantitatively estimated using two different methods, the conservative component and mass balance method, along Imgok Creek in Korea. The conservative component method assumes that SO₄ is a perfectly conservative component and calculates D_i and R_i from the concentration ratios of SO₄. The mass balance method solves the simultaneous equations relating the concentrations of dissolved components to their precipitation stoichiometries to obtain D_i and R_i. The results from both methods are little different, indicating that SO₄ concentration is a good indicator of dilution for Imgok creek. The calculated D_i's of pollutants quickly decrease from the site of AMD input to the site a few km downstream, but then remain more or less constant over the reaches farther downstream. This is because D_i loses its sensitivity in the reaches where difference in SO₄ concentration between the main stream and combining tributaries significantly diminishes. The calculated R_i's show that approximately 90, 95, and 75% of the original Fe input were removed from the streamwater in October 1996, April 1997, and October 1997, respectively. Aluminum was almost completely removed in April 1997, but only 50% of the original Al was removed in October 1997. The removal of Fe was due to the precipitation of schwertmannite or ferrihydrite and Al due to amorphous Al₄(OH)₁₀SO₄. The maximum removal fraction of dissolved SO₄ was only 5%. The other metals from AMD were significantly removed from the stream water only in April 1997. These metals were removed not by precipitation but by adsorption on and/or coprecipitation with Fe/Al-compounds. The relatively abundant freshwater supply in April 1997 might raise stream pH higher than the adsorption edge and consequently, contribute to rapid metal attenuation by forcing not only more precipitation but also more adsorption of the dissolved metals.  相似文献   

Activity coefficients of MgCO^o₃ and CaSO^o₄ ion pairs as a function of ionic strength     

Eric J Reardon  Donald Langmuir 《Geochimica et cosmochimica acta》1976,40(5):549-554

Based on potentiometric data and gypsum solubility in mixed salt solutions, respectively, the activity coefficients of MgCO^o₃ and CaSO^o₄ ion pairs decrease with ionic strength (I) at 25°C. Computed γ's for the ion pairs fit the empirical equation log γ_i = ? BI. B coefficients of 0.63 ±0.10 for MgCO^o₃ and 0.45 ± 0.15 for CaSO^o₄ are obtained from linear regression of log γ_i values vs I between 0.04 and 0.6 molal. Assumptions that the activity coefficients of these neutral ion pairs equal unity or are approximated by the Setchenow expression (log γ_i = kI) are therefore invalid at moderate ionic strengths. Log γ_i = ? BI is the same general form as the equation of Kirkwood (Chem. Rev.24, 233–251, 1939) for neutral dipoles.  相似文献   

Evolution of the orbital-plane orientations in the two-protoplanet three-body problem with variable masses     

M. Zh. Minglibayev  G. M. Mayemerova 《Astronomy Reports》2014,58(9):667-677

The three body problem with variable masses with two of the bodies being protoplanets is analyzed. The protoplanetary masses are assumed to be much less than the protosolar mass: m ₁(t) ? m ₀(t), m ₂(t) ? m ₀(t). The variations of the body masses over time are assumed to be known. The masses vary isotropically with different rates: ? ₀/m ₀≠? ₁/m ₁, ? ₀/m ₀≠? ₂/m ₂, ? ₁/m ₁≠? ₂/m ₂. The bodies are treated like material points. The problem is described by analogy to the second system of Poincaré elements, based on the equations of motion in a Jacobian coordinate system. Individual aperiodic motions in a quasi-conical cross section are used as the initial, unperturbed, intermediate motions. The expression for the perturbing function does not include terms proportional to third and higher powers of the small masses m ₁ and m ₂. A new analytical expression for the perturbing function analogous to the second system of the Poincaré variables is obtained in the formulation considered using a classical scheme. The analogs of the eccentricities e ₁ and e ₂ and the orbital inclinations i ₁ and i ₂ are considered to be small. The perturbing function accurate to within terms of second order in the small quantities e ₁, e ₂, i ₁, and i ₂ is calculated in a symbolic form using Mathematica package. The equations for the secular perturbations in this protoplanetary three-body problem, with the bodies treated as points with masses varying isotropically with different rates, are obtained. General rigorous analytical solutions to these equations for the secular perturbations describing the evolution of the orbital planes are derived for oblique elements, for arbitrary mass-variation laws. An analog of the Laplace theorem is proved for the orbital inclinations. Analytical formulas are obtained for the temporal variation of the longitudes of the ascending nodes and the inclinations for arbitrary mass variations with different rates. It is shown that the Jacobian node theorem, which is valid in the classical three-body problem with constantmasses, is violated in this problem, unless special initial conditions apply.  相似文献   

Empirical models relating viscosity and tracer diffusion in magmatic silicate melts   总被引：2，自引：0，他引：2  

James E. Mungall 《Geochimica et cosmochimica acta》2002,66(1):125-143

The Adam-Gibbs equations describing relaxation in silicate melts are applied to diffusion of trace components of multicomponent liquids. The Adam-Gibbs theory is used as a starting point to derive an explicit relation between viscosity and diffusion including non-Arrhenian temperature dependence. The general form of the equation is D_iη = A_iexp{Δ(s_cE_i)/TS_c}, where D is diffusivity, η is melt viscosity, T is absolute temperature, Δ(s_cE_i) is the difference between the products of activation energies and local configurational entropies for viscous and diffusive relaxation, A_i is a constant that depends on the characteristics of the diffusing solute particles, and S_c is configurational entropy of the melt. The general equation will be impractical for most predictive purposes due to the paucity of configurational entropy data for silicate melts. Under most magmatic conditions the proposed non-Arrhenian behaviour can be neglected, allowing the general equation to be simplified to a generalized form of the Eyring equation to describe diffusion of solutes that interact weakly with the melt structure: D_iη/T = Q_iexp{ΔE_i/RT}, where Q_i and ΔE_i depend on the characteristics of the solute and the melt structure. If the diffusing solute interacts strongly with the melt structure or is a network-forming cation itself, then ΔE_i = 0, and the relation between viscosity and diffusion has the functional form of the classic Eyring and Stokes-Einstein equations; D_iη/T = Q_i. If the diffusing solute can make diffusive jumps without requiring cooperative rearrangement of the melt structure, the diffusivity is entirely decoupled from melt viscosity and should be Arrhenian, i.e., D_i = Q_iexp{B_i/T}. A dataset of 594 published diffusivities in melts ranging from the system CAS through diopside, basalt, andesite, anhydrous rhyolite, hydrous rhyolite, and peralkaline rhyolite to albite, orthoclase, and jadeite is compared with the model equations. Alkali diffusion is completely decoupled from melt viscosity but is related to melt structure. Network-modifying cations with field strength Z_i²/r between 1 and 10 interact weakly with the melt network and can be modelled with the extended form of the Eyring equation. Diffusivities of cations with high field strength have activation energies essentially equal to that of viscous flow and can be modelled with a simple reciprocal Eyring-type dependence on viscosity. The values of Q_i, ΔE_i and B_i for each cation are different and can be related to the cation charge and radius as well as the composition of the melt through the parameters Z_i²/r, M/O, and Al/(Na + K + H). I present empirical fit parameters to the model equations that permit prediction of cation diffusivities given only charge and radius of the cation and temperature, composition and viscosity of the melt, for the entire range of temperatures accessible to magmas near to or above their liquidus, for magmas ranging in composition from basalt through andesite to hydrous or anhydrous rhyolite. Pressure effects are implicitly accounted for by corrections to melt viscosity. Ninety percent of diffusivities predicted by the models are within 0.6 log units of the measured values.  相似文献   

K-H₃OFe₃(SO₄)₂(OH)₆铁矾的XRD研究     

许涛  邹来昌  阮仁满  廖占丕  苏秀珠  苏妤芸  黄丽娟 《岩石矿物学杂志》2013,32(6):995-1000

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。  相似文献   

A new method of material balance evaluation in metamorphic differentiated systems     

K. R. Chakraborty 《Contributions to Mineralogy and Petrology》1977,65(1):101-110

The methods used by earlier workers for evaluating material balance in core-mantle-matrix type differentiated systems are examined in detail. It is demonstrated that these methods can be successfully employed only when the true core-mantle volume ratio is known. On geometric grounds, it is rarely possible to have a reliable estimate of this ratio from natural specimen. Consequently, the scope of balance evaluation by these methods is severely restricted. From theoretical consideration of mass transfer relations in differentiated systems, a new computational method is proposed that can be effectively employed for quantitative balance evaluation without any prior knowledge of the core-mantle volume ratio provided the chemical analyses of the core, mantle and matrix are available. This method involves the application of the following mass balance equation: $$m_1 x_1^i + m_2 x_2^i = m_0 x_0^i {\text{ (}}i = {\text{1,2}}...{\text{,}}n{\text{)}}$$ where m ₁ and m ₂ are the mass of the core and mantle respectively, m ₀ is the mass of the matrix involved in differentiation, and x ₁ ⁱ , x ₂ ⁱ , x ₀ ⁱ are the weight fractions of the component i in the core, mantle and matrix respectively. This method would also permit a quantitative estimation of the materials added to or removed from the system. Three differentiated systems previously investigated by Mehnert (1951, 1968), Loberg (1963) and Kretz (1966) are selected for balance evaluation by the proposed method and the results are compared with the published balance analyses.  相似文献   

Practical Research on Fuzzy Risk of Water Resources in Jinhua City,China     

Li-Hua Feng  Gao-Yuan Luo 《Mathematical Geosciences》2011,43(1):121-132

A fuzzy expected value of the possibility-probability distribution is a set with _boxclose(x)\underline{E}_{\alpha}(x) and [`(E)]<sub>a</sub>(x)\overline{E}_{\alpha}(x) as its boundaries. The fuzzy expected values E<sub>a</sub>(x)\underline{E}_{\alpha}(x) and [`(E)]_a(x)\overline{E}_{\alpha}(x) of a possibility-probability distribution represent the fuzzy risk values being calculated. Using these values under a given α level, three risk values can be calculated: a conservative risk value, a venture risk value, and a maximum probability risk value. Calculation of the fuzzy expected value of Jinhua City’s water resource risk has been performed based on the interior-exterior set model. This model is first used to evaluate the risk of water resources in Jinhua City: it not only solves an imprecise probability estimation, which results from small samples and unclear risk relationship, but it also explores the implicit risk information of the raw data as much as possible. Both of these achievements can make analyses more objective and comprehensive, which makes it easy to regulate options for policy-makers. Hence, the fuzzy risk analysis provides a new way to assess water resources.  相似文献   

Sr,Nd, and Hf Isotope Composition of Rocks of the Reft Gabbro–Diorite–Tonalite Complex (Eastern Slope of the Middle Urals): Petrological and Geological Implications     

V. N. Smirnov  K. S. Ivanov  Yu. L. Ronkin  P. A. Serov  A. Gerdes 《Geochemistry International》2018,56(6):495-508

This paper reports Rb–Sr and Sm–Nd isotope data on the gabbro–diorite–tonalite rock association of the Reft massif (eastern margin of the Middle Urals) and Lu–Hf isotope data on zircon populations from these rocks. In terms of Nd and Hf isotope composition, the rocks of the studied association are subdivided into two distinctly different groups. The first group consists of gabbros and diorites, as well as plagioclase granites from thin dikes and veins cutting across the gabbros. In terms of ⁴³Nd/¹⁴⁴Nd _i = 0.512518–0.512573 (ε_Nd(T) = +8.6...+9.7) and ¹⁷⁶Hf/¹⁷⁷Hf _i = 0.282961–0.283019 (ε_Hf(T) = +15.9...+17.9), these rocks are practically identical to depleted mantle. Their Nd and Hf model ages show wide variations, but in general are close to their crystallization time. The second group is represented by tonalites and quartz diorites, which compose a large body occupying over half of the massif area. These rocks are characterized by the lower values of ¹⁴³Nd/¹⁴⁴Nd _i = 0.512265–0.512388 (ε_Nd(T) = +3.7...+6.0) and ¹⁷⁶Hf/¹⁷⁷Hf _i = 0.282826–0.282870 (ε_Hf(T) = +11.1...+12.7). The T_DM values of the second group are much (two–three times) higher than their geological age (crystallization time), which indicates sufficiently long crustal residence time of their source. The initial ⁸⁷Sr/⁸⁶Sr in the rocks of both the groups varies from 0.70348 to 0.70495. This is likely explained by the different saturation of melts with fluid enriched in radiogenic Sr. The source of this fluid could be seawater that was buried in a subduction zone with oceanic sediments and released during slab dehydration. Obtained data make it possible to conclude that the formation of the studied gabbro–diorite–tonalite association is a result of spatially and temporally close magma formation processes in the crust and mantle, with insignificant contribution of differentiation of mantle basite magma.  相似文献   

Simulation of geological surfaces using fractals   总被引：2，自引：0，他引：2  

E. A. Yfantis  G. T. Flatman  E. J. Englund 《Mathematical Geology》1988,20(6):667-672

Methods suggested in the past for simulated ore concentration or pollution concentration over an area of interest, subject to the condition that the simulated surface is passing through specifying points, are based on the assumption of normality. A new method is introduced here which is a generalization of the subdivision method used in fractals. This method is based on the construction of a fractal plane-to-line functionf(x, y, R, e, u), where(x, y) is in[a, b]×[c, d], R is the autocorrelation function,e is the resolution limit, andu is a random real function on [–1, 1]. The simulation using fractals escapes from any distribution assumptions of the data. The given network of points is connected to form quadrilaterals; each one of the quadrilaterals is split based on ways which are extensions of the well-known subdivision method. The quadrilaterals continue to split and grow until resolution obtained in bothx andy directions is smaller than a prespecified resolution. If thex coordinate of theith quadrilateral is in[a _i ,b _i ] and they coordinate is in[c _i ,d _i ], the growth of this quadrilateral is a function of(b _i –a _i ) and(d _i –c _i ); the quadrilateral could grow toward the positive or negativez axis with equal probability forming four new quadrilaterals having a common vertex.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.  相似文献   

Empirical law for fault-creep events     

S.Thomas Crough  Robert O. Burford 《Tectonophysics》1977,42(1):T53-T59

Fault-creep events measured on the San Andreas and related faults near Hollister, California, can be described by a rheological model consisting of a spring, power-law dashpotand sliding block connected in series. An empirical creep-event law, derived from many creep-event records analyzed within the constraints of the model, provides a remarkably simple and accurate representation of creep-event behavior. The empirical creep law is expressed by the equation: D(t)= D_f [1?1/{ct(n?1)D_f^n?1+1}/^(n?1)] where D is the value of displacement at time t following the onset of an event, D_f is the final equilibrium value of the event displacementand C is a proportionality constant. This discovery should help determine whether the time—displacement character of creep events is controlled by the material properties of fault gouge, or by other parameters.  相似文献   

Paleo-depths reconstruction of the last 550,000 years based on the transfer function on recent and Quaternary benthic foraminifers of the East Corsica margin     

《Comptes Rendus Geoscience》2018,350(8):476-486

In this study, the model H(i) = 109.6103 + C₁ × F1(i) + C₂ × F₂(i) + … + C₃₃ × F₃₃(i) obtained from depth modelling based on 33 recent benthic foraminifer species distribution, has been applied to the fossil benthic foraminifers from the borehole GDEC-4-2 drilled at a water depth of 491 m, in the East-Corsica basin, covering the last 550,000 years. The obtained variations of the paleo-depths show a medium correlation with the oscillations of the relative sea level and also with the fluctuations of the oxygen isotopic ratio (δ¹⁸O G. bulloides and δ¹⁸O C. pachyderma–C. wuellerstorfi). This newly developed transfer function is accompanied by an error margin of ± 86 m, suggesting that this model will probably be more suitable for a time scale of the order of a million years where sea level variations are recorded with larger amplitudes. Without considering these problems related to amplitudes, it also turns out that the “eustatic” signal of the microfauna is accompanied by a “trophic” signal, which should not to be neglected, especially at a millennial scale time resolution. Thus, the application of this method would require taking into account the bottom trophic effects strongly controlling the distribution of benthic foraminifer assemblages.  相似文献   

Evolution of the isotopic composition of carbon and oxygen in a calcite precipitating H₂O-CO₂-CaCO₃ solution and the related isotopic composition of calcite in stalagmites     

Wolfgang Dreybrodt 《Geochimica et cosmochimica acta》2008,72(19):4712-4724

The isotopic composition of carbon and oxygen in a calcite precipitating CO₂-H₂O-CaCO₃ solution is preserved in the calcite precipitated. For the interpretation of isotopic proxies from stalagmites knowledge of the evolution of δ¹³C and δ¹⁸O in the solution during precipitation is required. A system of differential equations is presented from which this evolution can be derived. Both, irreversible loss of carbon and oxygen from the solution with precipitation time τ and exchange of oxygen in the carbonates with the oxygen in the water with exchange time T are considered. For carbon, where no exchange is active, a modified equation of Rayleigh-distillation is found, which takes into account that precipitation stops at c_eq, the saturation concentration of DIC with respect to calcite, and that c_eq as well as the precipitation time τ is slightly different for the heavy and the light isotope. This, however, requires introducing a new parameter γ = (A_eq/B_eq)/(A₀/B₀), which has to be determined experimentally. (A_eq/B_eq) is the isotopic ratio for the heavy (A) and the light isotope (B) at both chemical and isotopic equilibrium and (A₀/B₀) is the initial isotopic ratio of the solution. In the case of oxygen, where exchange is present, the isotopic shifts are reduced with increasing values of the precipitation time τ. For τ ? T the solution stays in isotopic equilibrium with the oxygen in the water during the entire time in which precipitation is active. The isotopic ratios in a calcite precipitating solution R(t)/R₀ = (1 + δ(t)/1000) for carbon are plotted versus those of oxygen. R₀ is the isotopic ratio at time t = 0, when precipitation starts and δ(t) the isotopic shift in the solution after time t. These show positive correlations for the first 50% of calcite, which can precipitate. Their slopes increase with increasing values of τ and they closely resemble Hendy-tests performed along growth layers of stalagmites. Our results show that stalagmites, which grow by high supply of water with drip times less than 50 s, exhibit positive correlations between δ¹³C and δ¹⁸O along a growth layer. But in spite of this the isotopic composition of oxygen in the solution at the apex is in isotopic equilibrium with the oxygen in the water, and therefore also that of calcite deposited at the apex.  相似文献