A primer in gibbs energy minimization for geophysicists

Gibbs energy minimization is the means by which the stable state of a system can be computed as a function of pressure, temperature and chemical composition from thermodynamic data. In this context, state implies knowledge of the identity, amount, and composition of the various phases of matter in heterogeneous systems. For seismic phenomena, which occur on time-scales that are short compared to the timescales of intra-phase equilibration, the Gibbs energy functions of the individual phases are equations of state that can be used to recover seismic wave speeds. Thermodynamic properties relevant to modelling of slower geodynamic processes are recovered by numeric differentiation of the Gibbs energy function of the system obtained by minimization. Gibbs energy minimization algorithms are categorized by whether they solve the non-linear optimization problem directly or solve a linearized formulation. The former express the objective function, the total Gibbs energy of the system, indirectly in terms of the partial molar Gibbs energies of phase species rather than directly in terms of the Gibbs energies of the possible phases. The indirect formulation of the objective function has the consequence that although these algorithms are capable of attaining high precision they have no generic means of treating phase separation and expertise is required to avoid local minima. In contrast, the solution of the fully linearized problem is completely robust, but offers limited resolution. Algorithms that iteratively refine linearized solutions offer a compromise between robustness and precision that is well suited to the demands of geophysical modeling.     

基于ARMA模型的隧道位移时间序列分析

在新奥法隧道施工中,隧道位移监测对于评价围岩稳定性和支护结构合理性起重要作用。目前大都采用AR模型对隧道位移进行时间序列分析,避开了非线性估计,致使拟合精度和模型实用性较差。为此,介绍了具有较高预测精度和较好适用条件的ARMA模型及其常用参数估计方法,基于其参数非线性估计带来的不便性,提出一种ARMA模型参数估计近似线性方法,把残差用Taylor级数一阶展开,将非线性估计线性化,用线性最小二乘法估计参数最终值。用该方法对重庆市大足县南环二路南山隧道位移监测数据进行时间序列建模分析,预测与实测值吻合较好,证明了该方法的实用性。     

Time series and postglacial forest ecology

Forest ecology suffers from a lack of long-term community records. Preserved pollen data are richer in such information than is generally realized. By applying suitable statistical techniques to pollen records, one can learn much about competition, succession, and population dynamics in past tree communities. In this study, preserved pollen records from Everitt Lake, Nova Scotia, are analyzed as time series. Time domain studies reveal the post-fire responses of individual tree taxa. Correlograms yield models of past forest succession patterns. The models explain some effects of changing fire frequency, thus suggesting mechanisms by which fire, competition, and climate combine to produce long-term forest composition changes. Frequency domain studies suggest relationships between disturbance cycles, stand composition, and forest mosaics. Fire frequencies are seen to be highest where fire-dependent species abound and most regular where tree stands have uniform, not mixed, composition.     

Time series analysis of CO concentrations from an Eastern Kentucky coal fire

Coal fires in natural outcrops, in abandoned and active coal mines, and in coal and coal-refuse piles are responsible for the uncontrolled emissions of gases, including CO, CO₂, H₂S, hydrocarbons, and volatile aromatics. Typically, measurements of gases at a mine vent are made over a short time interval, perhaps no more than 10 min, including the time for replicate measurements. Such timing provides little information on longer-term variations in emissions, although comparisons of seasonal measurements suggest such changes do occur. To address this problem, we placed temperature and CO data loggers in coal fire vents to collect time series measurements for a period of up to three weeks. For one experiment, 11 days of data at one-minute intervals indicated that the CO emissions were generally in the 400–550 ppmv range. However near daily depressions in CO concentrations occurred and in some cases fell below 50 ppmv; followed by an increase to ~ 700–800 ppmv; in turn followed by a return to the ambient conditions. Data for a separate 21-day collection period in a different vent of the same fire exhibited similar trends, albeit at a higher CO concentration. The drop in CO concentration may be associated with a meteorologically-driven inhalation cycle of the fire, whereby air diluted the combustion generated CO. We propose this was followed by an increase in the intensity of the fire due to increased O₂ from the inhaled air, producing increased CO concentrations, before settling back to the ambient conditions.     

南极地区SSM/I微波辐射计亮温时间序列分析

简单介绍了微波辐射的原理与应用现状,利用美国国防气象卫星计划DMSP F系列卫星携带的SSM/I辐射计南极地区极投影网格亮温数据进行了分析与处理。结合微波亮温等温线图和南极等高线图分析了南极地区亮温分布的特点。选取8个特征区域,对1992-2000年的日亮温数据进行了时间序列分析,分析了冰盖和冰架的亮温特性、季节和年度变化、短期波动等特征。研究表明南极大陆外围冰架和南极半岛地区的亮温呈增高趋势,而内陆冰盖地区则保持相对稳定;揭示了近年来随全球气候的变暖,南极冰架和南极半岛的融化正在加剧的趋势。     

基于递归图理论的沉降时间序列可预测分析

在实际沉降监测中,由于不确定性因素的影响,导致基于实测沉降数据的工后沉降预测误差较大。采用递归图和递归定量分析方法对沉降时间序列的可预测性进行分析,选择出预测效果好的沉降时间序列,进行准确的工后沉降预测。通过对无砟轨道整体道床的沉降时间序列进行可预测性分析得出:（1）沉降时间序列具有混沌特性;（2）沉降时间序列的递归图颜色分布越规律、色彩深浅变化越均匀,沿着主对角线出现的白色区域越小,沉降时间序列的可预测性越强;（3）通过提取递归定量指标随时间变化的曲线,可以直接确定预测时间起点;（4）利用递归图求取二阶任意熵作为沉降时间序列的可预测步长因子,可推算出预测效果最佳的沉降时间序列。     

The inverse problem of the theory of degenerate dwarfs

Based on the radii and masses of degenerate dwarfs derived from HIPPARCOS and other observations, we estimate the microscopic parameters of a Chandrasekhar model (the relativistic parameter at the stellar center x ₀, and the chemical-composition parameter μ _e = A/Z, where A is the mass number and Z is the nuclear charge). We have obtained analytical expressions for the macroscopic characteristics (mass, radius, energy) as functions of x ₀ and μ _e . From the calculated dependence of the energy on these parameters, we have found constraints on the range of variability of x ₀, which are in good agreement with the observed radius distribution of dwarfs. The critical value of x ₀ at which stability breaks down due to general-relativisitc effects is found more accurately than previously. We propose a generalized model with an inhomogeneous (coordinate-dependent) chemical composition, with μ _e = μ _e (r).     

Harmonic hierarchy of mantle and lithospheric convective cycles: Time series analysis of hafnium isotopes of zircon

Hafnium isotopes of zircon represent a well-dated proxy for the evolution of magmatic systems through Earth history. Time series analysis on the hafnium isotopes of zircon reveals a hierarchy of statistically significant periodic signals spanning multiple orders of magnitude (10⁶–10⁹ year cycles). We attribute the hierarchy of cyclicity to organizing mechanisms of mantle and lithospheric convection at various time scales, ranging from short-term cycles in magmatism and subduction to long-term cycles related to oceans, supercontinents, and superoceans. A ∼600-Myr supercontinent cycle is the strongest signal in the global hafnium database and the phase relationship implies elevated mantle-derived magmatism during supercontinent tenure and elevated crustal reworking during plate reorganization, as expected. A half-supercontinent cycle (Wilson cycle) and a double-supercontinent cycle (superocean cycle) are also present, harmonic with the supercontinent cycle, and related to each other by amplitude modulation. Analysis of local magmatic systems of the circum-Pacific subduction girdle surrounding Pangaea reveal similar significant and harmonic cycles of ∼6 and ∼20 Myr attributed to magmatic cycles and ∼60, ∼120, and ∼240 Myr attributed to subduction cycles. All subduction systems reveal a prevalent ∼60 Myr cycle attributed to an upper mantle convective cycle that has two phase relationships, suggesting that advancing and retreating arc systems can be identified with time series analysis. The harmonic hierarchy of geodynamic cycles identified herein controlled by mantle convection on long time scales and lithospheric convection on short time scales arguably completes the picture of cyclicity in the Earth system, complimenting well-known orbital, oceanic, and astronomical cycles.     

Time series analysis of mantle cycles Part I: Periodicities and correlations among seven global isotopic databases

In this study, seven isotopic databases are presented and analyzed to identify mantle and crustal episodes on a global scale by focusing on periodicity ranging from 70 to 200 million years (Myr). The databases are the largest, or among the largest, compiled for each type of data – with an objective of finding some samples from every region of every continent, to make each database as global as conceivably possible. The databases contain zircon Lu/Hf isotopic data, whole-rock Sm/Nd isotopic data, U/Pb detrital zircon ages, U/Pb igneous zircon ages, U/Pb non-zircon ages, whole-rock Re/Os isotopic data, and large igneous province ages. Part I of this study focuses on the periodicities of age histograms and geochemical averages developed from the seven databases, via spectral and cross-correlation analyses. Natural physical cycles often propagate in exact integer multiples of a fundamental cycle, referred to as harmonics. The tests show that harmonic geological cycles of ～93.5 and ～187 Myr have persisted throughout terrestrial history, and the cyclicities are statistically significant for U/Pb igneous zircon ages, U/Pb detrital zircon ages, U/Pb zircon-rim ages, large igneous province ages, mean ε_Hf(t) for all samples, mean ε_Hf(t) values for igneous-only samples, and relative abundance of mafic rocks. Equally important, cross-correlation analyses show these seven time-series are nearly synchronous (±7 Myr) with a model consisting of periodicities of 93.5 and 187 Myr. Additionally, the similarities between peaks in the 93.5 and 187 Myr mantle cycles and terminal ages of established and suspected superchrons provide a framework for predicting and testing superchron periodicity.     

系列尺度岩石结构面相似表面模型制作的逆向控制技术研究

制作与原岩结构面相似表面形态的模型试样是开展结构面力学模型试验的关键。基于不同尺度岩石结构面模型试样的制作特点,研制上、下盘完全吻合的系列尺度试样模具,并设计上、下盘吻合结构面试样的制作工艺,使得原岩结构面可以多次重复利用,提高原岩结构面的使用效率,降低取样成本和试验周期,实现在同一块结构面上不同尺度结构面模型的制作。利用表面形态相似性评价技术,验证制作工艺的可行性,结果表明,按照该逆向控制技术设计制作的模型试样,能复制出和原岩结构面表面形态一样、上、下盘结构面吻合度高的模型试样,符合制作不同尺度模型结构面的要求,可克服原岩结构面上下盘吻合度差、不能多种尺度取样的缺点,为开展具有真实表面形态的结构面抗剪强度尺寸效应试验研究提供了条件。     

矿井涌水量混沌时间序列分析与预测

矿井地下水系统是个非线性系统,由于地下水系统的复杂性,很难完全确定影响矿井涌水量的因素,因此传统的矿井涌水预测表现出较大的局限性。而混沌时间序列分析能够利用单变量处理方法,分析矿井地下水系统中,由于多因素耦合作用所产生的矿井涌水量时间序列。通过对某矿区1985年9月至2005年2月矿井涌水量时间序列资料的分析,显示矿井涌水量时间序列具有混沌特征;通过对比预测值和实测值,表明预测精度高。因此,混沌时间序列分析方法用于矿井涌水量预测是可行的。     

A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task. Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering. In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational cost significantly, using only the time needed to obtain a sample of the posterior probability density function. The use of the information theory principles for the experimental design and for the ill-posedness diagnosis is also introduced. Finally, a case study based on a highly instrumented well test found in the literature is presented. The results obtained are compared with the ones computed by the maximum likelihood estimation approach.     

Comparison of two inverse analysis techniques for learning deep excavation response

Performance observation is a necessary part of the design and construction process in geotechnical engineering. For deep urban excavations, empirical and numerical methods are used to predict potential deformations and their impacts on surrounding structures. Two inverse analysis approaches are described and compared for an excavation project in downtown Chicago. The first approach is a parameter optimization approach based on genetic algorithm (GA). GA is a stochastic global search technique for optimizing an objective function with linear or non-linear constraints. The second approach, self-learning simulations (SelfSim), is an inverse analysis technique that combines finite element method, continuously evolving material models, and field measurements. The optimization based on genetic algorithm approach identifies material properties of an existing soil model, and SelfSim approach extracts the underlying soil behavior unconstrained by a specific assumption on soil constitutive behavior. The two inverse analysis approaches capture well lateral wall deflections and maximum surface settlements. The GA optimization approach tends to overpredict surface settlements at some distance from the excavation as it is constrained by a specific form of the material constitutive model (i.e. hardening soil model); while the surface settlements computed using SelfSim approach match the observed ones due to its ability to learn small strain non-linearity of soil implied in the measured settlements.     

构造应力场边界载荷反演的有限元逆逼近法

构造应力场问题的边界条件、加载方式是地应力场分析的难题,由于构造运动未知和地质构造复杂,无法直接求解。边界力反演是进行构造应力场研究的重要手段。从弹性力学基本方程出发,针对油气储层地应力场反问题,结合对区域构造应力场认识,利用阻尼最小二乘法建立了应力场反演的约束模型,提出了一种用于反演构造应力场边界力的反分析方法,该方法根据部分实测点的应力值进行边界力反演,并与有限元方法和有限差分法相结合,以边界力为参量逼近目标函数。根据研究区少量地应力实测资料采用该方法进行最优化计算,使得计算应力场与实测应力达到最优拟合,以弥补目前的回归反演方法和边界载荷调整法的不足来提高计算精度。算例表明了该方法的有效性,可用于解决构造应力场边界力的反演问题。     

Probabilistic analysis of the inverse analysis of an excavation problem

This study presents the probabilistic analysis of the inverse analysis of an excavation problem. Two techniques are used during two successive stages. First, a genetic algorithm inverse analysis is conducted to identify soil parameters from in situ measurements (i.e. first stage of the construction project). For a given tolerable error between the measurement and the response of the numerical model the genetic algorithm is able to generate a statistical set of soil parameters, which may then serve as input data to a stochastic finite element method. The second analysis allows predicting a confidence interval for the final behaviour of the geotechnical structure (i.e. second stage of the project). The tools employed in this study have already been presented in previous papers, but the originality herein consists of coupling them. To illustrate this method, a synthetic excavation problem with a very simple geometry is used.     

水文序列小波分析中分解层数选择方法

小波分解层数的合理选择是水文序列小波分析结果的重要影响因素。在详细分析和定量描述不同类型噪声的能量分布规律的基础上,依据水文序列中确定成分和噪声成分的能量分布规律的差异,提出了一个小波分解层数选择方法。通过对不同类型模拟序列和不同特性实测水文序列进行分析,验证了所提方法的有效性和实用性。结果表明:序列组成、噪声含量等因素对小波分解层数的选择结果有较大影响,但噪声类型对小波分解层数选择结果影响较小;应用该方法确定小波分解层数的同时,还可以有效地识别和区分各层上是确定成分或是噪声成分,进而可为序列模拟预测提供依据。由于所提方法基于水文序列不同成分变化特性的差异建立,因此有较好的物理依据且分析结果合理可靠。     

洪水频率分析中PDS模型研究进展

为了从实测洪水资料中获取更多的信息,提出PDS(Partial duration series)洪水频率分析模型并得到发展。介绍了PDS模型及其导出的AMS(Annual Maximal Series)模型的基本理论,综述了两种模型之间的比较研究。总结了PDS模型应用的关键技术,包括独立性判别、阈值的选取、超定量次数概率分布的选择。描述了PDS模型在区域洪水频率分析、PDS模型与贝叶斯理论结合研究的新进展,展望了PDS模型进一步研究的前景。     

Time series analysis of mantle cycles Part Ⅱ:The geologic record in zircons,large igneous provinces and mantle lithosphere

Igneous and detrital zircons have six major U/Pb isotopic age peaks in common(2700 Ma,1875 Ma.1045 Ma,625 Ma,265 Ma and 90 Ma).For igneous rocks,each age peak is comprised of subpeaks with distinct geographic distributions and a subpeak age range per age peak ≤100 Myr.There are eight major LIP age peaks(found on≥10 crustal provinces)of which only four are in common to major detrital zircon age peaks(2715 Ma,1875 Ma,825 Ma,90 Ma).Of the whole-rock Re depletion ages,58% have correspo nding detrital zircon age peaks and 55% have corresponding LIP age peaks.Ten age pea ks are fou nd in common to igneous zircon,detrital zircon,LIP,and Re depletion age time series(3225 Ma,2875 Ma,2145 Ma,2085 Ma,1985 Ma,1785 Ma,1455 Ma,1175 Ma,825 Ma,and 90 Ma).and these are very robust peaks on a global scale as recorded in both crustal and mantle rocks.About 50% of the age peaks in each of these time series correspond to predicted peaks in a 94-Myr mantle cycle,including four of the ten peaks in common to all four time series(2875 Ma,1785 Ma,825 Ma and 90 Ma).Age peak widths and subpeak ranges per age peak suggest that mantle events responsible for age peaks are100 Myr and many50 Myr in duration.Age peak geographic distributions show three populations(≤1000 Ma,2500-1000 Ma,2500 Ma),with the number of new provinces in which age peaks are represented decreasing with time within each population.The breaks between the populations(at 2.5 Ga and 1 Ga)fall near the onsets of two transitions in Earth history.The First Transition may represent a change from stagnant-lid tectonics into plate tectonics and the Second Transition,the onset of subduction of continental crust.The major factor controlling geographic distribution of age peaks is the changing locations of orogeny.Before ～2 Ga,age subpeaks and peaks are housed in orogens within or around the edges of crustal provinces,mostly in accretionary orogens.but beginning at 1.9 Ga,collisional orogens become more important.The coincidence in duration between magmatic flare-ups in Phanerozoic arcs and duration of age subpeaks(10-30 Myr)is consiste nt with subpeaks representing periods of enhanced arcrelated magmatism.probably caused by increased subduction flux.The correlation of isotopic age peaks between time series supports a cause and effect relationship between mantle plume activity,continental magma production at convergent margins,and crustal deformation.Correlation of over half of the detrital zircon age peaks(and six of the nine major peaks)with Re depletion age peaks supports an interpretation of the zircon peaks as crustal growth rather than selective preservation peaks.     

试论成矿系列与矿产资源评价

成矿系列研究的内容是矿床的区域成矿规律,研究目的之一是根据矿床的自然分类原则指导地质找矿,确定找矿目标和可能的范围.矿产资源评价的工作内容是依据这一理论,结合物探、化探、遥感、数学等工具,确定出与已知成矿系列相类似区域的成矿可能性,从而达到预测找矿的目的.成矿系列理论为矿产资源评价提供指导,矿产资源评价则为成矿系列理论的实际应用提供平台;同时,矿产资源评价的结果也是对成矿系列理论的验证,可据此完成对成矿规律认识的修正,两者相辅相成.在中国新一轮25种重要矿产资源预测评价工作中,明确提出了要以成矿系列理论为指导,开展未发现的矿产资源的潜力评价.通过该项目的实施,将实现两者的有机结合,使成矿预测工作更有成效,同时,将使成矿系列的研究更加深入.