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.     

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.     

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).     

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.     

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.     

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。     

Error estimates for parameters in inverse parametrical problems. Light-curve analysis for classical eclipsing binaries

Parameters and their error intervals numerically estimated for the observed light curve of the binary eclipsing system YZ Cas as well as for one-, two-, three-, and four-parameter functions, and the associated parameters and their error intervals numerically estimated. The error intervals are calculated using differential corrections method, Monte-Carlo simulations, and confidence areas. We study the error intervals and the reliability of the techniques used.     

Time series transfer model relating temperature to behavior of glacier termini

The Box-Jenkins transfer model technique is used to build a time series model relating mean June–July–August air temperature and behavior of glacier termini. Data are from the Austrian Alps. Glacier behavior is the fraction of observed glaciers in the region that recede each season. The model indicates a good fit (r=0.84), with temperature effects diminishing after the concurrent year but having appreciable impact for approximately 4 yr.First authorship was determined by a randomizing device.     

裂隙地下水反分析中若干问题探析

本文以反演介质参数为例,讨论了模型的建立、反问题数值计算中实际参数采集及其对成果的影响,有关数值法的适用性、唯一性。     

浅析传统塑性位势理论与广义塑性位势理论

就传统塑性位势理论与广义塑性位势理论(考虑和不考虑应力主轴旋转两种情况下)进行了系统的综述与比较。两种位势理论就解决金属与岩土变形机制问题均获得了很大的成功(尤其是后者);浅析了广义塑性位势理论遇到的困境和发展前景。     

Time series analyses of suspended sediment concentrations at North Inlet,South Carolina

Daily water samples have been collected at three stations in the North Inlet (South Carolina) marshestuary system since February 1981 as part of the NSF Long-Term Ecological Research (LTER) project. As a result of this sampling regime, nearly continuous time series of inorganic and organic suspended sediment, particulate organic carbon (POC), Secchi disk, salinity, and water temperature are now available. Power spectrum analysis of these data reveals that most of the explainable variance in the inorganic suspended sediment, POC, and Secchi disk data is related to a yearly cycle that is strongly coherent with water temperature such that high turbidity is associated with high water temperature. Only a small fraction of the explainable variance is associated with frequencies that can be related to the semidiurnal tide. Simple correlation analysis also indicates that turbidity is more closely associated with water temperature than with tide height or salinity. The ratio of POC to inorganic suspended sediment shows no discernible power spectra peaks and is weakly, but inversely, correlated with temperature. From these results we hypothesize that temperature-regulated bioturbation is the main factor controlling turbidity variations in the system. The lack of a strong inverse correlation between turbidity and salinity suggests that river runoff has little immediate impact on the suspended sediment of nearshore coastal waters in systems similar to North Inlet.     

基于时变监测数据的降雨滑坡多目标随机反分析

基于非饱和土流-固耦合理论和贝叶斯理论,建立了边坡的非饱和土流-固耦合随机反演模型,提出了基于马尔科夫链的多目标随机反分析方法,利用位移和孔隙水压力时变监测数据进行多目标和单目标随机反演,并对反演结果进行比较分析。结果表明,多目标随机反分析参数后验分布标准差较单目标随机反分析明显减小。单目标随机反分析只对本目标进行优化,对其他目标的预测误差较大。多目标随机反分析能同时对所有目标进行优化,反演结果对所有目标误差均较小,95%置信区间较单目标明显收窄,采用不同类型监测数据的多目标随机反分析所得结果更为可靠,预测更为准确。     

Statistical inverse analysis based on genetic algorithm and principal component analysis: Applications to excavation problems and pressuremeter tests

This study concerns the identification of constitutive models from geotechnical measurements by inverse analysis. Soil parameters are identified from measured horizontal displacements of sheet pile walls and from a measured pressuremeter curve. An optimization method based on a genetic algorithm (GA) and a principal component analysis (PCA), developed and tested on synthetic data in a previous paper, is applied. These applications show that the conclusions deduced from synthetic problems can be extrapolated to real problems. The GA is a robust optimization method that is able to deal with the non‐uniqueness of the solution in identifying a set of solutions for a given uncertainty on the measurements. This set is then characterized by a PCA that gives a first‐order approximation of the solution as an ellipsoid. When the solution set is not too curved in the research space, this ellipsoid characterizes the soil properties considering the measured data and the tolerate margins for the response of the numerical model. Besides, optimizations from different measurements provide solution sets with a common area in the research space. This intersection gives a more relevant and accurate identification of parameters. Finally, we show that these identified parameters permit to reproduce geotechnical measurements not used in the identification process. Copyright © 2009 John Wiley & Sons, Ltd.     

A method for GB-InSAR temporal analysis considering the atmospheric correlation in time series

Natural Hazards - GB-InSAR, with high time-spatial resolution and high accuracy, shows great potential in landslide monitoring. However, the accuracy of GB-InSAR is usually reduced by the...     

Nonlinear time series analysis of the ionospheric measurements

The applications of the tools of nonlinear time-series analysis to measurements obtained by digital ionosonde PARUS, created at IZMIRAN, is considered. Small-scale structure of the electron density Ne at F-region of ionosphere is examined by exploring observables of reflected high-frequency radio wave.Time series corresponding to given transmitter frequency f and virtual height h and conforming to usual, not perturbed, day ionogram are examined. Using the standard correlation algorithm, we have determined that for an embedding dimension n = 15, computed correlation dimension D2(n) reaches its saturation, D2 4.Reliability of the estimation of the correlation dimension was confirmed by applying to our sets of measurements J. Theiler's modification of standard algorithm. The test of time difference, smoothing procedure, calculation of the largest Liapounov exponent, and analysis of the surrogate data were employed in our study of data sets. Although our sets of measurements contain a significant random noise, nonlinear time-series analysis clear up, that the dynamics of unperturbed ionosphere, generating this time series, exhibits low-dimensional behavior.     

Using inverse modeling and hierarchical cluster analysis for hydrochemical characterization of springs and Talkhab River in Tang-Bijar oilfield,Iran

Hierarchical cluster analysis (HCA) and inverse modeling (PH REdox EQuilibrium (in C language) (PHREEQC)) were simultaneously useful approaches in interpreting surface water hydrochemistry within Talkhab River in the Tang-Bijar oilfield, Iran, where large uncertainties exist in the understanding of the water quality system. Q-mode HCA applied to the data revealed three major surface water associations distinguished on the basis of the major causes of variation in the hydrochemistry. The three water groups were classified as upstream waters (group 1: Ca–SO₄), intermediate waters (group 2: Ca–SO₄–Cl), and downstream waters (group 3: Na–Cl). Geochemical reaction models were constructed using PHREEQC to establish the reactions associated with the different mineral phases through inverse modeling. The hydrochemical compositions of the water groups and the mass balance calculations indicate that the dominant processes and reactions responsible for the hydrochemical evolution in the system are (1) dissolution of evaporites, (2) precipitation of carbonate minerals, (3) silicate weathering reactions, (4) limited mixing with saline water, and (5) ion exchange.