Graphic Biostratigraphic Correlation Using Genetic Algorithms

The most generally used method for estimating the basin-wide sequence and scaling of first and last occurrences, based on their occurrence in local sections, is Shaw’s graphic correlation method. The key step in this method is the determination of the line of correlation (LOC), which represents the best estimate of the correlation between two local sections, or between a local section and a composite standard. In general, available techniques for fitting the LOC for multiple sections are tedious, subjective, or computationally expensive. A new method employing genetic algorithms can dramatically reduce the effort involved in determining the LOC and produces stable biostratigraphic correlations and composite range charts objectively and efficiently. Genetic algorithms are an artificial intelligence technique that excels in locating the optimum solution from a large number of alternative choices. In the case of the LOC, the alternative choices are the number of line segments comprising the complete line and the positions of each segment’s beginning and end points. For a given number of segments, a wide range of alternative LOCs can be rapidly evaluated and a potential optimum fit determined. It is also possible to estimate the point when no further refinement of the fit by adding line segments is necessary. Genetic algorithms can also be applied to other methods for quantitative biostratigraphy.     

甘肃靖远石炭系纳缪尔阶高分辨率生物地层研究

依据对甘肃靖远纳缪尔阶的定量地层研究 ,介绍了图形对比法的基本原理和操作过程 ,建立了靖远石炭系纳缪尔阶生物地层复合标准 ,确定了剖面间的精确对比关系 ,提出了榆树梁剖面是该区发育最为齐全的剖面。榆树梁东沟剖面纳缪尔期地层与榆树梁剖面同期沉积相比 ,缺失了约 30 m厚的地层 ,大水沟剖面靖远组仅相当于榆树梁剖面靖远组中部。     

The match game: New stratigraphic correlation algorithms

New algorithms for automatic correlation of geologic strata are introduced. The algorithms are extensions of the Smith and Waterman (1980) dynamic programming technique and include several features that greatly increase the utility for sedimentary sequences. Gaps in correlation (unconformities) caused by local nondeposition or eroded strata can include in a single event several strata. Furthermore, these gaps can be weighted as a single event, rather than as the sum of gap events for each strata. In addition, one or several adjacent strata in a second column can be correlated (matched) with one or several strata in a second column. Deletions within one of these multiple matches are also possible. The new algorithms include the method of minimum distance and the method of maximum similarity. Within this context, a similarity algorithm is given to locate and correlate the best matching segments or intervals from each stratigraphic column. All correlations within a preset distance of the optimum likewise can be produced for any of these algorithms. An example of specific assignments of these weight functions is given for correlation of well logs from the San Juan Basin.     

模糊加权优化适线法的改进及统计特征分析

水文序列长度有限,频率曲线参数估计存在抽样误差,采用加权适线法能够很好地减小误差。模糊加权优化适线法的诺模图长度有限,而且隶属度函数不是以样本无穷大为前提,对模糊加权优化适线法改进,提出半降正态分布的隶属度函数,运用大样本统计试验方法延长诺模图。以理想数据、蒙特卡洛随机数和实测序列对改进的方法检验,以无偏性和有效性为评价指标,运用评分法和百分率法对统计结果分析评价。结果表明改进的模糊加权优化适线法的统计特性好,适线精度高,能够促进模糊加权优化适线法在实际工程中的推广应用。     

Application of graphic correlation technique on Paleocene–Early Eocene benthic foraminifera, Rub’ Al-Khali Basin and neighboring regions

The measured ranges of 60 benthic foraminiferal species of Umm er Radhuma Formation (UeR) (Paleocene–Early Eocene age) in five wells of Rub’ Al-Khali Basin, Saudi Arabia, and two surface sections (Wadi Mashib and Say’un), from Yemen, have been assembled by a graphic correlation technique into a composite standard section (CSS). This composite standard allows building a chronostratigraphic model subdividing UeR into 50 composite standard section time units. The adjustment of benthic foraminiferal ranges of the study area by a quantitative approach improved its resolution in correlation and enhances its potential in biozonation and dating. The analysis of graphic correlation technique reveals significant information regarding accumulation rate in the CSS and the individual sections. Generally, sediments of Paleocene–Early Eocene age in the study area are characterized by a low rate of accumulation. The Paleocene/Eocene boundary of Umm er Radhuma Formation is defined in the chronostratigraphic model to be at a composite standard section time units ?14.8. This boundary is projected into individual sections by the graphic correlation technique and allowed a precise correlation of these sections. A synchroneity analysis of composite standard section events is carried out and enabled testing of reliability of Umm er Radhuma Formation benthic foraminifera biozonation.     

Shortest link method for contact detection in discrete element method

With the increasing demand for discrete element simulations with larger number of particles and more realistic particle geometries, the need for efficient contact detection algorithms is more evident. To date, the class of common plane (CP) methods is among the most effective and widely used contact detection algorithms in discrete element simulations of polygonal and polyhedral particles. This paper introduces a new approach to obtain the CP by employing a newly introduced concept of ‘shortest link’. Among all the possible line segments that connect any point on the surface of particle A to any point on the surface of particle B, the one with the shortest length defines the shortest link between the two particles. The perpendicular bisector plane of the shortest link fulfils all the conditions of a CP, suggesting that CP can be obtained by seeking the shortest link. A new algorithm, called shortest link method (SLM), is proposed to obtain the shortest link and subsequently the CP between any two polyhedral particles. Comparison of the analysis time between SLM and previously introduced algorithms demonstrate that SLM results in a substantial speed up for polyhedral particles contact detection. Copyright © 2006 John Wiley & Sons, Ltd.     

A Multiple Composite Fingerprinting Method and Its Application

Fingerprinting technique provides an essential means for estimating source contributions of watershed sediments, in which a single group of “optimum composite fingerprints” has been widely used in the literature to estimate sediment provenance. This type of methods is not restricted by the scale or process of sediment transportation so that similar procedures can be applied in sediment provenance research for aeolian depositions. However, recent studies found no direct link (positive relationship) between the ability of the tracer group to discriminate sources and its rigor in estimating source contributions after optimization. Here, we introduced a recently developed multiple composite fingerprinting method with additional screening based on analytical solutions, and further reviewed its verification in watersheds at different scales. It turned out that compared to Monte Carlo optimization method, a reasonable estimation can be achieved using the mean of the maximum number of composite fingerprints that given analytical solution to the mixing model, but the computational cost can be reduced significantly. The reliability of this new method was also tested in source contribution estimating of aeolian sediments, and the provenance quantification of reservoir sediment in an arid region experiencing both wind and water sediments.     

Composite flow laws derived from high temperature experimental data on limestone and marble

An interesting feature of recently published experimental data on high temperature deformation of Solnhofen limestone and Carrara marble is that it is not possible, for either rock, to fit isothermal points on a log strain-rate vs. log stress plot to a single straight line as required for a flow law of the familiar form e = Aexp(- H/RT)σⁿ. Instead for Solnhofen limestone the data can be well fitted to two straight line segments suggesting a change from power law with high stress exponent (at high stress) to power law with low stress exponent at low stress. However, the constant strain-rate data are even better fitted by a single composite flow law formed by addition of the two power laws; a single flow law operates throughout but the strain-rate contributions of the two components change in response to changing stress. Published microstructural evidence supports this composite flow law approach.For Carrara marble constant data provides much poorer control and it is possible to propose several composite flow laws (formed by addition of two or three separate power-law components) all of which provide reasonable correspondence with the data. Stress relaxation data is then used both to test these flow models and to suggest others. Flow models that are broadly compatible with constant and stress relaxation data can then be tested against microstructural measurements.It is suggested that, by treating a set of composite flow laws as alternative hypotheses to be tested against all available data, a more realistic Theological model will result. Composite flow laws have the major advantage of being able to represent a smooth transition from one dominant deformation mechanism to another irrespective of how wide the transition zone may be.     

利用温度全局优化法探测堤坝多重集中渗漏

利用地温探测堤坝工程中的多重集中渗漏通道位置是一种反问题,为取得全局最优解及突破现有方法的局限性,采用不同优化算法相互配合的温度全局最优化方法,以达到有效准确探测显著集中渗漏通道的位置。结合各算法优势及目标函数不连续性等特点,选用全局搜索(GS)、多初始点(MS)及遗传算法(GA)3种方法联合补充优化。首先利用GS搜索局部最优点; 然后结合目标函数不连续点及上述局部最优点,人工增加MS优化起始点进行多初始点优化; 最后依据上述局部解,利用GA混合算法优化,从而有效提高全局最优化的概率。根据堤坝工程集中渗漏通道低温补给的特点,对优化目标函数进行了具有特定物理意义的修正; 为减少每次迭代的优化参数,基于温度测试精度提出分步优化方法,根据温度或修正目标函数残差吸引盆特征确定某步优化的集中渗漏数量; 由修正残差与温度测量精度相对大小确定优化是否终止,对应修正残差最小的优化结果为集中渗漏通道位置的真实解。结合工程实例,计算了某水库左坝肩的多重集中渗漏通道位置,分步优化了两个主要的集中渗漏位置,直接法优化3个集中渗漏位置。文献及工程实践证明了该法的正确性及有效性,为了堤坝等水利工程岩土体的集中渗漏整治提供了科学依据。     

基于B-DEM的颗粒聚合体应力计算和破碎路径模拟

结合边界元法和离散元法,提出一种可以进行计算颗粒内部应力和破碎路径的方法。该方法利用离散元法求解颗粒的相互作用和每个颗粒上的荷载。然后利用边界元法计算颗粒的应力分布,为了实现动态平衡,将颗粒的加速度视为恒定大小的体力。但体力导致边界积分方程中出现域积分,故采用直线积分法将域积分转化为边界积分,以保证边界元法降维的优势。为了提高边界元的计算效率,对于几何形状相似的颗粒,以其中一个颗粒作为模板颗粒,只需要计算模板颗粒在局部坐标系中的系数矩阵,其他相似颗粒可以通过局部和全局坐标系之间的映射获得。在得到应力后,基于Hoek-Brown准则来判断颗粒是否破碎。此外,将破坏路径简化为直线,并采用最小二乘法拟合得到破坏路径。     

Optimizing post-mining land use for pit area in open-pit mining using fuzzy decision making method

Open-pit mining method has severe environmental impacts which should be prevented, monitored, controlled, and reduced by mined-land reclamation process. After mine closure, a permanent post-mining land use should be implemented as an appropriate choice for using different sections of mined land. The most appropriate alternative of post-mining land use for each section of mined land is presented as the optimum post-mining land use. Pit area among different sections of mined land has more significant effects on the environment and also on defining the optimum post-mining land use for other sections of mined land. Though there are several alternatives and criteria for defining the optimum post-mining land use, the multi-attribute decision-making methods can be efficient techniques in this regard. The nature of the effective parameters used for defining the optimum post-mining land use is the same as Fuzzy numbers including incremental changes without definite limits. Thus, application of the Fuzzy multi-attribute decision-making modeling can produce more reliable results than that of other techniques. As well, pair-wise comparisons and judgments through Fuzzy numbers have proper consistency with the nature of the effective parameters; therefore, a model is developed to attain the optimum post-mining land use for pit area through Fuzzy analytical hierarchy processing. As a case study, the model was implemented in Sungun copper mine in the Northwest of Iran. Forestry?Clumber production was defined as the optimum post-mining land use containing the greatest relative importance coefficient 3.019 for the pit area in this mine.     

2D modeling of clastic accumulation in clinoforms under marine conditions

The 2D modeling of clastic accumulation in clinoforms under marine conditions is performed. For this purpose, two algorithms are used: the first, “geometric” one implies that the shapes of sedimentary bodies are defined by geometric methods; the second is a “diffusion” method, which is based on numerical solution of the diffusion equation. Modeling of the test section is made using different versions of these algorithms. Comparative analysis of modeling results suggests that the best fit with real sections is achieved by a combination of the geometric and diffusion algorithms.     

复合形进化重组方法在水文地质参数识别中的应用

水文地质逆问题和地下水资源管理模型的优化求解一直是水文地质学研究的一个热点.本文将复合形进化重组方法引入求解水文地质逆问题,通过一个测试函数对该方法的优化性能进行了检验,进而将该方法应用于水文地质参数的识别.比较复合形进化重组方法与遗传算法的计算结果表明,复合形进化重组方法具有很强的全局优化能力,是求解水文地质逆问题非...     

Aptian综合年代地层事件:定量地层学的运用

以往发表的年代地层数据都是以Ma形式出现,以关键物种的首现面和末现面来界定的。一般而言,这些年龄是在用某种方法确定的某两个层的年龄基础上通过插值获得的,很大程度上仍然是估计值,而不是可以检验的科学结论。我们需要的是一个可以评价的、剖面重现的、标本重现的而且插值方法是经过严格检验的数据库。图形对比技术正是一个有用的方法,它可以综合众多剖面的分散分布的事件,并可以验证这些事件的顺序和年代。图形对比技术是一个定量的、非统计的方法,可以判别两个剖面之间存在的同时代关系。物种时限和非生物事件投点到X/Y图解上,时限可以通过对比线综合到单个的时间尺度上。其他剖面的数据通过重复以上过程把每个剖面的数据综合进来。获得的时限通过评价有这些物种出现的图形解而得到验证。Aptian阶(约124~112 Ma)时期环境发生巨大变化,用来确定Aptian阶的许多关键生物事件和年代地层事件并不都出现在同一个剖面。因此,这些事件的相对年龄始终是不确定的,也不是相关的。两个事件被提出来用于界定Aptian 阶的底界,包括菊石Deshayesites tuarkyricus 和磁极性带CM0。然而这两个事件标准地层剖面相隔600 km。图形对比显示这两次事件出现在7 万年间隔内。通过这一方法,来自23 条Barremian Aptian Albian     

Stress and faulting in southeast Australia as derived from the strongest earthquakes in the region

In an attempt to clarify the state of stress in Southeast Australia, the spatial and dynamic behaviour of the strongest events in the region (with magnitude greater than 5.0) has been studied in the light of the most recent numerical modelling of the crust. Although the local seismicity has little obvious spatial correlation with the mapped structures, the strongest events line up in a very narrow strip with a NW–SE direction. Composite fault-plane solutions, based on data from all of these earthquakes, allows the general characteristics of the local stress field to be determined, and shows that the orientation of the main compressive stress lies in an E–W direction. Taking into account the number of inconsistent data (40%) for this composite solution and the fault-plane solutions for some individual events, an improved result can be obtained by domain analysis, which shows that northern and southern zones have different orientation of the compressional axes. Although the composite solution for the events in the northern domain shows the same E–W orientation of the main compression as for the whole region, the composite solution for the southern zone reveals a rotation of the compression axis to an azimuth of 120–130°. From the relation between the energy and seismic moment the maximum value of the stress-drop for the whole of SE Australia is estimated as ∼2.0 MPa.     

复合地层隧道围岩强度实时估算研究

隧道TBM开挖过程中经常会遇到复合岩层,在这种地质环境下,隧道掘进机（tunnel boring machine,简称TBM）开挖过程中的隧道围岩强度很难估计,隧道开挖掌子面和围岩容易发生坍塌。为了提高隧道掘进效率、预防事故发生,对开挖隧道围岩强度进行实时估算方面的研究很有必要。在重庆轨道九号线隧道TBM施工中,通过室内试验和现场实测数据发现,TBM推力F_N与岩石强度成正比、TBM扭矩推力比T/F_N（T为扭矩）与贯入度p^0.5成正比例关系。针对砂质泥岩、砂岩和灰岩组成的复合岩层,提出了一种利用现场实测推力F_N和扭矩T的值来快速估算开挖隧道围岩强度的方法,进一步对TBM实测数据进行线性拟合,从而得到估算公式中两个常数α₁、α₂的取值方法,并在10多个隧道实际工程中得到验证。结果表明,对于这种复合岩层地质环境,两个常数α₁、α₂的值与滚刀数量n和滚刀直径d相关。该研究成果为实时快速估算开挖隧道围岩强度提供了一种新的切实可行的思路,能提高隧道TBM施工的可靠性和安全性,具有重要的应用价值。     

A modification of minimum norm quadratic estimation of a generalized covariance function for use with large data sets

Marshall and Mardia (1985) and Kitanidis (1985) have suggested using minimum norm quadratic estimation as a method to estimate parameters of a generalized covariance function. Unfortunately, this method is difficult to use with large data sets as it requires inversion of an n × n matrix, where n is number of observations. These authors suggest replacing the matrix to be inverted by the identity matrix, which eliminates the computational burden, although with a considerable loss of efficiency. As an alternative, the data set can be broken into subsets, and minimum norm quadratic estimates of parameters of the generalized covariance function can be obtained within each subset. These local estimates can be averaged to obtain global estimates. This procedure also avoids large matrix inversions, but with less loss in efficiency.     

Stratigraphical Time——Correlation and Mass Extinction Event Near Permian——Triassic Boundary in South China

Shaw’s method used to correlate40 sections across the Permo-Triassic boundaryin South China is applied in the paper.Two steps are adopted to get an Integral Compo-site Section(ICS)by synthesizing these data:First,South China is divided into fiveareas and composite section developed for each area.Then the second step,theChangxing composite section is regarded as a composite standard(CSRS)while the ICSis produced by matching the CSRS with composite sections of the other areas.Threebiozones in the Changxingian and two biozones in the Griesbachian can be discerned onthe basis of computing Z values in the ICS.These biozones are marked by the Z values which quantitatively represent their time ranges;therefore,they may increase accuracy ofstratigraphic time correlation.The mass extinction at the end of the Permian is an ab-rupt event that is supported by the relative rate of extinction near the P/T boundary.About90％of invertebrate species died out by the end of the Permian.The duration ofthe mass extinction     

A generalized image and boundaries of the Bazhenov Formation: constraints from well log data for Salym-type sections (West Siberia)

A technique akin to Galton’s composite portraiture is suggested for creating a generalized image of a stratigraphic unit based on well log data from a group of well sections. The procedure begins with superimposing stratigraphically equivalent section points according to pairwise correlation models followed by weighted summation of similar logs. The superimposition highlights persistent common features of the sections, while their minor individual details become suppressed. A generalized model of the Bazhenov Formation in the Salym area has been constructed from gamma-ray, apparent resistivity, and self-potential logs. Radioactivity and resistivity anomalies, which are often used as constraints on the Bazhenov Formation boundaries, show a significant spatial discrepancy. According to the correlation, the formation volume in each well depends on the depth interval corresponding to the hypostratotype. The results were used to map the Bazhenov Formation thickness and its standard deviation, as well as average values of different logs.     

Correlation of well logs as a multidimensional optimization problem

We consider a variant of automatic correlation between well sections based on construction of multidimensional functions of differences between fragments of logs. The solution is obtained either by successive correlation between the boundaries based on the projective model of Haites and definition of the boundary position at the minimum of the difference function or by construction of the lines of optimal trajectories on a 2D Zhekovskii’s plot. These algorithms are implemented as a program package for original interpretation of well data and as a plug-in for the automatic correlation module of the Schlumberger Petrel software using the Ocean development tools.© 2015, V.S. Sobolev IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved.