亚失稳阶段雁列断层热场演化的实验研究

寻找地震前兆是国内外地震预报的难点.在实验室开展岩石变形实验,观测相关物理量的演化特征和规律,是前兆探索中重要的基础工作.本文对压性雁列断层进行变形实验,根据应力时间曲线将具有前兆意义的变形阶段分为强偏离线性阶段、亚失稳阶段和失稳阶段,利用红外热像仪记录各个阶段的热场变化,特别是亚失稳阶段的热场表现.研究结果显示:强偏离线性阶段,岩桥区挤压升温;亚失稳阶段,断层带增温,且高温点扩展连通,断层带内侧卸载降温,断层带上的协同化增温和断层带内侧(包含岩桥区)的协同化降温是失稳前的重要信号;失稳阶段,应力释放,标本整体降温,只有断层带因摩擦升温.总之,亚失稳阶段的热场具有明显特征,利于识别出亚失稳态;不同变形阶段、不同构造部位温度变化不同,在寻找与构造活动相关的热异常时,应考虑变形所处的阶段及异常所处的构造部位.     

2016年门源MS6.4地震前亚失稳短期前兆综合分析

1 研究背景 地震预报要取得防灾减灾实效,关键在于短—临预报.亚失稳是断层失稳前区域应力由积累为主转变为释放为主的最后阶段,马瑾等(2012,2014)总结了震前应力积累、亚稳态、亚失稳态3个阶段的不同特点,指出失稳错动是由断层各部位独立活动向协同化活动的转化过程,偏离线性的亚稳态是应力释放、协同作用的开始,亚失稳阶段应力释放已占据优势.     

芦山MS 7.0与岷县—漳县MS 6.6强震前跨断层形变亚失稳前兆

正地震预报要取得防灾减灾实效,关键在于短—临预报。亚失稳是断层失稳前区域应力由积累为主转变为释放为主的关键阶段,也是断层从稳定到失稳的最后阶段。马瑾等(2012,2014)讨论了震前应力积累、应力—时间过程中偏离线性、峰值后亚失稳态3个阶段的不同特点,总结失稳错动是由断层各部位独立活动向协同化活动的转化过程,     

强震前断裂亚失稳阶段及失稳部位的特征研究——以新疆南天山西段为例

我们把处于亚失稳阶段的断裂简称为亚失稳断裂,亚失稳阶段是断层临近失稳的最后阶段,识别这个阶段并判断出地震最终的发生位置是一个关键的科学问题.参考实验室关于断层亚失稳应力状态的研究结果,以6.8级以上地震为研究的目标地震,提出判定具备发生6.8级以上地震的亚失稳断裂研究方法：①构造区Benioff应变积累支持6.8级以上地震发生;②从高应变积累构造区中找出高应变积累且应变开始缓慢释放的断裂;③区分断裂的积累段和释放段,根据断裂释放段的协同化程度判定其是否处于亚失稳阶段,寻找失稳部位;④断裂Benioff应变是否符合加速释放模型,分析亚失稳断裂发震的紧迫性.本文以南天山西段为研究区,使用亚失稳断裂判定方法对2008年10月5日乌恰6.8级地震进行回溯性研究,结果显示卡兹克阿尔特断裂在主震前具备上述4个条件,预测取得较好的效果;进而使用该方法对研究区现今应力状态进行探索性预测研究,发现目前柯坪断裂符合亚失稳状态条件的前三条,需关注该断裂的地震活动.     

断裂亚失稳阶段及失稳部位特征的初步研究-以南天山西段和汶川地震为例

亚失稳阶段是指应力从峰值时刻到产生快速应力降起始时刻之间的阶段,是断层临近失稳的最后阶段,也是区域应力状态由积累为主转变为释放为主的阶段。识别断层的亚失稳应力状态、探讨强震亚失稳阶段即将面临的失稳部位的特征,寻找确认方法是一个很有现实意义,又很有挑战意义的科学问题。在实验室得到的断层亚失稳阶段的特点为野外识别亚失稳应力状态打下了基础。论文结合实验室已有结果,对处于亚失稳应力状态断层的特点进行了初步探索,研究了失稳前发震断裂的演化,分析了断裂协同化过程及应力状态;初步得到野外强震前断层的亚失稳阶段特征、演化过程以及可能的判定指标。地震发生过程中构造应力和应变的变化可以用Benioff应变分析法对其地震活动进行定量描述,分析研究区应变积累释放特征,探讨震前发震断裂是否存在地震加速活动现象或平静现象,以便与实验室应变观测结合起来进行分析。论文首先分析了前人利用Benioff应变研究加速释放方法的研究结果,探讨了其存在的问题,作者改进了已有方法。文中结合实验室研究结果给出了亚失稳断裂的研究方法,继而对南天山断裂带西段发生过2008年乌恰6.8级地震的卡兹克阿尔特断裂开展了回溯性研究,并使用该方法在研究区对目前的应力状态进行了预测性研究。其次以汶川M_S8.0地震为例,研究地震前后由于介质变化引起的远震转换波到时差的变化特征,从而分析震源区介质所处的应力状态。本项研究在以下方面取得进展:(1)把处于亚失稳阶段的断裂简称为亚失稳断裂,参考实验室关于断层亚失稳应力状态的研究结果,以Benioff应变积累达到支持7级以上地震发生的断裂为研究目标,提出判定亚失稳断裂的4步研究方法:(1)构造区Benioff应变积累足以支持7级以上地震发生;(2)从高应变积累构造区中找出高应变积累且应变开始缓慢释放的断裂;(3)区分断裂的积累段和释放段,根据断裂释放段的协同化程度判定其是否处于亚失稳阶段,寻找失稳部位;(4)判断断裂Benioff应变是否符合加速释放模型,分析亚失稳断裂发震的紧迫性。(2)文中在使用累积Benioff应变的加速释放模型方法时,地震序列的空间范围按断裂选取;在时间尺度选取上,取断裂Benioff应变积累释放曲线上最近的一次积累—缓慢释放时段进行分析。实验室岩石随着应力加载,亚失稳阶段应变积累、释放特征主要出现在断层附近。空间的这种选取方法根据实验室亚失稳阶段研究结果,有一定的构造物理意义。(3)本文以南天山西段为研究区,使用亚失稳断裂判定方法对2008年10月5日乌恰6.8级地震进行回溯性研究,结果显示,卡兹克阿尔特断裂在主震前满足亚失稳断裂判定方法的4个条件,取得了较好的效果;进而使用该方法对研究区现今应力状态进行预测性研究,发现目前柯坪断裂符合亚失稳状态条件的前3条:(1)南天山西段研究区的Benioff应变积累支持7级以上地震发生;(2)柯坪断裂累积Benioff应变支持6.8级以上地震发生,并且Benioff应变积累释放曲线出现波动、转平的趋势;(3)柯坪断裂77.5°—80°E的段落转为应变积累区,位于77.5°E以西的区域应变开始释放;但柯坪断裂目前不符合第4条,地震Benioff应变的释放不符合条件加速模型,表明断裂尚未进入加速协同化阶段。目前仍需密切关注该断裂的地震活动发展情况。(4)利用远震初至波穿越地壳、上地幔等速度界面时产生的一系列PS型透射转换波,测定远震PS转换波与初至P波的到时差Δt_(ps)=t_(ps)-t_p随时间的变化特征有可能监测孕震区转换界面以上有限的地层空间内介质物性的变化。选取2001—2012年作为研究时段,利用四川地震台网的YZP和JJS两台站记录到的兴都库什、苏门答腊南部地区两组震中距变化小于3°的远震,得到两个台站在2008年5月12日汶川M_S8.0地震前后记录的转换波到时差Δt_(ps)的变化特征。结果表明,在2006年以前Δt_(ps)有一个缓慢增大的趋势;汶川地震前约2年左右的时间段内Δt_(ps)出现明显低值过程,最大降幅达0.2—0.3 s左右,超过测量误差4—5倍;震前约2—3个月低值有一定程度的回返。表明本文提出的远震转换波方法在地震监测中有很好的应用前景,值得进一步实验研究。     

2010年河津ML 4.8地震前亚失稳现象探讨

<正>1研究背景亚失稳态力学机理及与之相关物理场的演化特性研究已成为学者关注的热点。断层带上存在相对弱和相对强的部位,前者往往首先弱化,表现为断层预滑、慢地震或弱震,成为应变释放开始部位,后者则为应力闭锁部位,并成为快速失稳开始部位（Noda et a1,2013）;地震始于预滑,即使是级联式的成核,也需要预滑为其创造条件（Mclaskey eta1,2014）;应力释放及协同化是亚失稳阶段的重要特点（马瑾等,2012）。亚失稳观测与研究对潜在地震的危险性以及危险时段判别意义重大。     

断层失稳过程超动态变形时空模式的实验研究

作为构造地震的基本物理模型,断层失稳是否可以被简单地划分为应变积累的粘滞阶段与应变快速释放的地震滑动阶段两个部分,并用弹簧滑块组合来解释是一个根本的问题。近几十年来,对失稳前断层状态的研究反映出很多研究者已经意识到这个阶段的复杂性,例如成核相、临界扩展尺度、局部化等研究的出现。亚失稳模型的提出把临震阶段的研究推向了深入,指出临震亚失稳阶段之中各种物理量存在规律性的时空演化特征,控制这些物理参数变化的根本原因是震源力学过程的时空演化规律。为此,需要研发高速多通道多参数并行连续记录的实验观测系统,依托这个系统对断层失稳变形的全过程,特别是失稳前几秒到微秒级别的瞬态变形过程,以及失稳滑动瞬态过程进行精细深入的观测,解析相关的震源力学问题。我们研发了一套64通道,16位分辨率,4 MHz采样频率并行连续采集的超动态变形场观测系统,首次实现了应变信号和声发射信号的同步采集。该系统在技术上处于国际同类实验室领先水平。基于该系统完成了多组实验,共获得209个失稳滑动事件,记录到约42 TB应变和声发射实验数据。实验证明,该系统具有很好的稳定性,为开展预滑、亚失稳、动态加速过程、失稳滑动瞬态过程等研究提供了一个全新的技术平台。以此系统为基础对断层失稳全过程进行观测,对断层亚失稳阶段,特别是亚失稳准动态阶段以及瞬态失稳阶段的变形场信息进行了精细深入的观测。获得以下结论:(1)伴随有断层局部卸载而出现的应变局部化加速是进入亚失稳准静态阶段的近场判据。在理论模型的描述中,亚失稳阶段的开始以样品宏观变形的应力曲线进入峰值后为标志。从沿断层的应变观测可以确认,峰后的整体应力下降在样品内部体现为个别段落的卸载,也就是说,从以全场稳态变形为主的应力积累阶段转变为局部卸载为主的亚失稳准静态阶段。在这个阶段中,断层各段通过相互加卸载作用使局部化进一步加强,该特点可作为进入亚失稳阶段的近场判据。(2)亚失稳准动态阶段存在应变波动的往复传递。亚失稳准动态阶段以逐点应变波浪式的往复传递为表现形式,在本文研究分析的实验中,准动态阶段可以分为3个子阶段(AA1、A1A2和A2A3阶段),每个子阶段对应一次应变波动的传递事件。第一阶段,应变波动的传递开始于断层中部并向上端的高应变区逐点释放;第二阶段,在上次应变传递的终点,一个新的应变波动出现并向断层下端反向传递,影响范围超过了第一阶段波动的起始位置并到达断层下端;第三阶段,在第二次应变波动到达的断层下端位置,再次出现新的向断层上端反向传递的应变波动。最后一次应变波动的传递贯穿了整条断层并到达断层上端的高应变区,使得累加应变达到了局部的剪切强度。最终从高应变区开始,整条断层带周边的应变能快速释放,造成"地震"。3个阶段中,应变波动传递的周期越来越短,速度越来越快,平均速度依次成几十倍递增。第一阶段,应变传递时间约7 s,平均速度约为16 mm/s;第二阶段,应变传递时间约0.16 s,平均速度约为920 mm/s;第三阶段,应变传递时间约0.017 s,平均速度约为17 600 mm/s(17.6 m/s)的速度扩展至整条断层。(3)准动态过程每个子阶段都存在短暂的准备期。准动态过程中,每个子阶段的应变传递开始前,在上一次应变传递的停止区域,会出现一个短暂的应变准备期,随后才能进入下一阶段的应变波动传递过程。第二子阶段的应变波动传递开始之前,在第一子阶段波动传递终点区域出现一个时长约为100 ms的应变准备期,随后开始第二阶段的应变波动传递;同样地,第三子阶段的应变波动传递开始,在第二子阶段应变波动传递终点区域出现一个时长约为25 ms的应变准备期,随后开始第三子阶段的应变波动传递;最终,在断层整体快速应变释放前,在第三子阶段应变波动传递终点区域出现一个时长约为3 ms的应变准备期,随后断层整体应变快速释放,发生"地震"。断层出现过渡带的原因可能是传递到端点的应变波动释放的应变并不足以引发断层整体滑动,需要重新积累应变直至产生下一次波动事件。应变准备期的出现,特别是断层瞬态失稳前的短暂应变准备期,可能为临震预测提供依据。(4)断层瞬态失稳初期存在同震高频应变震荡。在断层瞬态失稳初期,存在数次高频应变震荡,频率约为2 k Hz,频谱上限约为15 k Hz,单次应变震荡周期约为0.5 ms。每次高频振荡都伴随有一次实验室地震(声发射)事件,称其为同震高频应变震荡。虽然每次高频震荡在时间上存在一定的先后关系,但是由于在测点等间距的情况下走时时差不同,且存在应变波反向传播的情况;另外,各点应变波振幅水平大致相同,没有从震荡初始位置向两侧振幅衰减的特征。所以各点之间并不表现为应变波的传播关系。(5)存在毫秒时间尺度的同震子事件。在断层失稳阶段,如果出现"双震",每次"子地震"都对应一个或数个高频同震应变振荡波。同时,各次高频震荡的发震位置可能不同。这与中频系统所看到的多点震源情况类似,也就说明在不同的时间尺度上都可以观测到多点震源的情形。(6)断层整体止滑前存在应变波动的反向传递。在数次高频震荡结束后,出现一个相对低频的反向应变波动从断层另一端传递至发震位置,本次反向脉冲并不伴随有声发射现象。此后,断层整体同震阶段结束,各点开始在自己的应变水平上进行阻尼式的高频震荡。这个反向传递的应变波动可能包含着地震停止和断层止滑的重要信息。(7)浅震源环境下的三轴试验验证。与此同时,为了验证亚失稳阶段和瞬态失稳阶段在浅震源压力环境下是否符合类似规律,在三轴围压容器内完成多组实验。浅震源环境下的断层失稳实验表明,亚失稳阶段和复杂的断层瞬态失稳阶段在浅震源压力环境下依然存在,其进程与在双轴加载系统环境下的观测结果相符。     

识别断层活动和失稳的热场标志——实验室的证据

利用一套双向伺服系统对含压性和张性雁列断层的标本进行变形实验,实验中应用红外热像仪和接触式测温仪同步记录岩石变形过程中热红外辐射的亮度温度场和温度场的变化;使用数字CCD相机同步采集标本表面的数字图像,并利用数字散斑方法对采集到的图像进行分析得到位移场和应变场的演化过程。实验结果表明:1)在断层贯通前压性雁列岩桥区温度最高,而张性雁列岩桥区温度最低;数字散斑结果显示压性岩桥区平均应变最高,而张性岩桥区平均应变最低。温度场对两类雁列断层在岩桥区相反的受力状态有清晰的响应,可以为判断断层应力状态提供标志。2)雁列断层经历了从岩桥区应力积累、破坏到断层失稳错动两个变形阶段,升温机制也由应变升温变为摩擦升温;伴随升温机制的转变,在岩桥区观测到断层失稳错动前的破坏降温、温度快速起伏以及升温脉冲等现象,是观测失稳前兆的最佳部位。3)在雁列岩桥区裂纹端点附近观测到升温脉冲,表现为温度快升快降,随后即出现断层带的快速升温。升温脉冲现象可能与裂纹端部的应力奇异集中和破裂扩展引起的应力释放有关。裂纹端部的扩展是断层失稳错动的条件,随后断层带的升温正是断层失稳错动造成的。断层带开始升温发生在失稳前2～3s内,岩桥区的降温发生在失稳     

汶川地震失稳机制的数值模拟研究

考虑断层的软化特性,建立垂直于龙门山断裂带并包含四川盆地和川西高原在内的汶川地震不稳定性地震力学模型.采用有限元方法计算得到了描述整个岩石力学系统稳定性状态和过程的平衡路径曲线.在此基础上,采用稳定性理论研究了汶川地震从孕育到发生的过程,讨论了断层倾角和断层材料参数对地震失稳的影响.数值模拟结果显示,系统只存在稳定的断层无震滑动和不稳定的地震失稳2种状态.断层倾角、初始内摩擦系数、初始黏聚力和强度曲线形状参数的增加会导致系统趋向不稳定的地震失稳状态.而强度曲线胖度参数的增加有助于系统进入稳定的断层缓慢无震滑动状态.地震失稳前,在平衡路径曲线的应力峰值点和失稳点之间,断层错动加速,应变能开始释放并且应力开始减小,是失稳的前兆.最后在失稳点发生应力突跳,地震发生,其间伴随应变能的急剧释放、应力降和断层突然错动.无论是稳定的断层无震滑动还是不稳定的地震失稳,系统重新进入应力和应变能增加状态后应力和应变能的增速由远场加载速度、岩石力学系统的结构和围岩材料属性决定,与断层软化特性参数无关.     

平直走滑断层亚失稳状态的位移协同化特征——基于数字图像相关方法的实验研究

亚失稳阶段是断层临近失稳的最后阶段,识别断层亚失稳状态,对评估断裂区内的断层失稳危险性具有重要意义．含平直走滑断层的岩石样品在卧式双轴伺服控制压机上加载产生黏滑,同时用高速相机以1000帧S_的速度记录样品变形,失稳过程中的数字图像,然后采用数字图像相关分析方法计算样品表面变形场,并通过定义表征断层位移累计值相对离散程度的协同化系数来描述断层失稳过程的协同化特征,结果表明：（1）局部预滑区进入亚失稳阶段之前,扩展速率非常缓慢;进入亚失稳I阶段后,扩展速率有所增加,但仍很缓慢,属于准静态扩展;在亚失稳II阶段,在占整个亚失稳阶段～1．5％的时间段内,断层先是以～0．9mS。的速率扩展,继而快速贯通整个观测区域,此时断层已转为准动态扩展．（2）在亚失稳I阶段断层位移协同化系数降为进入亚失稳前的一半,在亚失稳II阶段这一系数再降为进入亚失稳前的四分之一．这一系数持续下降意味着断层位移协同化作用的加强,亦可作为断层进入亚失稳阶段的特征之一．（3）此外,在断层失稳滑动阶段,观测区内断层出现三次整体滑动：初始滑动,快速滑动和调整滑动．断层在三次滑动之间存在两次短暂的停顿过程．     

A Monte Carlo study of rainfall forecasting with a stochastic model

A procedure for short-term rainfall forecasting in real-time is developed and a study of the role of sampling on forecast ability is conducted. Ground level rainfall fields are forecasted using a stochastic space-time rainfall model in state-space form. Updating of the rainfall field in real-time is accomplished using a distributed parameter Kalman filter to optimally combine measurement information and forecast model estimates. The influence of sampling density on forecast accuracy is evaluated using a series of a simulated rainfall events generated with the same stochastic rainfall model. Sampling was conducted at five different network spatial densities. The results quantify the influence of sampling network density on real-time rainfall field forecasting. Statistical analyses of the rainfall field residuals illustrate improvement in one hour lead time forecasts at higher measurement densities.     

Earthquake Engineering and Engineering Vibration Aims And Scope

正This journal is established by the Institute of Engineering Mechanics(IEM),China Earthquake Administration,to promote scientific exchange between Chinese and foreign scientists and engineers so as to improve the theory and practice of earthquake hazards mitigation,preparedness,and recovery.To accomplish this purpose,the journal aims to attract a balanced number of papers between Chinese and     

Solute concentrations in the lower niger river and the source rock contribution

Water quality analyses for the Niger River for the 1980/81 hydrological year are presented. The samples were collected from the main river at Lokoja, and from two main tributaries, the Kaduna and the Benue Rivers. Different water types were distinguished by the concentrations of major ions. The type Ca > Na > Mg > K - HCO₃ > SO₄ > Cl was represented at all stations during at least part of the year. Chloride was found to dominate the sulphate ion in the Kaduna and Niger, while the Benue maintained a higher concentration of sulphate relative to chloride all year round. Distinct patterns of seasonal variation in the ion concentrations were observed, particularly for the samples collected at Lokoja. Low ion concentrations were prominent during periods of high discharge, while low flow periods coincided with high dissolved ion concentrations. The contribution of rainwater to the total dissolved solids in the river waters was assessed indirectly using rainwater chemistry data from the Gulf of Guinea. The estimated rainwater contribution to the Lower Niger amounts to 5.15 mg 1^?1. Geochemical weathering calculations involving reactions of the four major minerals of granitic rocks - anorthite, biotite, albite, and K-feldspar - with carbon dioxide and water, can account for the average water composition of the Lower Niger. The proportion of the ionic components was also related to the occurrence of the respective element in the minerals.     

Scenario predictions for potential near-field and far-field earthquakes affecting Hong Kong

Historical earthquakes noted in the written records of the South China region, including Hong Kong, are not well delineated along identified prominent fault sources. Despite the lack of any definitive, localised trend in the spatial distribution of seismic activity in the region, there does appear to be some major disparity in the seismic activity rates (especially for large magnitude earthquakes) between the near-field and the far-field regions of Hong Kong. Despite this observation, previous studies of the regional seismic activity and seismic ground motion hazard (the latter using a probabilistic seismic hazard assessment, PSHA) have considered very broad source zone regions, in which uniform levels of seismic activity have been assumed. The present paper further scrutinises this broad source zone (BSZ) approach by adopting a novel expanding circular disc (ECD) method to determine the rates of earthquake recurrence. Such a method is intended to counter-check previously developed models by determining earthquake scenario events in terms of magnitude–distance (M–R) pairs or combinations, having defined values of average return period. Unlike the BSZ approach, the ECD method specifically accounts for the supposed variations in the seismic activity rates between events in the near-field and the far-field of Hong Kong.The form of the developed method is particularly suited to the determination of design-level earthquake ground motions for bedrock sites, since it assumes a directionally-independent attenuation model as described in the companion paper. It is found that, whilst the BSZ approach may indicate the overall average levels of hazard that are representative of the South China region as a whole, it does not capture the large disparity in seismic activity rates between near-field and far-field events. This important feature is expected to have a significant impact upon engineering assessments of the seismic safety of structures in Hong Kong and elsewhere in the South China region. For example, it is found that for events with M≥6, the seismic activity rate (normalised by time and area) in the very far-field is around 3.5 times larger than in the near-field and medium-field of Hong Kong. The resulting design M-R combinations, covering a range of return periods from 70 to 2500 years, are limited, for very long return periods and for distant events, by the maximum credible earthquake (MCE) magnitude. Intensive research to determine this seismic hazard parameter is recommended, in order to refine further the results of the ECD analysis, which presently conservatively assumes the MCE to range between M=6 in the near-field of Hong Kong to M=8 in the very far-field, at distances greater than 280 km from Hong Kong.     

Depositional ages and characteristics of Middle–Upper Jurassic and Lower Cretaceous lacustrine deposits in southeastern Mongolia

Lower Cretaceous lacustrine oil shales are widely distributed in southeastern Mongolia. Due to the high organic carbon content of oil shale, many geochemical studies and petroleum exploration have been conducted. Although most of the oil shales are considered to be Early Cretaceous in age, a recent study reveals that some were deposited in the Middle Jurassic. The present study aims at establishing depositional ages and characteristics of the Jurassic and Cretaceous lacustrine deposits in Mongolia. The Lower Cretaceous Shinekhudag Formation is about 250 m thick and composed of alternating beds of shale and dolomite. The Middle Jurassic Eedemt Formation is about 150 m thick and composed of alternating beds of shale, dolomitic marl, and siltstone. The alternations of shale and dolomite in both formations were formed by lake level changes, reflecting precipitation changes. Shales were deposited in the center of a deep lake during highstand, while dolomites were formed by primary precipitation during lowstand. Based on the radiometric age dating, the Shinekhudag Formation was deposited between 123.8 ±2.0 Ma and 118.5 ±0.9 Ma of the early Aptian. The Eedemt Formation was deposited at around 165–158 Ma of Callovian–Oxfordian. The calculated sedimentation rate of the Shinekhudag Formation is between 4.7 ±2.6 cm/ky and 10.0 ±7.6 cm/ky. Shales in the Shinekhudag Formation show micrometer‐scale lamination, consisting of algal organic matter and detrital clay mineral couplets. Given the average thickness of micro‐laminae and calculated sedimentation rate, the micro‐lamination is most likely of varve origin. Both Middle–Upper Jurassic and Lower Cretaceous lacustrine oil shales were deposited in intracontinental basins in the paleo‐Asian continent. Tectonic processes and basin evolution basically controlled the deposition of these oil shales. In addition, enhanced precipitation under humid climate during the early Aptian and the Callovian–Oxfordian was another key factor inducing the widespread oil shale deposition in Mongolia.     

THEORETICAL APPROACH TO THE SOLUTION OF THE INFILTRATION PROBLEM

ABSTRACT

The one-dimensional transient downward entry of water in unsaturated soils is investigated theoretically. The mathematical equation describing the infiltration process is derived by combining Darcy's dynamic equation of motion with the continuity and thermodynamic state equations adjusted for the unsaturated flow conditions. The resulting equation together with the corresponding initial and boundary conditions constitues a mathematical initial boundary value problem requiring the solution of a nonlinear partial differential equation of the parabolic type. The volumetric water content is taken as the dependent variable and the time and the position along the vertical direction are taken as the independent variables. The governing equation is of such nature that a solution exists for t > 0 and is uniquely determined if two relationships are defined, together with the specified state of the system, at the initial time t = 0 and at the two boundaries. The two required relations are those of pressure versus permeability and pressure versus volumetric water content.

Since the partial differential equation has strong non-linear terms, a discrete solution is obtained by approximating the derivatives with finite-differences at discrete mesh points in the solution domain and integrated for the corresponding initial and boundary conditions. The use of an implicit difference scheme is employed in order to generate a system of simultaneous non-linear equations that has to be solved for each time increment. For n mesh points the two boundary conditions provide two equations and the repetition of the recurrence formula provides n—2 equations, the total being n equations for each time increment. The solution of the system is obtained by matrix inversion and particularly with a back-substitution technique. The FORTRAN statements used for obtaining the solution with an electronic digital computer (IBM 704) are presented together with the input data.

Analysis of the errors involved in the numerical solution is made and the stability and convergence of the solution of the approximate difference equation to that of the differential equation is investigated. The method applied is that of making a Fourier series expansion of a whole line of errors and then following the progress of the general term of the series expansion and also the behavior of each constituent harmonic. The errors (forming a continuous function of points in an abstract Banach space) are represented by vectors with the Fourier coefficients constituting a second Banach space. The amplification factor of the difference equation is shown to be always less than unity which guarantees the stability of the employed implicit recurrence scheme.

Experiments conducted on a vertical column packed uniformly with very fine sand, show a satisfactory agreement between the theoretically and experimentally obtained values. Many experimental results are shown in an attempt to explain the infiltration phenomenon with emphasis on the shape and movement of the wet front, and the effects of the degree of compaction, initial water content and deaired water on the infiltration rate.     

Late Permian post‐ophiolitic trondhjemites from Central Iran: a mark of subduction role in growth of Paleozoic continental crust

Late Permian trondhjemites in the Anarak area occur as stocks and dykes, which cross cut the Anarak ophiolite and its overlying metasedimentary rocks, and are exposed along the northern Anarak east–west main faults. These leucocratic intrusive bodies have enclaves of all ophiolitic units and metamorphic rocks. They are composed of amphibole, plagioclase (oligoclase), quartz, zircon and muscovite. Secondary minerals are chlorite (pycnochlorite), epidote, albite, magnetite and calcite. Whole‐rock major‐ and trace‐element analyses reveal that they are characterized by high SiO ₂ (67.8–71.0 wt%), Al ₂ O ₃ (14.9–17.1 wt%) and Na ₂ O (5.3–8.6 wt%), low K ₂ O (0.1–1.5 wt%; average: 0.8 wt%), low Rb/Sr ratio (0.01–0.40; average: 0.09), low Y (3–6 ppm), negative Ti, Nb and Ta anomalies, slightly negative or positive Eu anomaly, LREE enrichment and fractionated HREE. These rocks present 2 to 40 times enrichment in inclined chondrite‐normalized REE patterns. Geochemical characteristics of the Anarak trondhjemites all reflect melting of a mafic protolith at more than 10 kbar. The field evidence and whole‐rock chemistry reveal that these rocks have been crystallized from magmas derived from melting of subducted Anarak oceanic crust. This study reveals that melting of garnet amphibolite was an important element of continent formation in the study area.