冀西北怀安地区中性辉石麻粒岩的锆石U-Pb、Lu-Hf及微量元素组成对区域退变质时代的制约

冀西北怀安地区位于华北克拉通北缘中段。其区域麻粒岩相变质峰期时间及所代表的碰撞造山时限一直存在不同认识。本文对出露于区内的中性辉石麻粒岩体(变石英闪长岩)进行锆石U-Pb、Lu-Hf及微量元素组成的分析研究,探讨其锆石同位素年龄的地质意义。该类岩石的矿物组合表明它们在中压麻粒岩峰期变质之后经历了角闪岩相退变质作用。锆石阴极发光显示,辉石麻粒岩中存在两种类型锆石:1)具双层结构锆石:核部锆石晶形保存相对完好并具生长环带,幔部为无内部结构的变质增生边;2)内部结构均一,无生长环带,为变质增生的新生锆石。其中具生长环带的核部锆石²⁰⁷Pb/²⁰⁶Pb年龄分布在2542~1902Ma(1σ),并与之相应的Th/U比值(0.10~1.92)、ΣHREE(59.1×10^-6~452×10^-6)和ε_Hf(t)值呈正相关关系,表明核部锆石曾发生过不同程度的变质重结晶作用。其中谐和度高且年龄大于2400Ma的锆石(Th/U=0.42~1.92)获得了2471±18Ma(2σ, MSWD=6.7)加权平均年龄,该年龄可近似代表原岩的形成时代;相应的单阶段Hf模式年龄(t_DM=2550~2621Ma,峰值2586Ma)和两阶段模式年龄(t_DM^C=2596~2716Ma,峰值2665Ma)以及与较高的ε_Hf(t)值(4.1~6.7),反映其原岩的源区具新生下地壳特征,暗示本区新太古代末发生过地壳增生事件。变质增生锆石具更低的Th/U(<0.10)和¹⁷⁶Lu/¹⁷⁷Hf比值(<0.0001)以及明显偏低的重稀土含量。结合岩相学分析表明,这些变质锆石应是麻粒岩相向角闪岩相退变质过程中的产物,非峰期麻粒岩相产物。锆石Ti温度计算结果(683~714 ℃)也进一步支持这种解释。它们获得的1831±7Ma(2σ, MSWD=2.5)加权平均年龄应代表中压麻粒岩相变质晚期至角闪岩相退变质时代。为此,我们认为本区麻粒岩广泛记录的1850~1800Ma的变质年龄应代表古元古代末地壳抬升退变质事件。     

皖南旌德花岗闪长岩与暗色包体的成因: 地球化学、锆石U-Pb年代学与Hf同位素制约

旌德复式岩体位于安徽南部,主体相花岗闪长岩中发育暗色包体。本文对花岗闪长岩与暗色包体进行了岩相学观察、全岩主微量元素分析、锆石U-Pb定年与Hf同位素测试。岩相学观察发现暗色包体为典型岩浆岩结构,且发育针状磷灰石。主量元素分析数据表明花岗闪长岩的SiO₂含量为66.04%~67.80%;暗色包体的SiO₂含量为54.63%~54.77%,为二长闪长岩。花岗闪长岩的Mg^#=38~40;暗色包体的Mg^#=44~45。微量元素分析数据表明花岗闪长岩与暗色包体的REE球粒陨石标准化图呈右倾型,Eu负异常;大离子亲石元素富集,高场强元素亏损。锆石U-Pb年代学与Hf同位素研究表明,花岗闪长岩与暗色包体的年龄分别为139.7±1.3Ma和142.3±1.7Ma,在误差范围内一致。花岗闪长岩锆石的ε_Hf(t)为-2.5~0.4,地壳模式年龄(t_DM^C)为1170~1350Ma;暗色包体锆石的ε_Hf(t)为-5.2~1.8,地壳模式年龄(t_DM^C)为1090~1530Ma。两者的t_DM^C峰值都在1.2~1.3Ga。这些数据表明花岗闪长岩中的暗色包体为同源岩浆混合成因,源区为年轻地壳,有可能为中新元古代古华南洋壳俯冲扬子板块形成的火山岛弧。旌德花岗闪长岩在Pearce et al.(1984)的构造判别图上落在岛弧花岗岩区。在Sr/Y-Y图解上落在经典岛弧岩浆岩区。花岗闪长岩的岩浆Zr饱和温度低(630~680℃),与锆石钛温度计(630~720℃)给出的结果基本一致。锆石的Ce(Ⅳ)/Ce(Ⅲ)高(240~530),指示岩浆具有高的氧逸度。旌德岩体的低温与高氧逸度特征说明岩体的源区物质受到过洋壳俯冲的影响。旌德岩体的成因可能与太平洋板块后撤诱发的地壳部分熔融有关。     

攀西地区大板山岩体的年代学、元素地球化学及其对铜镍硫化物矿床成因的约束

大板山镁铁-超镁铁质杂岩体位于攀西地区西北部,受金河-菁河断裂带控制,主要岩石类型有辉长岩、苏长辉长岩和二辉橄榄岩。本次研究集中于苏长辉长岩和二辉橄榄岩,其中,二辉橄榄岩具有明显的堆晶结构,橄榄石Fo值最高可达81.4。二辉橄榄岩SiO₂含量为42.93%~44.18%,苏长辉长岩SiO₂含量为44.89%~52.76%,稀土总量(∑REE)相对较低(23.2×10^-6~61.7×10^-6),并均呈现出近平行的、相对平缓的右倾稀土元素配分模式,说明其为同源岩浆演化的关系。此外,大部分样品相对富集大离子亲石元素(LILE;如Rb、Sr、Ba等),适度亏损高场强元素(HFSE;如Nb、Ta、Ti等)。结合其较低的SiO₂含量和微量元素比值(如Th/Ta和La/Nb等),表明岩浆未遭受大量的地壳混染。岩相学和岩石地球化学特征均显示了非常明显的分离结晶作用。根据(Tb/Yb)_PM-(Yb/Sm)_PM图解,大板山岩体的原始岩浆主要来源于岩石圈地幔轻度富集不相容元素的尖晶石相二辉橄榄岩。二辉橄榄岩样品中橄榄石Fo-NiO图解中多数点落在硫化物未熔离的范围,且样品全岩Cu/Zr比值为7.04~103,而苏长辉长岩中Cu/Zr比值为0.88~5.56,反映了二辉橄榄岩-苏长辉长岩可能经历了由S不饱和到过饱和的过程。推测硫化物的熔离可能是岩浆在上地壳岩浆房中发生了以橄榄石和辉石为主的分离结晶作用,造成硫化物达到过饱和。锆石LA-ICP-MS测年表明,岩体年龄为259.69±0.61Ma,与峨眉山大火成岩省其它镁铁-超镁铁质岩体的形成时间基本一致。     

藏南冈底斯岩基东段朗县杂岩早白垩世岩浆作用:新特提斯洋二次俯冲

新特提斯洋长期俯冲消减作用在早白垩世可能经历二次俯冲启动或板片俯冲几何形态的重大转换。确定西藏南部冈底斯岩基早白垩世岩浆作用的岩石地球化学特征和作用方式是甄别上述过程的关键,对理解新特提斯洋的俯冲演化过程至关重要。本文就冈底斯岩基东段朗县杂岩中保存的各类早白垩世岩浆岩,开展了锆石U-Pb地质年代学和Hf同位素、全岩元素和同位素（Sr-Nd）组成分析。数据结果表明：1）基性岩侵位时代为早白垩世晚期（103.6~100.8Ma）,为高钾钙碱性偏铝质岩石,锆石ε_Hf（t）=+0.3~+5.7,全岩ε_Nd（t）=-0.8和-0.3,暗示其岩浆源区具有大量俯冲沉积物或流体的混入,为沉积物熔体和流体交代的地幔楔物质部分熔融的产物,经历了一定程度的角闪石分离结晶作用;2）中性岩形成于99.8~97.6Ma,略晚于基性岩,其主量元素与基性岩具有较好的线性关系,全岩ε_Nd（t）=+1.1,具有较多的地幔物质参与,为基性岩浆进一步演化形成;3）酸性岩（脉体）记录了多阶段岩浆作用（124.1~95.3Ma）,根据同位素组成不同进一步划分为两类,第一类具有较低的全岩ε_Nd（t）值（-8.3~-6.0）,其岩浆源区显示富集特征,t_DM2=1385~1586Ma,由古老地壳物质的再熔融形成;第二类的锆石ε_Hf（t）值（-2.8~+3.2）变化较大,岩脉的锆石ε_Hf（t）=+0.4~+8.1,t_DM=428~906Ma,全岩ε_Nd（t）=+0.1和+0.8,表明岩浆源区具有不均一性,为古老地壳物质被富流体地幔岩浆改造形成;和4）镁铁质包体的主量元素与寄主花岗岩具有较好的线性关系,锆石的Hf同位素组成变化较大（ε_Hf（t）=-9.3~+4.1）,变化范围可达13个ε单位,为岩浆混合成因。寄主花岗岩和角闪辉长岩分别作为酸性和基性端元,是基性岩浆与其诱发古老地壳熔融形成的花岗质岩浆经混合形成。结合冈底斯岩基早白垩世岩浆岩的研究结果,朗县杂岩在早白垩世（124~97Ma）的岩浆作用具有明显的岩浆混合现象,锆石Hf和全岩Sr-Nd同位素组成变化较大,可达13个ε单位,其岩浆源区复杂且富含流体,代表了新特提斯洋在早期（240~144Ma）经历漫长的俯冲之后,在早白垩世时期（~120Ma）俯冲带发生跃迁或俯冲角度达到临界点,导致大量俯冲沉积物和流体沿俯冲带俯冲下去,与发生部分熔融的地幔楔物质混合,底侵导致上覆古老地壳物质的再熔融,形成早白垩世复杂的岩浆岩组合,很可能是新特提斯洋二次俯冲开始的标志。     

满洲里南部白音高老组流纹岩锆石U-Pb定年及岩石成因

满洲里南部白音高老组火山岩主要由流纹岩组成,含少量珍珠岩和流纹质凝灰岩。LA-ICPMS锆石U-Pb定年结果显示,流纹岩形成于141~139Ma的早白垩世早期。岩石地球化学研究表明,火山岩具有高硅富碱、贫钙镁和高FeO^T/MgO比值的特征; 稀土丰度总量较高(∑REE介于103×10^-6~488×10^-6),轻重稀土分馏明显［(La/ Yb)_N=4.12~30.94)］,Eu负异常显著(δEu=0.12~0.46); 微量元素以富集Rb、Th、U、K,强烈亏损Ba、Sr、P、Ti,中等亏损Nb、Ta和高Ga/Al值为特征,与A-型花岗岩特征相似。锆石¹⁷⁶Hf/¹⁷⁷Hf比值介于0.282785~0.282970之间,ε_Hf(t)值均为正值,介于3.78~9.98之间。流纹岩岩浆来源于斜长石稳定区玄武质下地壳物质的部分熔融,形成于非造山板内伸展构造环境。     

皖南歙县邓家坞钼矿床年代学及Hf同位素地球化学研究

歙县邓家坞片麻状花岗闪长岩体位于扬子陆块南缘,区内钼矿体主要产于岩体与变质流纹凝灰岩的外接触带上,受区内北东向的断裂控制。歙县邓家坞花岗闪长岩具有强过铝质的特征,为S-型花岗岩,属于高钾钙碱性系列岩石。岩石富集大离子亲石元素(Rb、Th、K),相对亏损高场强元素(Nb、Ta、Ti),稀土元素含量较低(ΣREE=114.3×10^-6~259.1×10^-6),轻重稀土分异明显(ΣLREE/ΣHREE=6.48~10.98),中等的Eu负异常(Eu_N/Eu_N^*=0.46~0.60),具有典型岛弧岩浆岩的特征。锆石U-Pb同位素定年结果显示²⁰⁶Pb/²³⁸U表面年龄为739~816Ma,加权平均年龄为772±11Ma (MSWD=5.0),表明邓家坞片麻状花岗闪长岩体形成于新元古代,与皖南新元古代花岗闪长岩的主成岩年龄(740~825Ma)基本一致。根据岩石Zr含量计算出歙县邓家坞花岗闪长岩的"锆石饱和温度"为792~827℃。锆石Hf同位素ε_Hf(t)为0.55~4.69,平均值为2.48,二阶段模式年龄(t_DM2)为1364~1565Ma,表明邓家坞片麻状花岗闪长岩源区主要为新生地壳组分。邓家坞钼矿5个辉钼矿样品Re-Os同位素定年的模式年龄为141.1~141.6Ma,等时线年龄为141.8±2.2Ma,表明该钼矿的成矿时代为早白垩世。邓家坞片麻状花岗闪长岩体不是成矿岩体,因此推测可能其深部有隐伏的早白垩世岩体。辉钼矿的Re含量为12.6×10^-6~43.8×10^-6,表明成矿物质以壳源为主。     

栖霞牙山花岗岩及其暗色包体地球化学特征及成因研究

栖霞牙山花岗岩体形成于中生代早白垩世（118 Ma）,其岩石类型以花岗岩和花岗闪长岩为主,岩体中发育大量的暗色闪长质微粒包体。通过对牙山花岗岩及其暗色包体地球化学特征研究表明,包体围岩w（SiO₂）=65.5%~68.82%,铝饱和度（A/CNK）为0.89~1.03<1.1,为准铝质钙碱性Ⅰ型花岗岩;暗色包体具有较低w（SiO₂）值（54.82%~60.89%）、高w（TFe₂O₃）值（6.11%~8.15%）、高w（MgO）值（3.57%~5.19%）的特征。稀土元素配分模式图显示二者皆为轻稀土富集的右倾型曲线,微量元素蛛网图中二者均表现为富集Ba、K等大离子亲石元素,亏损Ta、Nb、Ti等高场强元素,具有大陆地壳的特征。暗色包体与寄主岩石的Sr同位素初始比值（⁸⁷Sr/⁸⁶Sr）_i分别为0.709 29~0.709 58和0.709 21~0.709 71,应为同源岩浆的产物。两阶段Nd模式年龄（T_2DM）分为2 291 Ma-2 391 Ma和2 208 Ma-2 353 Ma,表明可能是古元古界陆壳物质部分熔融的产物。Pb同位素特征显示牙山岩体的原始岩浆以下地壳为主,w（Nb）/w（Ta）值介于下地壳与原始地幔之间,表明可能受到幔源物质的影响,包体中大量磷灰石呈针状结晶状态,进一步暗示存在岩浆混合作用。综上并结合区域构造背景认为,牙山岩体为早白垩世中晚期起源于火山弧环境的壳源特征花岗岩,形成过程中存在幔源物质的加入,它的形成与太平洋板块的俯冲作用密切相关。     

西藏拉萨地块南缘晚白垩世镁铁质岩浆作用的年代学、地球化学及意义

镁铁质岩石所反映出的壳幔作用信息可以为地壳增生发生的时间和方式提供可靠的证据。本文报道了南部拉萨地块东段朗县至米林之间晚白垩世镁铁质岩石的岩石学、锆石U-Pb年代学、全岩地球化学以及锆石Hf同位素数据。锆石U-Pb定年结果表明,角闪辉长岩侵位于98~88Ma,高Al₂O₃(17.25%~19.46%),低MgO含量(3.89%~5.07%)及Mg^#(44~50),与高铝玄武岩特征相似,属于中钾钙碱性岩石,富集大离子亲石元素(LILE)、亏损高场强元素(HFSE),铕异常不明显(δEu=0.82~1.06),(⁸⁷Sr/⁸⁶Sr)_i值为0.70427,ε_Nd(t)值为3.0,具有高且正的锆石ε_Hf(t)值(+11.8~+17.2)。这些晚白垩世镁铁质岩石可能是来自俯冲板片的沉积物熔体交代地幔楔物质发生部分熔融并经历一定程度镁铁质矿物分离结晶作用产物。     

西藏波密花岗岩体的年代学、地球化学特征及其意义

波密岩体位于西藏东南部,处于班公湖-怒江蛇绿混杂岩带与印度河-雅鲁藏布蛇绿混杂岩带之间,整体呈NW向延伸,面积约29km²。本文对波密花岗岩体进行了系统的岩石学、地球化学及同位素年代学研究。结果显示,波密岩体主要以黑云母石英闪长岩与黑云母花岗闪长岩为主,两个花岗闪长岩的LA-ICP-MS锆石U-Pb年龄分别为113.1±2.3Ma和113.4±2.1Ma。花岗岩类SiO₂介于64.11%~66.63%,K₂O+Na₂O=6.36%~7.54%,全碱含量较高,属于高钾钙碱系列。稀土元素含量为114.9×10^-6~182.8×10^-6,分配曲线均呈右倾趋势。另外,A/CNK为0.80~0.95,波密岩体有高K,高Si,低P的特点,大离子亲石元素(Rb、K)富集,高场强元素(Nb、Ta、P、Ti)亏损,属于偏铝质I型花岗岩。2件样品37个测点的锆石ε_Hf(t)值不均一,几乎全为负值(-13.72~-0.08),反映岩浆可能源于古老地壳;地壳模式年龄(t_DM^C)集中于891~2047Ma之间。综合分析波密岩体地球化学及锆石年龄数据,均与中冈底斯及弧背断隆带中早白垩世的岩体特征相似。因此本文推断波密岩体的成因为中冈底斯早白垩世带状岩浆大爆发事件在东部的延续。     

西藏南拉萨地体尼木地区侏罗纪花岗岩地球化学与岩石成因

冈底斯岩基是新特提斯洋北向俯冲和印度-欧亚大陆碰撞的重要岩浆记录,尼木地区位于冈底斯岩基中部。本文报道了尼木地区寄主二长花岗岩和辉长质包体的锆石U-Pb年代学、元素地球化学和锆石Hf同位素。锆石U-Pb定年结果表明,寄主花岗岩（197~190Ma）和包体（195Ma）同期侵位,形成于早侏罗纪。寄主二长花岗岩为弱过铝质高钾钙碱性系列岩石,富集轻稀土和K、U、Sr等大离子亲石元素,亏损Nb、Ta、Ti等高场强元素,锆石ε_Hf（t）值为+13.9~+16.0,其可能来源于初生地壳的部分熔融;辉长质包体为准铝质钙碱性系列岩石,具有与寄主岩相似的稀土和微量元素分配特征,锆石ε_Hf（t）值为+13.8~+16.0,其可能代表了侏罗纪形成的新生下地壳,即寄主岩石的岩浆源区;结合前人研究,本文认为尼木地区的寄主花岗岩和暗色包体可能与新特提斯洋北向俯冲引起的地幔和初生地壳的部分熔融有关。     

东濮凹陷北部沙河街组三段中亚段沉积环境分析

东濮凹陷北部沙三中亚段广泛发育盐岩和烃源岩,这两个看似不能共存的物质却在这里互层共生。该时期研究区沉积特征为多盐韵律与多层烃源岩互层共生、连续沉积,单个盐韵律厚度从几米到十几米,烃源岩有机质丰度高、类型好。平面上,两者在湖盆沉积沉降中心共生;垂向上,高有机质丰度、好干酪根类型与高盐度地层具有较好的对应关系。因而成为恢复古气候和古环境的重要研究对象。通过岩石学、古生物学以及Sr/Ba、B/Ga、(V+Ni+Mn)、Fe/Mn、Sr/Cu、Mg/Ca、V/(V+Ni)、稀土元素含量和氯同位素等方法对凹陷北部沙三中亚段的沉积环境进行研究。结果表明,凹陷北部沙三中亚段为深水沉积的还原环境,古盐度较高,达到半咸水-咸水沉积;微量元素和孢粉化石特征表明研究区沙三中亚段为温暖潮湿的环境。     

The Importance of the Precipitation and the Susceptibility of the Slopes for the Triggering of Landslides Along the Roads

In order to characterise the influence of the heavyrains on the observed landslides during the 1996–1997hydrological cycle, rainfall records for the last 100years are analysed from 104 stations in easternAndalusia. Regarding the amounts of rain recordedbetween October 1996 and March 1997 in the 104stations studied, 31 presented new all-time records;15 presented values that were 80–100% of thepre-1995 record; 49 stations, 80–50%; and 9stations, < 50%. A map has been devised of thesusceptibility of the materials through which thesouth-eastern Andalusian road network crosses,together with an inventory of the damage caused byinstability phenomena on banks and cuttings of theroad network during the winter of 1996–1997. Therelationships between the rainfall during the studyperiod, the damage caused to the road network and thesusceptibility of the materials affected are analysed.The results indicate that there is a clearcorrespondence between the rainfall recorded and thesusceptibility of the materials with the inventorieddamage. It is concluded that the widespread seriousdamage caused in early 1997 to the roads andsurrounding areas in the Alpujarra region and thecoast of the Province of Granada was mainly caused bythe extraordinarily heavy rains. However, considerablyless damage was observed where the susceptibility ofthe terrain is low, thus highlighting the extremeusefulness of terrain-susceptibility maps for riskprevention and territorial planning.     

郯庐断裂南段研究进展与断裂性质讨论

据1：5万区域地质调查和专题研究资料，就郯庐断裂带是否南延与消失的原因，其与大别—苏鲁造山带交截形成的假位错效应，以及与中新生代沉积盆地形成演化的关系等作了新的阐述。在此基础上，讨论了郯庐断裂带是否为巨大的左行平移断层或转换断层。认为郯庐断裂带可能是在“古郯庐带”的基础上于早侏罗世重新活动、白垩纪强烈活动的地堑型枢纽断裂带。     

塘口水电站坝基岩体透水性和渗漏问题分析

塘口水电站大坝基础座落在断层和裂隙较发育的龟裂纹灰岩上,岩体完整性差、透水性强,多年运行后,大坝灌浆廊道和排水廊道出现多处集中性漏水,为确保大坝安全和电站正常发电,根据渗漏性质和成因,采用对灌浆廊道补充帷幕灌浆,对排水廊道进行固结+帷幕+回填灌浆。通过灌浆处理后,效果良好,表明灌浆工程有效的将导致坝基渗漏的上下游的裂隙通道封闭,并顺利的经受了随后的汛期洪水考验,大坝安全得到保障。     

Unity of the national and the international in the socio-cultural development of the peoples of the USSR

International unity is becoming ever stronger in this country owing to an increasing similarity in the development of the cultural environment. This comprises the provision of all the country's republics with a sufficient number of schools, theatres, and other institutions and cultural information media in accordance with the needs of the population. An important part is played by the rise in ‘the general educational level, as well as the level of professional qualifications and skills. Among all the Soviet nations and nationalities, this rise being more rapid among formerly backward peoples. Prominent among the factors of internationalization is the progressive development of the nationalities’ cultural resources, while professional culture is being increasingly brought within the reach of the masses.The implementation of the nationalities policy promotes the all-round development of all Soviet nations and nationalities, their drawing together, the upsurge of the individual capabilities of every Soviet citizen.     

某高速公路下伏煤矿采空区稳定性分析

在论述某高速公路下伏砦脖煤矿采空区地质、采矿和工程地质特征的基础上, 进行了稳定性数值模拟分析, 定性与定量地分析与评价了该煤矿采空区的地表变形特征及稳定性。研究结果表明: 该煤矿采空区的变形尚未完成, 对拟建的高速公路将产生很大的危害, 必须采取相应的工程治理措施。      

Report of the restudy of the defined global stratotype of the base of the Silurian System

The Global Stratotype Section and Point （GSSP） for the base of the Silurian System was defined in 1985. Since that time, a number of researchers have suggested that this section has serious deficiencies for use as a GSSP. As a result, in 2000, the Subcommission on Silurian Stratigraphy （SSS） proposed undertaking a formal restu@ of this GSSP, which was subsequently approved by the International Commission of Stratigraphy （ICS）. The result of this restudy was the formal proposal that the current GSSP, at 1.6 m above the base of the Birkhill Shale, at Dob＇s Linn, Scotland, should be maintained as the same locality and stratigraphic level, but the bios- tratigraphical definition of the boundary should be revised. The previously defined, basal Silurian grapto- lite zone, the Parakidograptus acuminatus Zone, should be subdivided into a lower Akidograptus ascensus Zone and a higher E acuminatus Zone. The base of the A. ascensus Zone, marked by the first appearance of A. ascensus, should be regarded as the biostratigraphic mark for the base of the Silurian. This proposal has now been formally approved by the SSS and ICS, and ratified by International Union of Geological Sciences. This is the first GSSP to undergo formal restudy and redefini- tion, and the proposal also included a recommended procedure for restudy of GSSPs.     

Calculation of the Inverse of the Covariance

In reservoir characterization, the covariance is often used to describe the spatial correlation and variation in rock properties or the uncertainty in rock properties. The inverse of the covariance, on the other hand, is seldom discussed in geostatistics. In this paper, I show that the inverse is required for simulation and estimation of Gaussian random fields, and that it can be identified with the differential operator in regularized inverse theory. Unfortunately, because the covariance matrix for parameters in reservoir models can be extremely large, calculation of the inverse can be a problem. In this paper, I discuss four methods of calculating the inverse of the covariance, two of which are analytical, and two of which are purely numerical. By taking advantage of the assumed stationarity of the covariance, none of the methods require inversion of the full covariance matrix.     

Deviation of the major axis of the inertia ellipsoid of the Moon from the direction toward the Earth

It is known from observations that the center of mass of the Moon does not coincide with the geometric center of its figure, and the line connecting these two centers is not aligned with the direction toward the center of the Earth, instead deviating toward the Southeast. This stationary deviation of the axis of the inertia ellipsoid of the Moon to the South of the direction toward the Earth is analyzed. A system of five linear differential equations describing the physical libration of the Moon in latitude is considered, and these equations are derived using a new vector method taking into account perturbations from the Earth and partly from the Sun. The characteristic equation of this system is obtained, and all five oscillation frequencies are found. Special attention is paid to the fifth (zero) frequency, for which the solution of the latitude libration equations are stationary and represents a previously unknown additional motion of the rotational axis of theMoon in a cone with a small opening angle. In contrast to the astronomical precession of the Earth, the rotation of the angular-velocity vector is in the positive direction (counter-clockwise), with the period T ₃ = 27.32 days. On this basis, this phenomenon has been named “quasi-precession.” This quasi-precession leads to a stationary inclination of the major axis of the inertia ellipsoid of theMoon to the South (for an observer on Earth), making it possible to explain one component of the observed deviation of the center of mass of the Moon from the direction toward the Earth. The opening angle of the quasiprecession cone is approximately 0.834″.