The critical inclination problem — 30 years of progress

The critical inclination problem in artificial satellite theory, first discovered 30 years ago, has aroused great interest and provoked much discussion and controversy in the intervening years. It was this problem which essentially provided the seed corn for the development of the theory of the Ideal Resonance Problem (IRP). The latter theory provides good first-approximation solutions to a number of important resonance problems in celestial mechanics. It is not applicable, however, to certain other interesting resonant systems within the solar system. For these resonances a new fundamental mathematical model of resonance, in the spirit of the IRP, has recently been formulated and successfully applied.This paper reviews the history of the critical inclination problem and highlights the controversies it has generated over the years. The Problem's strong connection with the IRP is outlined with both thenormal andabnormal forms featuring. Finally, with reference to the critical inclination problem, the essential properties of the newer fundamental model are described and compared with the IRP. A strong correspondence is established between recent independent investigations of a variety of resonance problems and earlier work of Andoyer.     

Secular resonances: New results

We integrated numerically, in the frame of the four body problem Sun-Jupiter-Saturn-asteroid the orbit of the asteroid 1974 MA, an Earth-crosser, which is located in a region where three resonances overlap: the two secular resonances ₅ and ₁₆ and the mean motion resonance 5/1. The numerical integration yields a qualitative orbital evolution of this particular region.     

Flow directions in ash-flow tuffs: a comparison of geological and magnetic susceptibility measurements, Tshirege member (upper Bandelier Tuff), Valles caldera, New Mexico, USA

This study concludes that the elongation axis (K ₁) of the ellipsoid of anisotropic magnetic susceptibility (AMS) is a suitable proxy for flow axis in ashflow tuffs. 153 oriented samples (176 specimens) were studied from 18 sites in the 1.1 Ma Tshirege member of the Bandelier Tuff. These sites are distributed around the Valles caldera at distances of 5–25 km outside of the rim.K ₁ axes correlate well with postulated radial flow axes at 13 sites.K ₁ also agrees with measured geological flow indicators, mainly imbricated larger clasts, at 7 sites. At 2 of the 5 sites where significant disagreement is seen between theoretical radial flow directions and measuredK ₁ axes, theK ₁ axes correspond well with geological flow indicators, indicating that the divergence of flow from the predicted radial flow pattern is real. Two major topographic buttresses are suggested as the cause of flow divergence for the Tshirege ash flows: the San Pedro buttress northwest of the caldera, and the San Miguel buttress in the southeast. In situK ₁ axes plunge about 7° toward the source at two-thirds of the sites; therefore the plunge ofK ₁ is a plausible in situ indicator for thedirection of flow. Multiple flow zones in sections of several meters thickness indicate changes of flow direction that are both rapid and large during ash-flow emplacement. These observations raisre the question of how best to represent mean flow directions in ash-flow sheets: by eigenvector methods, by vector-sum methods, or by modes. A method for measuring imbrication of larger clasts using apparent dips in vertical joints is outlined. Imbrication, determined in this way at one-third of the sites, dips toward the source, i.e., up-flow. The minimum (K ₃) axis of the AMS ellipsoid correlates with the flow foliation rather than with the larger clast imbrication. The flow axes of ash flows correspond with theK ₁ axes, not with the declination ofK ₃ axes as suggested by some authors. Initial dip of the sampled ash flows is not large and does not affect the paleomagnetic remanence direction, which is reversed with a mean ofD=173.5°,I=-38.4°, ₉₅=3.4°N=18. This mean is not different at the 95% confidence level from that of earlier workers. The mean pole, at 098.0°E, 74.8°N,A ₉₅=3.3°,N=18, is about 15° far-sided relative to the expected time-averaged geomagnetic pole, suggesting a history of emplacement too short to adequately average secular variation.     

High pressure experimental calibration of the olivine-orthopyroxene-spinel oxygen geobarometer: implications for the oxidation state of the upper mantle

Synthetic spinel harzburgite and lherzolite assemblages were equilibrated between 1040 and 1300° C and 0.3 to 2.7 GPa, under controlled oxygen fugacity (f _{O 2}). f _{O 2} was buffered with conventional and open double-capsule techniques, using the Fe−FeO, WC-WO₂-C, Ni−NiO, and Fe₃O₄−Fe₂O₃ buffers, and graphite, olivine, and PdAg alloys as sample containers. Experiments were carried out in a piston-cylinder apparatus under fluid-excess conditions. Within the P-T-X range of the experiments, the redox ratio Fe³⁺/ΣFe in spinel is a linear function of f _{O 2} (0.02 at IW, 0.1 at WCO, 0.25 at NNO, and 0.75 at MH). It is independent of temperature at given Δlog(f _{O 2}), but decreases slightly with increasing Cr content in spinel. The Fe³⁺/ΣFe ratio falls with increasing pressure at given Δlog(f _{O 2}), consistent with a pressure correction based on partial molar volume data. At a specific temperature, degree of melting and bulk composition, the Cr/(Cr+Al) ratio of a spinel rises with increasing f _{O 2}. A linear least-squares fit to the experimental data gives the semi-empirical oxygen barometer in terms of divergence from the fayalite-magnetite-quartz (FMQ) buffer:

A field and theoretical analysis of garnet+chlorite+chloritoid+biotite assemblages from the tri-state (MA,CT, NY) area,USA

The prograde evolution of minerals in metapelites of a Barrovian sequence from the tri-state area (Massachusetts, Connecticut, New York) of the Taconic Range involves assemblages with garnet (Ga), chlorite (Ch), chloritoid (Ct), biotite (Bi) and staurolite (St). Detailed petrologic observations, mineral compositions and chemical zoning in garnet show: (1) garnet high in Mn and Fe but low in Mg is stable with chlorite at grades below those where chloritoid+biotite is found; (2) early formed garnet reacted partially to form Ct+Bi at intermediate grades; (3) at higher grades garnet (with low Mn)+chlorite is again produced, at the expense of chloritoid+biotite, suggesting a reversal in the continuous reaction involving the phases Ga, Ch, Ct and Bi. Thermodynamic modeling of the assemblage Ga+Ch+Ct+Bi±St in the MnKFMASH system reveals: (1) in the MnKFASH system the prograde reaction is Ga+Ch=Ct+Bi whereas in the KFMASH system the prograde reaction is the opposite: Ct+Bi=Ga+Ch; (2) the Ga–Ch–Ct–Bi–St invariant point in the KFMASH system occurs twice, at approximately 6.5 kbar, 545° C and 14.8 kbar, 580° C (although one of them may be metastable in a complex phase system); the appearance of the petrogenetic grid is markedly different from that of Albee, but similar to that of Spear and Cheney; (3) as a consequence, in the KFMASH system, chloritoid+biotite are stable over a wide range of P-T conditions whereas garnet+chlorite assemblages are restricted to a narrow band of P-T conditions; (4) MnO increases the stability field of Ga+Ch relative to both Ct+Bi at low temperatures, and St+Bi at high temperatures; (5) in natural samples the occurrence of Ct+Bi is controlled more by bulk Mg–Fe(-Mn) composition than P-T conditions. Specifically, Ct+Bi is restricted to bulk compositions with Fe/(Mg+Fe+Mn)>0.6. Rocks with Fe/(Mg+Fe+Mn)<0.5 are likely to display only chlorite+biotite at low grade. These observations are consistent with Wang and Spear and Spear and Cheney.     

山西地震综合数据处理系统

《山西地震综合数据处理系统》是遵循《国家地震局数据库技术规范》,以PDP-11/23~+小型机与IBM/PC联机为硬件支撑,以网状型数据库为核心,含前期处理、库管理、数据检索、科学计算、分析会商5个子系统的较大型应用软件系统。具有对数据进行收集、录入、预处理、存储、管理、加工及应用等功能。整个系统通过总控菜单程序实现了异种机间上百个模块的调度,使查询-处理一体化。该系统把地震数据库、日常监测数据处理、专家地震预报系统有机地衔接于一体,可直接服务于地震科研和震情会商。该系统的建设是山西省重大科技攻关项目,也是国家地震局的合同制项目。     

The effect of bulk rock composition on the stability of amphibole in the upper mantle: Implications for solidus positions and mantle metasomatism

Summary The stability of pargasitic amphibole in the upper mantle is a function of water content and bulk rock composition, and under water-undersaturated conditions, the stability of amphibole controls the solidus position. Experiments in the system Tinaquillo peridotite +0.2% H₂O, a refractory peridotite under water-undersaturated conditions, show that amphibole is stable to 1030°C and 26 kb. In contrast, pargasitic amphibole is stable to 1150°C and 30 kb in Hawaiian pyrolite, a more fertile peridotite composition. This indicates that under water-undersaturated conditions, the most fertile part of a crystallizing mantle diapir with an inhomogeneous composition will solidify first while a more refractory component will contain an alkali-rich melt which will have the ability to metasomatize adjacent regions. The relative stabilities of amphibole in refractory and fertile bulk compositions may result in increasing rather than diminishing chemical contrasts in high temperature lherzolite, i.e. a process of metamorphic differentiation. Ti, Fe, Al and Na metasomatism can therefore be considered a normal occurrence associated with the upward migration and solidification of an H₂O-bearing mantle diapir.

---

Der Einfluß der Gesamtgesteins-Zusammensetzung auf die Stabilität von Amphibol im oberen Mantel: Bedeutung für Solidus-Positionen und Mantel-Metasomatose

Zusammenfassung Die Stabilität pargasitischer Amphibole im oberen Mantel ist eine Funktion von Wassergehalt und Gesamtgesteins-Zusammensetzung. Unter wasser-untersättigten Bedingungen, kontrolliert die Stabilität von Amphibol die Solidus-Position. Experimente in dem System Tinaquillo Peridotit +0,2% H₂O, einem refraktären Peridotit unter wasser-untersättigten Bedingungen, zeigen daß Amphibol bis 1030°C und 26 Kb stabil ist. Im Gegensatz dazu ist pargasitische Hornblende in einem Hawaii-Pyrolit, von mehr fertiler Peridotit-Zuammensetzung, bis 1150°C und 30 Kb stabil. Das zeigt, daß bei wasser-untersättigten Bedingungen der am meisten produktive Teil eines kristallisierenden Mantel-Diapirs mit inhomogener Zusammensetzung sich zuerst verfestigen wird, während eine mehr refraktäre Komponente eine alkali-reiche Schmelze enthalten wird, die wiederum die Fähigkeit hat, umliegende Bereiche metasomatisch zu beeinflussen. Die relativen Stabilitäten von Amphibol in refraktären und fertilen Gesamtzusammensetzungen können dazu führen, daß die chemischen Gegensätze in Hochtemperaturlherzoliten eher zunehmen als abnehmen, d. h. ein Prozeß metamorpher Differentiation. Ti, Fe, Al und Na Metasomatose können deshalb als ein verbreiteter Vorgang, der mit der Aufwärtsbewegung und Verfestigung eines H₂O-führenden Mantel-Diapirs assoziiert ist, betrachtet werden.

---

---

With 4 Figures     

Littoral '92

Reports

Littoral '92     

岩体三维节点偶对分析及其应用

本文讨论了节点偶对分析的三维扩展。节点偶对分析是针对摩擦滑动节理单元的约束边界进行的序列矢量判定。在三维节理单元的分析中,几何约束和相应的力学判据极为复杂,采用节点偶对等效结合力方法才能迎刃而解。文中对三维转向节理模型的分析得到合理的结果,它表明本文所提出的方法可成功地应用于节理岩体的有限元分析。     

Geochemistry of Gneiss-Granulite transformation in the “incipient charnockite” zones of southern India

Summary Upper amphibolite facies gneisses in the southern Indian Shield show local transformation into veins, clots and patches of orthopyroxene-bearing dry granulites (incipient charnockites). Depending upon the protolith composition, these desiccated zones are classified into ortho- and para-charnockites and have developed within rocks of distinct mineralogy and chemistry at different time intervals through the structurally-controlled influx of carbon dioxide-rich fluids. Our geochemical investigations at five critical quarry sections indicate that the incipient charnockites have undepleted chemistry and very low K/Rb values. In the paracharnockite localities, where granulite formation is characterized by consumption of garnet, biotite and quartz to produce orthopyroxene, loss of Rb and Ba and enrichment of Ti are observed. In contrast, the orthocharnockite localities show marked LILE enrichment with gain of K, Rb and Ba and loss of CaO, suggesting extensive replacement of plagioclase in the gneisses by K-feldspar in the charnockite through K-Na-Ca exchange reactions with influxing carbonic fluids. The marked depletion in Fe, Mg, Ti and P in these rocks correlates with progressive dissolution of hornblende, biotite, magnetite and accessory apatite. Our study indicates that gneiss to granulite transformation, even if on a local scale, is not an isochemical phenomenon, but attended by distinct element mobilities, although they are contrastingly different from the geochemical trends in some regional high grade terrains.

---

Geochemie von Gneiss-Granulit-Übergängen in den Incipient Charnockite Zonen von Süd-Indien

Zusammenfassung Gneise der oberen Amphibolit-Fazies im Südteil des Indischen Schildes zeigen lokal Umwandlungen in Adern, and unregelmäßigen Bereichen von orthopyroxen-führenden trockenen Granuliten (Incipient Charnockites). In Abhängigkeit von der Zusammensetzung des Ausgangsgesteins werden diese Zonen in Ortho- und Paracharnockite eingeteilt. Sie entwickelten sich in Gesteinen von charakteristischer mineralogischer und chemischer Zusammensetzung zu verschiedenen Zeit-Intervallen durch die tektonisch kontrollierte Zufuhr von kohlendioxid-reichen Fluiden. Unsere geochemischen Untersuchungen an fünf strategisch ausgewählten Steinbruchen zeigen, daß die Incipient Charnockite eine nicht verarmte chemische Zusammensetzung und sehr niedrige K/Rb Werte haben. In den Paracharnockit-Lokalitäten, wo Granulitbildung charakterisiert wird durch das Verschwinden von Granat, Biotit und Quartz, aus denen Orthopyroxene gebildet werden, ist Verlust von Rb und Ba und Anreicherung an Ti zu beobachten. Im Gegensatz dazu zeigen die Orthocharnockite eindeutige LILE Anreicherung mit Zunahme von K, Rb, und Ba und Verlust von Ca0. Dies weist auf extensiven Ersatz von Plagioklas in den Gneisen durch K-Feldspat in den Charnockiten durch K-Na-Ca Austausch-Reaktionen mit zugeführten C0₂-Fluiden hin. Die deutliche Verarmung an Fe, Mg, Ti und P in diesen Gesteinen wird mit zunehmender Auflösung von Hornblende, Biotit, Magnetit und akzessorischem Apatit erKlärt. Unsere Untersuchungen zeigen, daß die Gneis-Granulit Transformation auch im lokalen Maßstab nicht ein isochemisches Phänomen ist, sondern durch charakteristische Elementtransporte charakterisiert wird. Diese unterscheiden sich jedoch deutlich von den geochemischen Trends, die in einigen regional-metamorphen high grade terrains zu beobachten sind.[/p]