The shallow water equations on the sphere and their Lagrange-Galerkin-solution

Summary ?The shallow water equations are formulated on the sphere in a three-dimensional coordinate system with the aid of tangential velocity components and differential operators. We introduce a modified semi-Lagrangian scheme for the discretization in time. The discretization in space is solved by linear finite elements. The grids we use are regular refinements of a macro triangulation which itself is derived from a highly symmetric polyeder also known as a bucky or soccer ball. The good numerical results show that this combination is a promising approach. The numerical algorithm is stable and its strength is the conservation of mass and energy. Received April 13, 2001; Revised December 18, 2001     

Human-biometeorological assessment of heat waves in Athens

The goal of this study is the analysis of heat waves and their impact on humans, using human biometeorological indices, which are based on the energy balance of the human body. The implications for humans are not only described through the intensity of the heat waves, but also through their duration over consecutive days. Both intensity and duration were analyzed for the Greater Athens Area during the period 1955 to 2001. The analysis was carried out using the daily physiologically equivalent temperature and the daily minimum air temperature. Based on these two parameters, the results showed an increase in the average duration of heat waves. Furthermore, the use of the Gaussian filter revealed the intra-annual variation of heat stress conditions and their relevance to humans. The results could be used for the management of the negative consequences of heat waves in cities suffering from environmental pollution and also for climate impact studies.     

A New Gastrioceras from Sinkiang

In the rich collection of fossils made in Sinkiang by Professor P.L.Yuan of the Tsinghua University,there are a few but very beautifulspecimens representing a new species of Gastrioceras.They were obtainedfrom Shihtsientan~1,a locality lying about 150 kilometers NNE of theChitai city~2 in northern Sinkiang.The writer takes the opportunity torecord sincere thanks to Professor P.L.Yuan for giving him the privilege     

Cenozoic stratigraphy and subsidence history of the South China Sea margin in the Taiwan region

Seismic reflection profiles and well data are used to determine the Cenozoic stratigraphic and tectonic development of the northern margin of the South China Sea. In the Taiwan region, this margin evolved from a Palaeogene rift to a latest Miocene–Recent foreland basin. This evolution is related to the opening of the South China Sea and its subsequent partial closure by the Taiwan orogeny. Seismic data, together with the subsidence analysis of deep wells, show that during rifting (～58–37 Ma), lithospheric extension occurred simultaneously in discrete rift belts. These belts form a >200 km wide rift zone and are associated with a stretching factor, β, in the range ～1.4–1.6. By ～37 Ma, the focus of rifting shifted to the present‐day continent–ocean boundary off southern Taiwan, which led to continental rupture and initial seafloor spreading of the South China Sea at ～30 Ma. Intense rifting during the rift–drift transition (～37–30 Ma) may have induced a transient, small‐scale mantle convection beneath the rift. The coeval crustal uplift (Oligocene uplift) of the previously rifted margin, which led to erosion and development of the breakup unconformity, was most likely caused by the induced convection. Oligocene uplift was followed by rapid, early post‐breakup subsidence (～30–18 Ma) possibly as the inferred induced convection abated following initial seafloor spreading. Rapid subsidence of the inner margin is interpreted as thermally controlled subsidence, whereas rapid subsidence in the outer shelf of the outer margin was accompanied by fault activity during the interval ～30–21 Ma. This extension in the outer margin (β～1.5) is manifested in the Tainan Basin, which formed on top of the deeply eroded Mesozoic basement. During the interval ～21–12.5 Ma, the entire margin experienced broad thermal subsidence. It was not until ～12.5 Ma that rifting resumed, being especially active in the Tainan Basin (β～1.1). Rifting ceased at ～6.5 Ma due to the orogeny caused by the overthrusting of the Luzon volcanic arc. The Taiwan orogeny created a foreland basin by loading and flexing the underlying rifted margin. The foreland flexure inherited the mechanical and thermal properties of the underlying rifted margin, thereby dividing the basin into north and south segments. The north segment developed on a lithosphere where the major rift/thermal event occurred ～58–30 Ma, and this segment shows minor normal faulting related to lithospheric flexure. In contrast, the south segment developed on a lithosphere, which experienced two more recent rift/thermal events during ～30–21 and ～12.5–6.5 Ma. The basal foreland surface of the south segment is highly faulted, especially along the previous northern rifted flank, thereby creating a deeper foreland flexure that trends obliquely to the strike of the orogen.     

On Tectonic History in Regions East of the Tibetan Plateau from Kansu to Yunnan

正 With 2 Plates During the recent five years I have joined several field parties in the carrying out of geological reconnaissances in regions between the valley of the Huangho and of the Yangtze and in the Sino-Tibetan borderland. This vast territory can be divided into six major geological units, e     

Palaeogeology of the Country around Hsiatsuchang before the Chihsia Transgression

正 The area extending from the Suiyang~2 city in the north to Tuanchi~3 in the south was surveyed by the writers in 1943. Apart from 2 few scattered outcrops of Cenozoic and recent deposits, the major stratigraphical units represented in this area are the Cambrian, the Ordovician, the Silurian, the Permian, and the Triassic systems. Gaps of some importance were observed between the     

Restudy of pyroxene-pyroxene equilibration temperatures for ordinary chrondrite meteorites

Electron microprobe analyses of orthopyroxene and Ca-clinopyroxene in 21 ordinary petrographic type 6 chondrites (7 H-, 8 L-, and 6 LL-group chondrites) result in differentK _D (distribution coefficient) values for H-, L-, and LL-group chondrites, which suggest different equilibration temperatures for each group. If we consider the Blander model (Blander 1972), the differences in Fe-Mg distributions for these groups reflect only their different Wo (CaSiO₃) contents, and are not due to differences in equalibration temperature. Ca-clinopyroxene and orthopyroxene in contact with each other give a lower analytical spread and more meaningful results than those analyzed at random. Olivine and orthopyroxene in nearly all analyzed chondrites are homogenous within and between grains; Ca-clinopyroxene shows heterogenous compositions in petrographic types 4 and 5, but is homogenous in type 6. Ca-clinopyroxene in disequilibrated chondrites contains unusual amounts of minor elements Al, Ti, and Cr, a feature that can be used to denote meteorites of this type. Equilibration temperatures for ordinary chondrites, based on the pyroxene-pyroxene geothermometer are not known, although a range of 750–950° C appears to be a fair estimate. The exact equilibration temperatures can be determined only after this geothermometer is carefully calibrated experimentally or empirically, with due consideration given to Wo content.     

Chemical evolution and petrogenetic implications of loparite in the layered,agpaitic Lovozero complex,Kola Peninsula,Russia

Summary Lovozero, the largest of the world’s layered peralkaline intrusions, includes gigantic deposits of Nb + REE-loparite ore. Loparite, (Na,Ce,Ca)₂(Ti,Nb)₂O₆, became a cumulus phase after crystallisation of about 35% of the ‘Differentiated Complex’, and its compositional evolution has been investigated through a 2.35 km section of the intrusion. The composition of the cumulus loparite changes systematically upwards through the intrusion with an increase in Na, Sr, Nb and Th and decrease in REE and Ti. This main trend of loparite evolution records differentiation of the peralkaline magma through crystallisation of 1600 m of the intrusion. The formation of the loparite ores was the result of several factors including the chemical evolution of the highly alkaline magma and mechanical accumulation of loparite at the base of a convecting unit. At later stages of evolution, when concentrations of alkalis and volatiles reached very high levels, loparite reacted with the residual melt to form a variety of minerals including barytolamprophyllite, lomonosovite, steenstrupine-(Ce), vuonnemite, nordite, nenadkevichite, REE, Sr-rich apatite, vitusite-(Ce), mosandrite, monazite-(Ce), cerite and Ba, Si-rich belovite. The absence of loparite ore in the “Eudialyte complex” is likely to be a result of the wide crystallisation field of lamprophyllite, which here became a cumulus phase. Received November 6, 2000; revised version accepted January 18, 2001     

Seepage and consolidation of bentonite saturated with pure- or salt-water by the method of unified molecular dynamics and homogenization analysis

Bentonite clay is a micro-inhomogeneous material, which consists of clay minerals (mainly montmorillonite), macro-grains (mainly quartz), water, air and others. Properties of the saturated bentonite clay are essentially characterized by the montmorillonite and water (i.e. montmorillonite hydrate). We analyze the molecular behavior of sodium montmorillonite hydrate Na_1/3Al₂[Si_11/3Al_1/3]O₁₀(OH)₂·nH₂O by applying a molecular dynamics (MD) simulation method. And by using the MD results we calculate the swelling property of the montmorillonite hydrate, and compare with an experimental result. Next, by using the same MD procedure we treat a montmorillonite mineral with a large number of external water molecules to check the properties of the water. Here we treat pure- and salt-water. Then we calculate the diffusivity and viscosity of water molecules and Na⁺ and Cl⁻ ions.

For extending the microscopic characteristics of constituent materials to a macroscopic seepage behavior of the micro-inhomogeneous material we apply a homogenization analysis (HA). That is, starting with the Navier–Stokes equation with distributed viscosity that is calculated by the former MD procedure we determine macroscopic permeability characteristics of bentonite for both cases of pure- and salt-water. Then, by using the permeability property we calculate long-term consolidation behavior of buffering clay, which is planed to be used for high-level radioactive waste (HLRW) management. Here the deformation is treated under the well-defined Cam clay model.     

Mineralogy,petrology and chemistry of lithic fragments from Luna 20 fines: origin of the cumulate ANT suite and its relationship to high-alumina and mare basalts

Bulk analyses of 157 lithic fragments of igneous origin and analyses of their constituent minerals (plagioclase, pyroxene, olivine, Mg-Al spinel, chromite, ilmenite, armalcolite, baddeleyite, zirkelite, K-feldspar, interstitial glass high in SiO₂ and K₂O) have been used to characterize the lunar highland rock suites at the Luna 20 site. The predominant suite is composed of ANT (anorthositic-noritic-troctolitic) rocks, as found at previous Apollo and Luna sites. This suite consists of an early cumulate member, spinel troctolite, and later cumulate rocks which are gradational from anorthosite to noritic and troctolitic anorthosite to anorthositic norite and troctolite; anorthositic norite is the most abundant rock type and its composition is close to the average composition for the highland rocks at this site. Spinel troctolite is a distinctive member of this suite and is characterized by the presence of Mg-Al spinel, magnesian olivine (average, Fo₈₃), and plagioclase. High-alumina basalt with low alkali content is another important rock type and melt of this composition may be parental to the cumulate ANT suite. Alkalic high-alumina basalt (KREEP) was not found in our sample, but may be genetically related to the ANT suite in that it may have formed by partial melting of rocks similar to those of the ANT suite. Fractional crystallization of low alkali, high-alumina basalt probably cannot produce alkalic high-alumina basalt because the enrichment in KREEP component is many times greater than the simultaneous change in major element components. Formation of alkalic high-alumina basalt by mechanical mixing of ANT rocks with very KREEP-rich components is not likely because the high-alumina basalt suite falls on a cotectic in the anorthiteolivine-silica system. Mare basalts may also be genetically related in that they may have been derived by remelting of rocks formed from residual liquids of fractional crystallization of parental low-alkali, high-alumina basalt, plus mafic cumulate crystals; the resultant melt would have a negative Eu anomaly and high $\text{Fe}\text{Mg}$ and $\text{pyroxene}\text{plagioclase}$ ratios.