Jupiter’s moment of inertia: A possible determination by Juno

The moment of inertia of a giant planet reveals important information about the planet’s internal density structure and this information is not identical to that contained in the gravitational moments. The forthcoming Juno mission to Jupiter might determine Jupiter’s normalized moment of inertia NMoI = C/MR² by measuring Jupiter’s pole precession and the Lense–Thirring acceleration of the spacecraft (C is the axial moment of inertia, and M and R are Jupiter’s mass and mean radius, respectively). We investigate the possible range of NMoI values for Jupiter based on its measured gravitational field using a simple core/envelope model of the planet assuming that J₂ and J₄ are perfectly known and are equal to their measured values. The model suggests that for fixed values of J₂ and J₄ a range of NMoI values between 0.2629 and 0.2645 can be found. The Radau–Darwin relation gives a NMoI value that is larger than the model values by less than 1%. A low NMoI of ∼0.236, inferred from a dynamical model (Ward, W.R., Canup, R.M. [2006]. Astrophys. J. 640, L91–L94) is inconsistent with this range, but the range is model dependent. Although we conclude that the NMoI is tightly constrained by the gravity coefficients, a measurement of Jupiter’s NMoI to a few tenths of percent by Juno could provide an important constraint on Jupiter’s internal structure. We carry out a simplified assessment of the error involved in Juno’s possible determination of Jupiter’s NMoI.     

Central magnetic anomalies of Nectarian-aged lunar impact basins: Probable evidence for an early core dynamo

A re-examination of all available low-altitude LP magnetometer data confirms that magnetic anomalies are present in at least four Nectarian-aged lunar basins: Moscoviense, Mendel-Rydberg, Humboldtianum, and Crisium. In three of the four cases, a single main anomaly is present near the basin center while, in the case of Crisium, anomalies are distributed in a semi-circular arc about the basin center. These distributions, together with a lack of other anomalies near the basins, indicate that the sources of the anomalies are genetically associated with the respective basin-forming events. These central basin anomalies are difficult to attribute to shock remanent magnetization of a shocked central uplift and most probably imply thermoremanent magnetization of impact melt rocks in a steady magnetizing field. Iterative forward modeling of the single strongest and most isolated anomaly, the northern Crisium anomaly, yields a paleomagnetic pole position at 81° ± 19°N, 143° ± 31°E, not far from the present rotational pole. Assuming no significant true polar wander since the Crisium impact, this position is consistent with that expected for a core dynamo magnetizing field. Further iterative forward modeling demonstrates that the remaining Crisium anomalies can be approximately simulated assuming a multiple source model with a single magnetization direction equal to that inferred for the northernmost anomaly. This result is most consistent with a steady, large-scale magnetizing field. The inferred mean magnetization intensity within the strongest basin sources is ∼1 A/m assuming a 1-km thickness for the source layer. Future low-altitude orbital and surface magnetometer measurements will more strongly constrain the depth and/or thicknesses of the sources.     

The phase diagram of water and the magnetic fields of Uranus and Neptune

The interior of giant planets can give valuable information on formation and evolution processes of planetary systems. However, the interior and evolution of Uranus and Neptune is still largely unknown. In this paper, we compare water-rich three-layer structure models of these planets with predictions of shell structures derived from magnetic field models. Uranus and Neptune have unusual non-dipolar magnetic fields contrary to that of the Earth. Extensive three-dimensional simulations of Stanley and Bloxham (Stanley, S., Bloxham, J. [2004]. Nature 428, 151-153) have indicated that such a magnetic field is generated in a rather thin shell of at most 0.3 planetary radii located below the H/He rich outer envelope and a conducting core that is fluid but stably stratified. Interior models rely on equation of state data for the planetary materials which have usually considerable uncertainties in the high-pressure domain. We present interior models for Uranus and Neptune that are based on ab initio equation of state data for hydrogen, helium, and water as the representative of all heavier elements or ices. Based on a detailed high-pressure phase diagram of water we can specify the region where superionic water should occur in the inner envelope. This superionic region correlates well with the location of the stably-stratified region as found in the dynamo models. Hence we suggest a significant impact of the phase diagram of water on the generation of the magnetic fields in Uranus and Neptune.     

Computing the fuzzy topological relations of spatial objects based on induced fuzzy topology

For modeling the topological relations between spatial objects, the concepts of a bound on the intersection of the boundary and interior, and the boundary and exterior are defined in this paper based on the newly developed computational fuzzy topology. Furthermore, the qualitative measures for the intersections are specified based on the α‐cut induced fuzzy topology, which are (A_α∧?A)(x)<1?α and ((A^c)_α∧?A)(x)<1?α. In other words, the intersection of the interior and boundary or boundary and exterior are always bounded by 1?α, where α is a value of a level cutting. Specifically, the following areas are covered: (a) the homeomorphic invariants of the fuzzy topology; (b) a definition of the connectivity of the newly developed fuzzy topology; (c) a model of the fuzzy topological relations between simple fuzzy regions in GIS; and (d) the quantitative values of topological relations can be calculated.     

北美西部内陆海盆Niobrara组的钙质超微化石及其环境意义——Ⅰ：钙质超微化石及其分带

北美西部内陆海盆上白垩统Niobrara组中的钙质超微化石十分丰富,且多保存良好,呈现典型的晚白垩世远洋钙质超微化石组合面貌,经系统鉴定,计有60属100余种和亚种。为适应不同的环境,Kansas西部和South Dakota东部的钙质超微化石组合面貌稍有不同。经与白垩纪颗石藻化石带对比,可将Kansas西部的Niobrara组划分为6个化石带(CC13～CC18)和8个亚带,其中,根据本文研究地区的化石序列,CC15和CC16带被进一步划分。根据与同一剖面所建立的无脊椎动物化石带对比,钙质超微化石CC17带的时代被重新厘定,即该带应始于中Santonian的晚期,结束于晚Santonian的早期,并据此将Santoniatr／Campanian的界线划在CC18带之内。     

Extended model of topological relations between spatial objects in geographic information systems

This paper presents an extended model for describing topological relations between two sets (objects) in geographic information systems (GIS). First, based on the definition of the topological relations between two objects, we uncover a sequence of topological relations between two convex sets.Second, an extended model for topological relations between two sets is proposed based on the new definition. The topological relations between two convex sets are expressed as a sequence of 4 × 4 matrices, which are the topological properties of A^o ∩ B^o, A^o\B, B^o\A, ∂A ∩ ∂B. The model is also extended for handling the properties of the topological relations between two non-convex sets, where the factor of first fundamental group is added to A ∪ B to handle these complex relations.The results show that the number of topological relations between the two sets is not as simple as finite but infinite and can be approximated by a sequence of matrices.     

Mars

Mars is the fourth planet out from the sun. It is a terrestrial planet with a density suggesting a composition roughly similar to that of the Earth. Its orbital period is 687 days, its orbital eccentricity is 0.093 and its rotational period is about 24 hours. Mars has two small moons of asteroidal shapes and sizes (about 11 and 6 km mean radius), the bigger of which, Phobos, orbits with decreasing semimajor orbit axis. The decrease of the orbit is caused by the dissipation of tidal energy in the Martian mantle. The other satellite, Deimos, orbits close to the synchronous position where the rotation period of a planet equals the orbital period of its satellite and has hardly evolved with time. Mars has a tenous atmosphere composed mostly of CO with strong winds and with large scale aeolian transport of surface material during dust storms and in sublimation-condensation cycles between the polar caps. The planet has a small magnetic field, probably not generated by dynamo action in the core but possibly due to remnant magnetization of crustal rock acquired earlier from a stronger magnetic field generated by a now dead core dynamo. A dynamo powered by thermal power alone would have ceased a few billions of years ago as the core cooled to an extent that it became stably stratified. Mars' topography and its gravity field are dominated by the Tharsis bulge, a huge dome of volcanic origin. Tharsis was the major center of volcanic activity, a second center is Elysium about 100° in longitude away. The Tharsis bulge is a major contributor to the non-hydrostaticity of the planet's figure. The moment of inertia factor together with the mass and the radius presently is the most useful constraint for geophysical models of the Martian interior. It has recently been determined by Doppler range measurements to the Mars Pathfinder Lander to be (Folkner et al. 1997). In addition, models of the interior structure use the chemistry of the SNC meteorites which are widely believed to have originated on Mars. According to the models, Mars is a differentiated planet with a 100 to 200 km thick basaltic crust, a metallic core with a radius of approximately half the planetary radius, and a silicate mantle. Mantle dynamics is essential in forming the elements of the surface tectonics. Models of mantle convection find that the pressure-induced phase transformations of -olivine to -spinel, -spinel to -spinel, and -spinel to perovskite play major roles in the evolution of mantle flow fields and mantle temperature. It is not very likely that the -spinel to perovskite transition is present in Mars today, but a few 100 km thick layer of perovskite may have been present in the lower mantle immediately above the core-mantle boundary early in the Martian history when mantle temperatures were hotter than today. The phase transitions act to reduce the number of upwellings to a few major plumes which is consistent with the bipolar distribution of volcanic centers of Mars. The phase transitions also cause a partial layering of the lower mantle which keeps the lower mantle and the core from extensive cooling over the past aeons. A relatively hot, fluid core is the most widely accepted explanation for the present lack of a self-generated magnetic field. Growth of an inner core which requires sub-liquidus temperatures in the core would have provided an efficient mechanism to power a dynamo up to the present day. Received 10 May 1997     

Vascoceras (Greenhornoceras) birchbyi Cobban & Scott from the Greenhorn Limestone (Lower Turonian) of Central Kansas

The Early Turonian ammonite, Vascoceras (Greenhornoceras) birchbyi Cobban & Scott, has been recorded at nine additional localities in Kansas, Colorado and New Mexico. Most significant is discovery of a specimen in Russell County, Kansas, that doubles the known longitudinal range of the species in the U.S. Western Interior. The species occurs in a single, thin, time-parallel limestone bed that apparently was deposited during a peak pulse of the Cenomanian-Turonian transgression.     

Love函数与地球内部的潮汐形变

把地球表面潮汐形变问题扩展到地球内部.定义了Love函数和几种潮汐形变因子,并对两个实际地球模型（1066A和PREM）进行数值计算和讨论,以了解地球内部的潮汐形变特征,专门讨论了Love函数导数以及应力固体潮张量的计算问题.本工作对了解全地球潮汐场以及潮汐触发地震等问题将有所帮助.     

Ammonite-based correlations in the Cenomanian-lower Turonian of north-west Europe, central Tunisia and the Western Interior (North America)

The biochronology of Cenomanian-early Turonian ammonite faunas from three key stratotype areas (north-west Europe, central Tunisia and the Western Interior of North America) has been analysed and revised by utilizing the unitary association method. This review is prompted by the huge amount of biostratigraphic data published during recent decades and by a taxonomic homogenisation of the ammonite faunas from these key areas. The Cenomanian and lower Turonian of Tunisia comprise twenty-four Unitary Association zones and the middle Cenomanian-lower Turonian of the Western Interior Basin twenty-three such zones. The unitary association method means a two-fold increase in resolution of these ammonite zonations compared to the standard, empirical schemes. Central Tunisia and the Western Interior are correlated with north-west Europe by constructing a zonation including all taxa common to these areas. These correlations highlight the variable completeness and resolution of the faunal record through space and time, and reveal a significant number of diachronous taxa between the three areas. These correlations enable the designation of a new global marker for the middle/upper Cenomanian boundary, which is characterised by the disappearance of the genera Turrilites, Acanthoceras and Cunningtoniceras and by the appearance of Eucalycoceras, Pseudocalycoceras and Euomphaloceras. The only synchronous datum known is the last occurrence of Turrilites acutus, which may thus be used as a marker for the middle/upper Cenomanian boundary, provided that it does not turn out to be diachronous in the light of any new data.