The Rotation of a Non-Rigid, Non-Symmetrical Earth I: Free Nutations

This work is the first of a series of papers in which the canonicaltheory of the rotation of the non-rigid Earth of Getino and Ferrandiz isextended to the case of the non-symmetrical Earth. Here, the freeHamiltonian for an Earth composed of a rigid mantle and a liquid corewith A B (A and B principal moments ofinertia) is developed and integrated, obtaining the complete analyticalsolution which includes the free frequencies, Chandler Wobble and Fluid CoreNutation, corresponding to the non-symmetrical Earth. We have evaluatednumerically the effect of the Earths equatorial non-symmetry on thefree nutations. Although the effects of the second order are negligeable,the changes in the normal mode periods (about 1 day) may be important.     

Motion of the Earth's inner core and related variations of polar motion and the rotational velocity

Correlations between the geomagnetic field parameters and polar motion were explained using the hypothesis of an inner core motion. For a number of periodic constituents of both phenomena it could be proved that this model works well. Secular variations of polar motion caused by inner core dynamics are in the same order of magnitude as the secular variation of the pole derived from pole coordinates of the International Latitude Service (ILS).     

The outer core rotation about an inclined axis from geomagnetic secular variations (Mitteilungen des Zentralinstituts für Physik der Erde,Nr. 1832)

Non-axisymmetric motions of the outer core of the Earth are important for the dynamo problem and the excitation of the decade variations of the polar motion. The components of the vector of a rigid rotation of the outer core about an inclined axis were estimated by a first-order approximation of the frozen- field theory of the geomagnetic secular variation from 1903.5 to 1975.5. The trends and quasi-periodic constituents of these quantities were computed. It was shown that the position and time behaviour of the rotational pole of the outer core differ considerably from the well-know co-ordinates of the dipole axis. Some periods of the equatorial components of the rotational vector are comparable with those of the axial component previously derived for a pure axial rotation. Additionally, the time behaviour of the pole path shows events like the well-known Markowitz wobble but naturally with other extent. These and other results suggested that the investigations are worth to be continued in future by some physical interpretations.     

On the “rotational angular momentum” of the oceans and the corresponding polar motion

Periodic polar motions caused by ocean tides are predicted. In the Liouville equations for rotational motion the complete excitation functions for the ocean tides have to be used. This does not depend on the fact that hydrodynamical ocean tide models do not consider the centrifugal acceleration. The observable polar motion of the Celestial Ephemeris Pole CEP (more exactly: the terrestrial location of the CEP) is tabulated for the ten ocean tides M₂, S₂, N₂, K₁, O₁, P₁, M f, M f′, M m, Ssa. Typical amplitudes for the largest ocean tides are 0.4 milliarcseconds. This is within the reach of geodetic VLBI and SLR observations.     

Chandler Wobble Period and Q Derived by Wavelet Transform

We apply complex Morlet wavelet transform to three polar motion dataseries, and derive quasi-instantaneous periods of the Chandler and annual wobbleby differencing the wavelet transform results versus the scale factor, and then findtheir zero points. The results show that the mean periods of the Chandler (annual)wobble are 430.71±1.07 (365.24±0.11) and 432.71±0.42 (365.23±0.18) mean solardays for the data sets of 1900-2001 and 1940-2001, respectively. The maximumrelative variation of the quasi-instantaneous period to the mean of the Chandlerwobble is less than 1.5% during 1900-2001 (3%--5% during 1920-1940), and thatof the annual wobble is less than 1.6% during 1900--2001. Quasi-instantaneous andmean values of Q are also derived by using the energy density-period profile of theChandler wobble. An asymptotic value of Q = 36.7 is obtained by fitting polynomialof exponential of σ~(-2) to the relationship between Q and σ during 1940--2001.     

利用奇异谱分析提高极移中长期预报精度

由于空间大地观测数据传输耗时及处理过程复杂, 导致极移测量值的获取存在时延, 无法满足对高精度的极移预报值有重大需求的应用领域. 针对极移复杂的时变特性, 提出一种基于奇异谱分析(singular spectrum analysis, SSA)的预报方法. 首先用SSA分离提取极移时序中的高频组分与低频组分; 其次建立最小二乘(least square, LS)外推与自回归(AutoreGressive, AR)模型对极移高频和低频组分进行组合预报. 结果表明, SSA方法能够准确地分离和提取极移低频和高频组分, 对低频和高频组分组合预报可以显著改善极移的中长期(30--365d)预报精度, 与国际地球自转和参考系服务局(International Earth Rotation and Reference Systems Service, IERS)提供的A公报中的极移预报值相比, SSA方法对极移PMX分量(本初子午线方向)和PMY分量(西90$^\circ$子午线方向)的中长期预报精度改进最高分别可达45.97%和62.44%. 研究结果验证了SSA方法对极移中长期预报改进的有效性.     

Earth analog for high-latitude landforms and recent flows on Mars: Icy debris fans in the Wrangell Volcanic Field, Alaska

New Mars Reconnaissance Orbiter HiRise and CRISM imagery of polar layered terrain of Mars reveals striking similarities to icy debris fans along the base of steep escarpments in Alaska formed in high-latitude periglacial environments. Process and morphologic observations of a deglaciating site in the Wrangell Mountains reveal a complex suite of supraglacial processes involved in the construction of icy debris fans. Snow, ice, and sediment are delivered to the fans from degradation of an upper-level icecap. Alaskan icy debris fans were studied during an 8-day reconnaissance mission in July 2006. We directly observed 289 major depositional events dominated by dry snow/ice avalanches, but also including icy debris flows, rockfalls, small jokulhlaups, and glacial calving. Small fans with larger catchments receive episodic icy debris flows triggered by outburst flows that mobilize rockfall sediment temporarily stored in catchments above the fan apex. Large fans with smaller catchments have better linkage to the upper icecap, providing a direct pathway for frequent large avalanches. The large, avalanche-dominated fans thicken rapidly from an overabundance of snow/ice supply to the point where they become hybrid fan-glaciers. Surficial geology evolves rapidly in this high-latitude environment through both depositional events and solar-driven albedo changes that occur daily. Ground penetrating radar surveys show that subsurface sedimentary architecture and fan evolution is similar to the active surface processes and deposits observed on the fans. Direct field observations of active geomorphic processes provide unique insights on the pace and nature of high-latitude landscape evolution during climate changes on both planets.     

Evidence for Amazonian northern mid-latitude regional glacial landsystems on Mars: Glacial flow models using GCM-driven climate results and comparisons to geological observations

A fretted valley system on Mars located at the northern mid-latitude dichotomy boundary contains lineated valley fill (LVF) with extensive flow-like features interpreted to be glacial in origin. We have modeled this deposit using glacial flow models linked to atmospheric general circulation models (GCM) for conditions consistent with the deposition of snow and ice in amounts sufficient to explain the interpreted glaciation. In the first glacial flow model simulation, sources were modeled in the alcoves only and were found to be consistent with the alpine valley glaciation interpretation for various environments of flow in the system. These results supported the interpretation of the observed LVF deposits as resulting from initial ice accumulation in the alcoves, accompanied by debris cover that led to advancing alpine glacial landsystems to the extent observed today, with preservation of their flow texture and the underlying ice during downwasting in the waning stages of glaciation. In the second glacial flow model simulation, the regional accumulation patterns predicted by a GCM linked to simulation of a glacial period were used. This glacial flow model simulation produced a much wider region of thick ice accumulation, and significant glaciation on the plateaus and in the regional plains surrounding the dichotomy boundary. Deglaciation produced decreasing ice thicknesses, with flow centered on the fretted valleys. As plateaus lost ice, scarps and cliffs of the valley and dichotomy boundary walls were exposed, providing considerable potential for the production of a rock debris cover that could preserve the underlying ice and the surface flow patterns seen today. In this model, the lineated valley fill and lobate debris aprons were the product of final retreat and downwasting of a much larger, regional glacial landsystem, rather than representing the maximum extent of an alpine valley glacial landsystem. These results favor the interpretation that periods of mid-latitude glaciation were characterized by extensive plateau and plains ice cover, rather than being restricted to alcoves and adjacent valleys, and that the observed lineated valley fill and lobate debris aprons represent debris-covered residual remnants of a once more extensive glaciation.     

中国地球自转和地壳运动监测的研究工作

主要介绍了１９９５年至１９９８年期间有关中国地球自转和地壳运动监测的研究工作及取 得的进展。     

Crater size-shape profiles for the moon and mercury: Terrain effects and interplanetary comparisons

New crater size-shape data were compiled for 221 fresh lunar craters and 152 youthful mercurian craters. Terraces and central peaks develop initially in fresh craters on the Moon in the 0–10 km diameter interval. Above a diameter of 65 km all craters are terraced and have central peaks. Swirl floor texture is most common in craters in the size range 20–30 km, but it occurs less frequently as terraces become a dominant feature of crater interiors. For the Moon there is a correlation between crater shape and geomorphic terrain type. For example, craters on the maria are more complex in terms of central peak and terrace detail at any given crater diameter than are craters in the highlands. These crater data suggest that there are significant differences in substrate and/or target properties between maria and highlands. Size-shape profiles for Mercury show that central peak and terrace onset is in the 10–20 km diameter interval; all craters are terraced at 65 km, and all have central peaks at 45 km. The crater data for Mercury show no clear cut terrain correlation. Comparison of lunar and mercurian data indicates that both central peaks and terraces are more abundant in craters in the diameter range 5–75 km on Mercury. Differences in crater shape between Mercury and the Moon may be due to differences in planetary gravitational acceleration (gMercury=2.3gMoon). Also differences between Mercury and the Moon in target and substrate and in modal impact velocity may contribute to affect crater shape.     

Antipodal effects of lunar basin-forming impacts: Initial 3D simulations and comparisons with observations

3D simulations of basin-scale lunar impacts are carried out to investigate: (a) the origins of strong crustal magnetic fields and unusual terrain observed to occur in regions antipodal to young large basins; and (b) the origin of enhanced magnetic and geochemical anomalies along the northwest periphery of the South Pole-Aitken (SPA) basin. The simulations demonstrate that a basin-forming impact produces a massive, hot, partially ionized cloud of vapor and melt that expands thermally around the Moon, converging near the basin antipode approximately 1 h after the impact for typical impact parameters. In agreement with previous work, analytic calculations of the interaction of this vapor-melt cloud with an initial ambient magnetic field predict a substantial temporary increase in field intensity in the antipodal region. The time of maximum field amplification coincides with a period when impacting ejecta also converge near the antipode. The latter produce antipodal shock stresses within the range of 5-25 GPa where stable shock remanent magnetization (SRM) of lunar soils has been found experimentally to occur. Calculated antipodal ejecta thicknesses are only marginally sufficient to explain the amplitudes of observed magnetic anomalies if mean magnetization intensities are comparable to those produced experimentally. This suggests that pre-existing ejecta materials, which would also contain abundant metallic iron remanence carriers, may be important anomaly sources, a possibility that is consistent with enhanced magnetic anomalies observed peripheral to SPA. The latter anomalies may be produced by amplified secondary ejecta impact shock waves in the thick SPA ejecta mantle occurring near the antipodes of the Imbrium and Serenitatis impacts. Together with converging seismic compressional waves, these antipodal impact shocks may have produced especially deep fracture zones along the northwest edge of SPA near the Imbrium antipode, allowing the ascent of magma with enhanced KREEP concentrations.     

Numerical assessment of the effects of topography and crustal thickness on martian seismograms using a coupled modal solution-spectral element method

The past 4 decades of Mars exploration have provided much information about the Mars surface, when its interior structure remains relatively poorly constrained. Today available data are compatible with a large range of model parameters. Seismology is able to provide valuable additional data but the number of seismographs will likely be quite limited, specially in the early-stage of future Mars seismic networks. It is thus of importance to be able to correctly isolate effects induced by the crust structure. Mars topography is characterized by spectacular reliefs like the Tharsis bulge or the Hellas basin and by the so-called “Mars dichotomy”: the north hemisphere is made up of low-altitude plains above a relatively thin crust when the south hemisphere is characterized by a thick crust sustaining high reliefs. The aim of this paper is to study the effects induced on seismograms by the topography of the surface and crust-mantle discontinuities. Synthetic seismograms were computed using the coupled spectral element-modal solution method, which reduces the numerical cost by limiting the use of the spectral element method to the regions where lateral variations, like the presence of a topography, are considered. Due to numerical cost, this study is limited to long period and thus focuses on surface waves, mainly on long period Rayleigh waves. We show that reliefs like the Tharsis bulge or the Hellas basin can induce an apparent velocity anomaly up to 0.5% when only the surface topography is introduced. Apparent anomalies can raise up to 1.0% when the surface topography is fully compensated by a mirror-image topography of the crust-mantle discontinuity. Travel-time of surface wave are systematically increased for seismometers in the north hemisphere of Mars and decreased in the south hemisphere. When comparing effects on seismograms by the Earth and Mars topography, we found them to be larger for the Earth. It is due to the fact that we work with a seismic velocity model of Mars with a mean crust thickness of 110 km when the crust thickness has a mean value of 50 km for the Earth. When changing the Mars model for a thinner crust with a mean thickness of 50 km, effects by the topography on Mars seismograms becomes of the same order when not larger than what is observed on the Earth.     

Barchan dune asymmetry: Observations from Mars and Earth

Barchan dune asymmetry refers to the extension of one barchan limb downwind. It is a common dune form on Earth and also occurs on Mars and Titan. A new classification of barchan limbs is presented where three types of limb morphology are identified: linear, kinked and beaded. These, along with other dune-scale morphological signatures, are used to identify three of the causes of barchan asymmetry on Mars: bi-directional winds, dune collision and the influence of inclined topography.The potential for specific dune asymmetric morphologies to indicate aspects of the formative wind regime on planetary surfaces is shown. For example, the placement of dune limbs can indicate the general direction and relative strength of formative oblique winds; an extreme barchan limb length may indicate a long duration oblique wind; a kinked limb may be evidence of the passage of a storm; beaded limbs may represent surface-wave instabilities caused by an increase in wind energy parallel to the dune. A preliminary application of these signatures finds evidence for bi-modal winds on Mars. However, these and other morphological signatures of wind direction and relative strength should be applied to planetary landforms with caution as more than one process (e.g., bi-modal winds and collision) may be operating together or sequentially on the dunefield. In addition, analysis should be undertaken at the dunefield scale and not on individual dunes. Finally, morphological data should be acquired from similar-scale dunes within a dunefield.In addition to bi-modal wind regimes on Mars, the frequent parallel alignment of the extended barchan limb to the dune suggests that dune collision is also an important cause of asymmetry on Mars. Some of the more complex dunefield patterns result from a combination of dune collision, limb extension and merging with downwind dunes.Dune asymmetric form does not inhibit dune migration in the Namib Desert or on Mars. Data from the Namib suggest that dune migration rates are similar for symmetric and asymmetric dunes. Further modeling and field studies are needed to refine our understanding of the potential range of limb and dune morphologies that can result from specific asymmetry causes.     

Europa's neutral cloud: morphology and comparisons to Io

Ground based observations of sodium escaping from Europa suggest the presence of an extended cloud of neutrals orbiting Jupiter. Using a Monte Carlo model we show that the large scale morphology differs from the sodium cloud at Io. At Europa, the trailing cloud is brighter and more extended than the leading cloud. We then use our results to consider the morphology of Europa's oxygen cloud.     

North polar region of Mars: Advances in stratigraphy, structure, and erosional modification

We have remapped the geology of the north polar plateau on Mars, Planum Boreum, and the surrounding plains of Vastitas Borealis using altimetry and image data along with thematic maps resulting from observations made by the Mars Global Surveyor, Mars Odyssey, Mars Express, and Mars Reconnaissance Orbiter spacecraft. New and revised geographic and geologic terminologies assist with effectively discussing the various features of this region. We identify 7 geologic units making up Planum Boreum and at least 3 for the circumpolar plains, which collectively span the entire Amazonian Period. The Planum Boreum units resolve at least 6 distinct depositional and 5 erosional episodes. The first major stage of activity includes the Early Amazonian (∼3 to 1 Ga) deposition (and subsequent erosion) of the thick (locally exceeding 1000 m) and evenly-layered Rupes Tenuis unit (Abrt), which ultimately formed approximately half of the base of Planum Boreum. As previously suggested, this unit may be sourced by materials derived from the nearby Scandia region, and we interpret that it may correlate with the deposits that regionally underlie pedestal craters in the surrounding lowland plains. The second major episode of activity during the Middle to Late Amazonian (1 Ga) began with a section of dark, sand-rich and light-toned ice-rich irregularly-bedded sequences (Planum Boreum cavi unit, Abb_c) along with deposition of evenly-bedded light-toned ice- and moderate-toned dust-rich layers (Planum Boreum 1 unit, Abb₁). These units have transgressive and gradational stratigraphic relationships. Materials in Olympia Planum underlying the dunes of Olympia Undae are interpreted to consist mostly of the Planum Boreum cavi unit (Abb_c). Planum Boreum materials were then deeply eroded to form spiral troughs, Chasma Boreale, and marginal scarps that define the major aspects of the polar plateau's current regional topography. Locally- to regionally-extensive (though vertically minor) episodes of deposition of evenly-bedded, light- and dark-toned layered materials and subsequent erosion of these materials persisted throughout the Late Amazonian. Sand saltation, including dune migration, is likely to account for much of the erosion of Planum Boreum, particularly at its margin, alluding to the lengthy sedimentological history of the circum-polar dune fields. Such erosion has been controlled largely by topographic effects on wind patterns and the variable resistance to erosion of materials (fresh and altered) and physiographic features. Some present-day dune fields may be hundreds of kilometers removed from possible sources along the margins of Planum Boreum, and dark materials, comprised of sand sheets, extend even farther downwind. These deposits also attest to the lengthy period of erosion following emplacement of the Planum Boreum 1 unit. We find no evidence for extensive glacial flow, topographic relaxation, or basal melting of Planum Boreum materials. However, minor development of normal faults and wrinkle ridges may suggest differential compaction of materials across buried scarps. Timing relations are poorly-defined mostly because resurfacing and other uncertainties prohibit precise determinations of surface impact crater densities. The majority of the stratigraphic record may predate the recent (<20 Ma) part of the orbitally-driven climate record that can be reliably calculated. Given the strong stratigraphic but loose temporal constraints of the north polar geologic record, a comparison of north and south polar stratigraphy permits a speculative scenario in which major Amazonian depositional and erosional episodes driven by global climate activity is plausible.     

The periodic variations of the core drift rate: global and zonal motions (Mitteilung des Zentralinstituts für Physik der Erde,Nr. 1746)

Toroidal zonal motions at the top of the Earth's core were computed from the observed secular variation and investigated with regard to their time dependence. Previously derived results for a pure westward drifting core could be re-examined. Additionally, the well-known 66.7 years period was found to be an oscillation of the zonal velocity field of third degree. With respect to periodic constituents, the total magnetic core-mantle coupling torque according to the zonal motions is comparable with that derived for a pure westward drifting core. Some differences in period lengthes and amplitudes do not remove previously stated differences between the spectra of the magnetic and mechanical torques on principle.     

Long-term evolution of Oort Cloud comets: methods and comparisons

Two long-term simulation methods for cometary orbits, a Monte Carlo method and a direct integration method, are compared with each other. The comparison is done in seven inclination and perihelion distance intervals, and shows differences in dynamical lifetime and capture probabilities for the following main reasons. We use a finite energy step approximation in the Monte Carlo method and the method considers only close approaches with the planets. The differences can be taken into account statistically and it is possible to calculate the correction factors for the capture probability and dynamical lifetime in the Monte Carlo method. Both corrections depend on the inclination and on the value of the minimum energy step. The capture probabilities of the short-period comets originating in the Oort Cloud are calculated by the corrected Monte Carlo method and compared with published results.     

WIYN Open Cluster Study – XVI. Optical/infrared photometry and comparisons with theoretical isochrones

We present combined optical/near-infrared photometry ( BVIK ) for six open clusters – M35, M37, NGC 1817, NGC 2477, NGC 2420 and M67. The open clusters span an age range from 150 Myr to 4 Gyr and have metal abundances from  [Fe/H]=−0.27  to +0.09 dex. We have utilized these data to test the robustness of theoretical main sequences constructed by several groups as denoted by the following designations – Padova, Baraffe, Y², Geneva and Siess. The comparisons of the models with the observations have been performed in the  [ M_V , ( B − V )₀], [ M_V , ( V − I )₀]  and  [ M_V , ( V − K )₀]  colour–magnitude diagrams as well as the distance-independent  [( V − K )₀, ( B − V )₀]  and  [( V − K )₀, ( V − I )₀]  two-colour diagrams. We conclude that none of the theoretical models reproduces the observational data in a consistent manner over the magnitude and colour range of the unevolved main sequence. In particular, there are significant zero-point and shape differences between the models and the observations. We speculate that the crux of the problem lies in the precise mismatch between theoretical and observational colour–temperature relations. These results underscore the importance of pursuing the study of stellar structure and stellar modelling with even greater intensity.     

Investigation of equilibria of a satellite subjected to gravitational and aerodynamic torques

Attitude motion of a satellite subjected to gravitational and aerodynamic torques in a circular orbit is investigated. In special case, when the center of pressure of aerodynamic forces is located on one of the principal central axes of inertia of the satellite, all equilibrium orientations are determined. Necessary and (or) sufficient conditions of stability are obtained for each equilibrium orientation. Evolution of domains where stability conditions take place is investigated. All bifurcation values of parameters corresponding to qualitative change of domains of stability are determined.     

Effective temperature vs. line‐depth ratio for ELODIE spectra: Gravity and rotational velocity effects

The dependence on the temperature of photospheric line‐depth ratios (LDRs) in the spectral range 6190–6280 Å is investigated by using a sample of 174 ELODIE Archive stellar spectra of luminosity class from V to III. The rotational broadening effect on LDRs is also studied. We provide useful calibrations of effective temperature versus LDRs for giant and main sequence stars with 3800 ≃ T_eff ≃6000 K and v sin i in the range 0–30 km s^–1. We found that, with the exception of very few line pairs, LDRs, measured at a spectral resolution as high as 42 000, depend on v sin i and that, by neglecting the rotational broadening effect, the T_eff determination can be wrong by ∼100 K in the worst cases. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)