Spectral analysis using orthonormal functions with a case study on the sea surface topography

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Spherical harmonics are orthonormalized using the Gram-Schmidt process in a function space. The problem of linear dependence of spherical harmonics over the oceans is studied using the Gram matrices and consequently three sets of orthonormal (ON) functions have been constructed. For the process an efficient formula for computing inner products of spherical harmonics has been developed. Important spectral properties of the ON functions are addressed. The ON functions may be used for representing the sea surface topography (SST) in the analysis of satellite altimeter data. The geoid error can be transformed to a representation by the ON functions and hence the comparison of powers of the geoid error and the SST signal only over the oceans is possible, leading to a better way of determining the cut-off frequency of the SST in the simultaneous solution using satellite altimeter data. As a case study, the modified Levitus SST is expanded into the ON functions. The results show that 99.90 per cent of that signal's energy is contained within degree 24 of the orthonormal functions. Such expansions also render better spectral behaviour of oceanic signals as compared to that from spherical harmonic expansions. The study shows that these generalized Fourier functions are suitable for spectral analyses of oceanic signals and they can be applied to future altimetric mission where the geoid and the SST are to be recovered.     

关于Stokes公式的球面卷积和平面卷积的注记

讨论了Stokes公式球面卷积和平面卷积形式的近似性和严密性问题,分析了Stokes函数球面卷积形式和平面卷积形式的关系,推导了其间的差值表达式,估算了最大差值及其对计算大地水准面差距的误差影响。同时指出,将顾及Stokes函数全项的平面卷积公式称为严密公式的提法,仅仅是相对仅顾及Stokes函数首项的简单平面卷积公式而言,认为更合理的提法应该是“高精度Stokes平面近似卷积公式”。理论分析表明,球面卷积不可能严格转化为等效的平面卷积。     

NOC model of the earth's main magnetic field

The international geomagnetic reference field (IGRF) is a standard model for describing the spatial structure and temporal variation of the earth抯 main magnetic field[1—3]. The first IGRF model, designated IGRF 1965, was adopted by IAGA in 1968[4]. In l…     

Ion probe dating of a migmatite in SW Sweden: the fate of zircon in crustal processes

A migmatitic orthogneiss in the Western Segment in the Sveconorwegian Province of the Baltic Shield was dated using the ion-probe U–Pb method on zircon grains, which were also analysed for rare earth elements. Mesosome zircons have 1.605±0.010 Ga magmatic cores, which places the gneiss protolith in the same 1.61–1.59 Ga time bracket as continental arc-related gneisses, abundant in this part of the Sveconorwegian Province. These cores show REE profiles with strong HREE enrichment, positive Ce- and negative Eu-anomalies, typical of magmatic zircon. Migmatite leucosomes are folded and parallel with or slightly discordant to the fabric. They contain a small population of zircon with cores and metamorphic rims, which are interpreted as xenocrysts incorporated in the leucosome during melting of the mesosome. CL-bright metamorphic embayments and rims on xenocrysts reflect 1.01±0.05 Ga Sveconorwegian metamorphic reworking. Ce-anomalies are nearly absent and Eu-anomalies are reduced relative to igneous spots. This is probably a feature of fluid controlled environments where Ce and Eu oxidation states are buffered by the metamorphic fluid. From this and discordant rims from the mesosome we also conclude that the rims formed by reworking of the older zircon where the Pb-loss was also fluid induced. In the leucosome veins, magmatic acicular zircon gives 0.92±0.01 Ga, ascribed to the crystallisation of the veins. They originated by local melting, probably augmented by magma that formed at a deeper level. Widespread granitic and noritic late-Sveconorwegian magmatism close to 0.92 Ga in other parts of the Western Segment has equivalents in the Norwegian sectors of the Sveconorwegian Province. Leucosome formation was therefore part of a regional event related to exhumation of the Sveconorwegian Eastern Segment. We also provide the first unequivocal evidence for ductile deformation related to late-Sveconorwegian magmatism.     

煤田地勘单位矿业权运作问题探讨

简述了我国矿业权市场建立和发展情况，提出了矿业权市场目前存在的诸多问题及对策建议；认为地勘单位必须树立矿业权经营理念，以此推动煤田地勘事业持续发展。     

The Deformation of Active Tectonic Blocks on the Chinese Mainland and Its Relationship with Seismic Activity

Based on the hypothesis of the active tectonic blocks on the Chinese continent and its adjacent regions (both the method of the DDA on a spherical surface and the GPS survey results observed from 1991 to 2001 are used), the movements and deformations of each active tectonicblock are calculated. The calculation results show that although the movements and deformations of active tectonic-blocks in the eastern region and in the western region of China are different, active tectonic blocks in the same active tectonic block region are coherent.Then, the relative velocities of the active tectonic-blocks‘ boundary zones are calculated, and the relationship between current crustal motion and strong seismic activities is discussed. Earthquakes (Ms≥7.0) on the Chinese continent since 1988 all occurred on boundary zones of active tectonic blocks with high slipping speed.     

An analysis of near-circular lunar mapping orbits

Numerical investigations have been carried out to analyse the evolution of lunar circular orbits and the influence of the higher order harmonics of the lunar gravity field. The aim is to select the appropriate near-circular orbit characteristics, which extend orbit life through passive orbit maintenance. The spherical harmonic terms that make major contributions to the orbital behaviour are identified through many case studies. It is found that for low circular orbits, the 7th and the 9th zonal harmonics have predominant effect in the case of orbits for which the evolution is stable and the life is longer, and also in the case of orbits for which the evolution is unstable and a crash takes place in a short duration. By analysing the contribution of the harmonic terms to the orbit behaviour, the appropriate near-circular orbit characteristics are identified.