Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields

The basic concepts of spectral and multiscale selective reconstruction of (geophysically relevant) vector fields on the sphere from error-affected data is outlined in detail. The reconstruction mechanism is formulated under the assumption that spectral as well as multiscale approximation is well-representable in terms of only a certain number of expansion coefficients at the various resolution levels. It is shown that spectral denoising by means of orthogonal expansions in terms of vector spherical harmonics reflects global a priori information of the noise (e.g., in form of a covariance tensor field), whereas multiscale signal-to-noise thresholding can be performed under locally dependent noise information within a multiresolution analysis in terms of spherical vector wavelets. An application of the multiscale formalism to Earth's magnetic field determination is presented.     

卫星测高问题的球谐级数解法

研究了球界面下卫星测高问题的解法，利用有限逼近方法得到了下列结论：若陆地部分是球冠，则卫星测高问题的解可以转换成关于球谐级数位系统的线性方程组。同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况。     

Fully normalized spherical cap harmonics: application to the analysis of sea-level data from TOPEX/POSEIDON and ERS-1

We introduce two sets of fully normalized harmonics for the spectral analysis of functions defined on a spherical cap. The harmonics are the products of Fourier functions and the fully normalized associated Legendre functions of non-integer degree. Using Sturm-Liouville theory for boundary-value problems, we present two convenient and stable formulae for computing the zeros of the associated Legendre functions that form two sets of orthogonal functions. Formulae for the stable numerical evaluation of the fully normalized associated Legendre functions of non-integer degree that avoid the gamma function are also derived. The result from the expansions of sea-level anomaly from altimetry into Set 2 fully normalized cap harmonics shows fast convergence of the series, and the degree variances decay rapidly without aliasing effects. The zero-degree coefficients (Set 2) of sea-level anomaly from TOPEX/ POSEIDON (T/P) and ERS-1 indicate an El Niño event during 1993 January-1993 July, and a La Niño event during 1993 November-1994 July, although the ERS-1 result is less obvious. Ocean circulations over the South China Sea and the Kuroshio area are clearly identified with the low-degree expansions of sea-surface topography (SST) from T/P and ERS-1. A cold-core eddy of 4° in diameter centred at 17.5°N, 118 E was detected with the expansion of SST from T/P cycle 47, and a property of the cap harmonics is used to compute this eddy's kinetic energy. The kinetic energy is at a low in winter and high in summer, and its variation seems to be periodic with an amplitude of 0.4 m² S^-2.     

探测冰盖和多年冻土层的融冰探头研发

The exploration of ice sheets by melting vertical holes into the ground has some tradition in terrestrial glaciology. Such probes have been used since the 1960's to investigate the vertical structure of the ice in Greenland and Antarctica and in alpine glaciers. In this paper we look into the possibility to develop similar devices for use on extraterrestrial icy bodies, like e.g. the polar areas on Mars or the icy satellites of the outer solar system. We report on some basic experiments performed in the cryo-vacuum laboratory of the Space Research Institute of the Austrian Academy of Sciences, Graz. In these experiments the penetration of a simple melting probe into compact and porous water ice (with a snow-like texture) was monitored, both under vacuum conditions and under air pressure. The observed penetration speeds for a given power supply are compared with a simple mathematical model. We conclude that a miniature melting probe with small overall dimensions and a reasonable power demand could well be part of the payload of a future planetary mission, for example to the poles of Mars. Such missions are currently under discussion in several space agencies. Moreover such probes could also e? ectively be used in terrestrial environments. A possible design is presented at the end of the paper.     

GOCE Gravity Field Processing Strategy

A processing strategy and the corresponding software architecture for the processing of GOCE (Gravity field and steady-state Ocean Circulation Explorer) observables is presented and described, with the major objective to compute a high-accuracy, high-resolution spherical harmonic model of the Earth's gravity field. The combination of two numerical solution strategies, i.e. the rigorous solution of the corresponding large normal equation systems applying parallel processing (on a PC cluster) as the core solver, and the fast semianalytic approach as a quick-look gravity field analysis (QL-GFA) tool, is proposed. Such a method fusion benefits from the advantages of the individual components: the rigorous inversion of the system providing also the full variance-covariance information, and the quickness enabling the consecutive production of intermediate gravity field solutions, for the purpose to analyse partial and incomplete data sets and to derive a diagnosis of the performance of the GOCE measurement system. The functionality and operability of the individual components are demonstrated in the framework of a closed loop simulation, which is based on a realistic mission scenario both in terms of the orbit configuration and the coloured measuring noise. Special concern is given to the accuracy of the recovered coefficients, the numerical behaviour, the required computing time, and the particular role of the individual modules within the processing chain. In the case of the core solver, it is demonstrated that the assembling and rigorous solution of large normal equation systems can be handled by using Beowulf clusters within a reasonable computing time. The application of the quick-look tool to partial data sets with short-term data gaps is demonstrated on the basis of several case studies. Additionally, the spectral analysis of the residuals of the adjustment is presented as a valuable tool for the verification of the noise characteristics of the GOCE gradiometer.     

Slow mass movement in the Kangchenjunga area, eastern Nepal Himalaya

Abstract   The rates of the accumulated and continuous displacement of solifluction lobes in the Kangchenjunga area, eastern Nepal Himalaya, were determined using glass fiber tubes and a strain probe. Ground temperature, precipitation and soil moisture were monitored at two sites, whose altitude differed by approximately 100 m, to understand the solifluction process. The average movement rate of the glass fiber tubes on a 31° slope at altitudes of 5412–5414 m a.s.l. was approximately 11 mm/year, being almost threefold greater than that observed on a 22° slope at 5322–5325 ma.s.l. There was no significant difference in the depth of displacement at these sites. The continuous displacement measurement near the ground surface at 5414 m showed permanent downslope movement from early July. Such movement may be attributed to additional moisture supply during the monsoon season. The amplitude of the displacement cycle was highest at the ground surface, and decreased to virtually zero at and below 20 cm in depth. Probable factors leading to the relatively slow rates of downslope displacement at the surface and depth at the studied altitudes are the lack of concurrence of the freeze–thaw cycles and the high moisture condition in the soil, and the low moisture retention capacity of the soil because of steep slopes and superficial desiccation. The rate of displacement may be more pronounced at altitudes above 5600 m because of the freeze–thaw cycles during the summer season.