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1.
In space-borne gravitational field determination, two challenges are inherent. First, the continuation of the data down to
the surface of the Earth is an ill-posed problem, requiring therefore regularization techniques. Second huge data sets result
requiring efficient numerical methods. In this paper, we show how locally supported wavelets on the sphere can be developed
by means of a spherical version of the so-called up function. By construction, the corresponding scaling functions and wavelets
are infinitely smooth, so that they can be used for regularization purposes. In particular, we show how the ill-posed pseudo-differential
equations coming from satellite missions can be regularized by efficient numerical schemes using locally supported wavelets.
These methods seem in particular to be interesting for regional gravity field modelling. 相似文献
2.
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. 相似文献
3.
The development of the phytoplankton spring bloom in Lake Zürich in 1983 was investigated using frequent sampling with short sampling intervals, which allowed the influence of short-term meteorological events on the bloom to be studied. The bloom can be divided into four distinct growth periods (March 1–April 28) and a period of collapse (April 29–May 16). During the four growth periods, growth pulses were found to be associated with high solar radiation, little wind and a shallow mixed layer, whereas stagnation or loss was associated with strong winds and a consequent deepening of the mixed layer, resulting in an unfavourable effective light climate. The population collapse was brought about by zooplankton grazing, possibly coupled with nutrient limitation and other factors. 相似文献
4.
Short-term risk forecasts of point precipitation are obtained with COTREC/RainCast, a technique for extrapolation of radar images. The risk forecasts are updated every 5 min for the next 0–2 h. Risk levels are defined for moderate, heavy and extreme precipitation. Warning messages are generated if, at the locations of 23 rain gauges, these risk levels are reached or exceeded. The time-resolved gauge data are used to judge if the warning messages are in time, early or late.Data over a period of 4 months (summer 2002) are used for verification. The largest number of warnings (1790) was obtained for moderate precipitation. About 55% of these warnings were in time, 23% were early and 22% were late. This finding is in a good agreement with the defined risk level for warnings (50%), indicating that the model for calculating the risk factors is reliable. Less warnings in time, and more late warnings were found for heavy and extreme precipitation. Hence, the risk levels need to be lowered for heavy and extreme precipitation, in order to reduce the number of late warnings. 相似文献
5.
An integrated wavelet concept of physical geodesy 总被引：4，自引：1，他引：3
For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial
gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection
between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept
of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can
be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical
geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an
integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing
the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential
outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of
band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding
to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique
derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking
and gradiometry.
Received: 28 February 1997 / Accepted: 17 November 1997 相似文献
6.
The purpose of GPS-satellite-to-satellite tracking (GPS-SST) is to determine the gravitational potential at the earth's surface from measured ranges (geometrical distances) between a low-flying satellite and the high-flying satellites of the Global Positioning System (GPS). In this paper, GPS-satellite-to-satellite tracking is reformulated as the problem of determining the gravitational potential of the earth from given gradients at satellite altitude. The uniqueness and stability of the solution are investigated. The essential tool is to split the gradient field into a normal part (i.e. the first-order radial derivative) and a tangential part (i.e. the surface gradient). Uniqueness is proved for polar, circular orbits corresponding to both types of data (first radial derivative and/or surface gradient). In both cases gravity recovery based on satellite-to-satellite tracking turns out to be an exponentially ill-posed problem. Regularization in terms of spherical wavelets is proposed as an appropriate solution method, based on the knowledge of the singular system. Finally, the extension of this method is generalized to a nonspherical earth and a non-spherical orbital surface, based on combined terrestrial and satellite data. 相似文献
7.
The purpose of this paper is the canonical connection of classical global gravity field determination following the concept of Stokes (Trans Camb Philos Soc 8:672–712, 1849), Bruns (Die Figur der Erde, Publikation Königl. Preussisch. Geodätisches Institut, P. Stankiewicz Buchdruckerei, Berlin, 1878), and Neumann (Vorlesungen über die Theorie des Potentials und der Kugelfunktionen. Teubner, Leipzig, pp 135–154, 1887) on the one hand and modern locally oriented multiscale computation by use of adaptive locally supported wavelets on the other hand. The essential tools are regularization methods of the Green, Neumann, and Stokes integral representations. The multiscale approximation is guaranteed simply as linear difference scheme by use of Green, Neumann, and Stokes wavelets. As an application, gravity anomalies caused by plumes are investigated for the Hawaiian and Iceland areas. 相似文献
8.
As a first approximation, the Earth is a sphere; as a second approximation, it may be considered an ellipsoid of revolution.
The deviations of the actual Earth’s gravity field from the ellipsoidal “normal” field are so small that they can be understood
to be linear. The splitting of the Earth’s gravity field into a “normal” and a remaining small “disturbing” field considerably
simplifies the problem of its determination. Under the assumption of an ellipsoidal Earth model, high observational accuracy
is achievable only if the deviation (deflection of the vertical) of the physical plumb line, to which measurements refer,
from the ellipsoidal normal is not ignored. Hence, the determination of the disturbing potential from known deflections of
the vertical is a central problem of physical geodesy. In this paper, we propose a new, well-promising method for modelling
the disturbing potential locally from the deflections of the vertical. Essential tools are integral formulae on the sphere
based on Green’s function with respect to the Beltrami operator. The determination of the disturbing potential from deflections
of the vertical is formulated as a multiscale procedure involving scale-dependent regularized versions of the surface gradient
of the Green function. The modelling process is based on a multiscale framework by use of locally supported surface curl-free
vector wavelets.
相似文献
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