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Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere 总被引：2，自引：1，他引：1
The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ
(or ℝ2) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same
problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis
can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole
sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case
of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem
in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity field missions.
Received: 10 June 1998 / Accepted: 20 May 1999 相似文献
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Alberta Albertella Federica Migliaccio Fernando Sansó 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):1-15
An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by a very accurate orbit determination, would allow a perfect estimation of the field. A true satellite experiences a number of perturbational, non-gravitational forces acting on the shell of the spacecraft; these can be revealed and accurately measured by a spaceborne accelerometer. If more accelerometers are flown in the same satellite, they naturally eliminate (to some extent) the common perturbational accelerations and their differences are affected by the second derivatives of the gravity fields only (gradiometry). The mission GOCE is based on this principle. Its peculiar dynamical observation equations are reviewed. The possibility of estimating the gravity field up to some harmonic degree (200) is illustrated. 相似文献
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GOCE, Satellite Gravimetry and Antarctic Mass Transports 总被引：1，自引：0，他引：1
Reiner Rummel Martin Horwath Weiyong Yi Alberta Albertella Wolfgang Bosch Roger Haagmans 《Surveys in Geophysics》2011,32(4-5):643-657
In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) was launched. Its objectives are the precise and detailed determination of the Earth’s gravity field and geoid. Its core instrument, a three axis gravitational gradiometer, measures the gravity gradient components V xx , V yy , V zz and V xz (second-order derivatives of the gravity potential V) with high precision and V xy , V yz with low precision, all in the instrument reference frame. The long wavelength gravity field is recovered from the orbit, measured by GPS (Global Positioning System). Characteristic elements of the mission are precise star tracking, a Sun-synchronous and very low (260 km) orbit, angular control by magnetic torquing and an extremely stiff and thermally stable instrument environment. GOCE is complementary to GRACE (Gravity Recovery and Climate Experiment), another satellite gravity mission, launched in 2002. While GRACE is designed to measure temporal gravity variations, albeit with limited spatial resolution, GOCE is aiming at maximum spatial resolution, at the expense of accuracy at large spatial scales. Thus, GOCE will not provide temporal variations but is tailored to the recovery of the fine scales of the stationary field. GRACE is very successful in delivering time series of large-scale mass changes of the Antarctic ice sheet, among other things. Currently, emphasis of respective GRACE analyses is on regional refinement and on changes of temporal trends. One of the challenges is the separation of ice mass changes from glacial isostatic adjustment. Already from a few months of GOCE data, detailed gravity gradients can be recovered. They are presented here for the area of Antarctica. As one application, GOCE gravity gradients are an important addition to the sparse gravity data of Antarctica. They will help studies of the crustal and lithospheric field. A second area of application is ocean circulation. The geoid surface from the gravity field model GOCO01S allows us now to generate rather detailed maps of the mean dynamic ocean topography and of geostrophic flow velocities in the region of the Antarctic Circumpolar Current. 相似文献
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In the framework of a boundary value problem (BVP), when areas on the boundary are void of data the solution of the problem
becomes undetermined and clearly more difficult. Physically, this could be the situation in which a gradiometer on a satellite
on a perfectly circular orbit covers a sphere with measured second radial derivatives: if the satellite orbit is not polar,
there are caps at satellite altitude which are not covered by data. A solution is presented based on an iterative algorithm,
under the hypothesis of using a finite-dimensional model as is usually done in the time-wise approach. The convergence of
the iterative solution is proved and a numerical example is shown to confirm the theoretical result.
Received: 14 August 2000 / Accepted: 12 April 2001 相似文献
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西加拿大盆地油砂储层中的泥夹层特征 总被引：3，自引：0，他引：3
西加拿大盆地含有丰富的油砂资源,主要产于阿尔伯达省东北部的下白垩统马克马里组(McMurray Formation)．该组含有不等的砂泥斜互层．这些砂泥斜互层(IHS)在局部很发育．描述其中的泥夹层为建立客观的储层模型提供了的重要数据．试图从6个方面对泥夹层进行描述并简要讨论如何利用这些描述结果去建立客观有效的储层模型． 相似文献
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The calculus of spherical harmonic representation of fields of geodetic interest is often performed by applying integral formulas to block-averaged quantities. Due to the dependence of the block areas on latitude, it is difficult to perform a rigorous computation; in this paper the effects of approximations related to the loss of orthogonality in the discretization and averaging procedures are numerically studied; a simple numerical approach to improve the efficiency of the estimates is presented. 相似文献
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Geoid models from the new generation of satellite gravity missions, such as GRACE and GOCE, in combination with sea surface
from satellite altimetry allow to obtain absolute dynamic ocean topography with rather high spatial resolution and accuracy.
However, this implies combination of data with fundamentally different characteristics and different spatial resolutions.
Spectral consistency would imply the removal of the short-scale features of the altimetric sea surface height by filtering,
to provide altimetric data consistent with the resolution of the geoid field. The goal must be to lose as little as possible
from the high precision of the altimetric signal. Using a one-dimensional example we show how the spectrum is changing when
a function defined only on a limited domain (ocean in the real case) is extended or not as to cover the complete domain (the
whole sphere in the real case). The results depend on the spectral characteristics of the altimetric signal and of the applied
filter. Referring to the periodicity condition, as it is requested in the case of Fourier analysis, the action of the two
classical filters (Ideal Low Pass and Gauss filter) and of two alternative procedures (wavelets and Slepian) is studied. 相似文献
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