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Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally
adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential
recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential.
The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus,
we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients,
in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly,
the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization
and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization
by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly,
the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level
of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the
fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state
Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process
converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive
to the synthesis of unobserved gravity gradients. 相似文献
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Urban system is shaped by the interactions between different regions and regions planned by the government, then reshaped by human activities and residents’ needs. Understanding the changes of regional structure and dynamics of city function based on the residents’ movement demand are important to evaluate and adjust the planning and management of urban services and internal structures. This paper constructed a probabilistic factor model on the basis of probabilistic latent semantic analysis and tensor decomposition, for purpose of understanding the higher order interactive population mobility and its impact on urban structure changes. First, a four-dimensional tensor of time (T)?×?week (W)?×?origin (O)?×?destination (D) was constructed to identify the day-to-day activities in three time modes and weekly regularity of weekday/weekend pattern. Then we reclassified the urban regions based on the space clustering formed by the space factor matrix and core tensor. Finally, we further analysed the space–time interaction on different time scales to deduce the actual function and connection strength of each region. Our research shows that the application of individual-based spatial–temporal data in human mobility and space–time interaction study can help to analyse urban spatial structure and understand the actual regional function from a new perspective. 相似文献
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全张量探测技术以其信息量大、精度高、干扰小等优点在地球物理领域中得到广泛应用.本文提出采用张量局部波数法来进行位场全张量数据的解释,首先给出了张量局部波数的定义,然后推导出利用张量局部波数法进行反演的基本公式.本文方法在进行张量数据反演时无需事先知道场源体的类型(构造指数)即可获得场源体的位置信息,且可根据位置参数对场源体的类型进行估计.通过理论模型证明张量局部波数法可以很好地完成位场全张量数据的反演工作,并将其与常规局部波数法进行对比,证明全张量局部波数法的反演结果更加准确,即使在测点分布不合理的情况下,张量局部波数法仍可以获得准确的结果.最后应用张量局部波数法对美国得克萨斯州实测重力数据进行了反演,其反演结果与已有的研究成果相一致. 相似文献
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G. Herget 《Rock Mechanics and Rock Engineering》1974,6(1):53-64
SummaryGround Stress Determinations in Canada Stress determinations with the biaxial (Doorstopper) and the triaxial strain cell of the C. S. I. R., South Africa, are discussed and show that the triaxial cell is the more desirable instrument if good rock conditions exist. Vertical and average horizontal stresses in Canada are similar in magnitude to those from other parts of the earth's crust and show that vertical stresses are related to weight of overburden and average horizontal stresses increase in most of the cases with 0.407 kg/cm2 per metre of depth. More data are necessary to make any prediction for the average horizontal stress beyond a depth of 800 m.Stress determinations and a tectonic analysis show that the unravelling of the geological stress-strain history allows some prediction of principal stress directions, but the attached uncertainties due to gaps in documentation require proof by stress determinations.With 8 Figures 相似文献
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TENSORIAL RESOLUTION:A DIRECT TRILINEAR DECOMPOSITION 总被引：4，自引：0，他引：4
EUGENIO SANCHEZ~ BRUCE R.KOWALSKI Laboratory for Chemometrics Department of Chemistry BG-.University of Washington Seattle WA U.S.A. Mobil Research Development Corporation Paulsboro Research Laboratory Billinsport Ro Paulsboro NJ U.S.A. 《地理学报(英文版)》1990,(1)
Modern instrumentation in chemistry routinely generates two-dimensional(second-order)arrays of data.Considering that most analyses need to compare several samples,the analyst ends up with a three-dimensional(third-order)array which is difficult to visualize or interpret with the conventional statisticaltools.Some of these data arrays follow the so-called trilinear model,(?)These trilinear arrays of data are known to have unique factor analysis decompositions which correspondto the true physical factors that form the data,i.e.given the array (?),a unique solution can be found inmany cases for each order X,Y and Z.This is in contrast to the well-known second-order bilinear datafactor analysis,where the abstract solutions obtained are not unique and at best cannot be easilycompared with the underlying physical factors owing to a rotational ambiguity.Trilinear decompositions have had the disadvantage,however,that a non-linear optimization withmany parameters is necessary to reach a least-squares solution.This paper will introduce a method forreducing the problem to a rectangular generalized eigenvalue-eigenvector equation where the eigenbectorsare the contravariant form(pseudo-inverse)of the actual factors.It is shown that the method works wellwhen the factors are linearly independent in at least two orders(e.g.X_(jr),and Y_(jr) are full rank matrices).Finally,it is shown how trilinear decompositions relate to multicomponent calibration,curve resolutionand chemical analysis. 相似文献