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We implement the wave equation on a spherical membrane, with a finite-difference algorithm that accounts for finite-frequency effects in the smooth-Earth approximation, and use the resulting 'membrane waves' as an analogue for surface wave propagation in the Earth. In this formulation, we derive fully numerical 2-D sensitivity kernels for phase anomaly measurements, and employ them in a preliminary tomographic application. To speed up the computation of kernels, so that it is practical to formulate the inverse problem also with respect to a laterally heterogeneous starting model, we calculate them via the adjoint method, based on backpropagation, and parallelize our software on a Linux cluster. Our method is a step forward from ray theory, as it surpasses the inherent infinite-frequency approximation. It differs from analytical Born theory in that it does not involve a far-field approximation, and accounts, in principle, for non-linear effects like multiple scattering and wave front healing. It is much cheaper than the more accurate, fully 3-D numerical solution of the Earth's equations of motion, which has not yet been applied to large-scale tomography. Our tomographic results and trade-off analysis are compatible with those found in the ray- and analytical-Born-theory approaches. 相似文献
314.
Linbin Zhang James W. Rector III G. Michael Hoversten Sergey Fomel 《Geophysical Journal International》2007,171(3):1308-1313
We present a split-step complex Padé-Fourier migration method based on the one-way wave equation. The downward-continuation operator is split into two downward-continuation operators: one operator is a phase-shift operator and the other operator is a finite-difference operator. A complex treatment of the propagation operator is applied to mitigate inaccuracies and instabilities due to evanescent waves. It produces high-quality images of complex structures with fewer numerical artefacts than those obtained using a real approximation of a square-root operator in the one-way wave equation. Tests on zero-offset data from the SEG/EAGE salt data show that the method improves the image quality at the cost of an additional 10 per cent computational time compared to the conventional Fourier finite-difference method. 相似文献
315.
WEI EnBo & LIU Ye Institute of Oceanology Chinese Academy of Sciences Qingdao China Graduate University of the Chinese Academy of Sciences Beijing China 《中国科学D辑(英文版)》2007,50(3):474-480
Based on the effective medium approximation theory of composites, the empirical model proposed by Pandey and Kakar is remedied to investigate the microwave emissivity of sea surface under wave breaking driven by strong wind. In the improved model, the effects of seawater bubbles, droplets and difference in temperature of air and sea interface (DTAS) on the emissivity of sea surface covered by whitecaps are discussed. The model results indicate that the effective emissivity of sea surface in-creases with DTAS increasing, and the impacts of bubble structures and thickness of whitecaps layer on the emissivity are included in the model by introducing the effective dielectric constant of whitecaps layer. Moreover, a good agreement is obtained by comparing the model results with the Rose’s ex-perimental data. 相似文献
316.
YU JinHai & PENG FuQing Institute of Geodesy Geophysics Chinese Academy of Sciences Wuhan China College of Earth Scienc Graduate University of Chinese Academy of Sciences Beijing China Zhenghou Institute of Surveying Mapping Zhengzhou China 《中国科学D辑(英文版)》2007,50(4):555-562
A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements. 相似文献
317.
I. Aavatsmark G. T. Eigestad R. A. Klausen M. F. Wheeler I. Yotov 《Computational Geosciences》2007,11(4):333-345
This paper investigates different variants of the multipoint flux approximation (MPFA) O-method in 2D, which rely on a transformation
to an orthogonal reference space. This approach yields a system of equations with a symmetric matrix of coefficients. Different
methods appear, depending on where the transformed permeability is evaluated. Midpoint and corner-point evaluations are considered.
Relations to mixed finite element (MFE) methods with different velocity finite element spaces are further discussed. Convergence
of the MPFA methods is investigated numerically. For corner-point evaluation of the reference permeability, the same convergence
behavior as the O-method in the physical space is achieved when the grids are refined uniformly or when grid perturbations
of order h
2 are allowed. For h
2-perturbed grids, the convergence of the normal velocities is slower for the midpoint evaluation than for the corner-point
evaluation. However, for rough grids, i.e., grids with perturbations of order h, contrary to the physical space method, convergence cannot be claimed for any of the investigated reference space methods.
The relations to the MFE methods are used to explain the loss of convergence.
Wheeler was partially supported by NSF grant DMS 0411413 and the DOE grant DE-FGO2-04ER25617. Yotov was supported in part
by the DOE grant DE-FG02-04ER25618, the NSF grant DMS 0411694 and the J. Tinsley Oden Faculty Fellowship, The University of
Texas at Austin. 相似文献
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319.
Michael W. Davis 《Mathematical Geology》1987,19(2):99-107
An algorithm for producing a nonconditional simulation by multiplying the square root of the covariance matrix by a random vector is described. First, the square root of a matrix (or a function of a matrix in general) is defined. The square root of the matrix can be approximated by a minimax matrix polynomial. The block Toeplitz structure of the covariance matrix is used to minimize storage. Finally, multiplication of the block Toeplitz matrix by the random vector can be evaluated as a convolution using the fast Fourier transform. This results in an algorithm which is not only efficient in terms of storage and computation but also easy to implement. 相似文献
320.