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91.
本文将非均质各向异性地层中电磁场耦合势Helmhotz方程分解为各向异性背景场方程与散射场方程,并应用算子展开技术推导出耦合势Born级数解,建立一套三维非均质各向异性地层中随钻超深前视电阻率测井响应各阶散射电磁场与非线性Born逼近的有效计算方法.首先,利用传输线法与二维插值技术确定背景电磁场空间分布,得到零阶Born逼近解,然后根据电磁场耦合势的Born级数解推导出各阶散射电磁场方程与递推关系,通过三维有限体积法实现各阶散射场耦合势方程的离散,在此基础上结合MKL PARDISO并行技术,通过递推方式逐步计算各阶散射电磁场,并根据Born级数部分和确定不同阶次的非线性Born逼近.最后利用数值模拟结果对正演算法加以检验,并深入研究分析各阶散射场的变化特征与Born级数的收敛性质.
相似文献92.
The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function (CDF) of the performance variable. The failure probability is obtained as the value of the complement CDF at a specif ied threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function (CGF) of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and effi ciency of the proposed methodology. 相似文献
93.
Michael A. H. Hedlin Peter M. Shearer 《Physics of the Earth and Planetary Interiors》2002,130(3-4):195-208
We investigate the utility of PKP coda waves for studying weak scattering from small-scale heterogeneity in the mid-mantle. Coda waves are potentially a useful probe of heterogeneity in the mid-mantle because they are not preferentially scattered near the CMB, as PKP precursors are, but are sensitive to scattering at all depths. PKP coda waves have not been used for this purpose historically because of interference with other late-arriving energy due to near-surface resonance and scattering. Any study of deep mantle scattering using coda waves requires the removal of near-surface effects from the data. We have analyzed 3624 recordings of PKP precursors and coda made by stations in the Incorporated Research Institutions for Seismology (IRIS) Global Seismographic Network (GSN). To study the range and time dependence of the scattered waves, we binned and stacked envelopes of the recordings. We have considered precursors that arrive within a 20 s window before PKP and coda waves in a 60 s window after PKP. The PKP scattered waves increase in amplitude rapidly with range as predicted by scattering theory. At ranges below 125°, we predict and observe essentially no scattered energy preceding PKP. Coda amplitudes at these ranges are independent of range and provide an estimate of energy due to near-surface effects that we can expect at all ranges. We use the average coda amplitude at ranges from 120 to 125° to correct coda amplitudes at other ranges. PKP coda waves show a strong dependence on time and range and are clearly influenced by scattering in the lower mantle. PKP coda waves, however, do not provide a tighter constraint on the vertical distribution of mantle heterogeneity than is provided by precursors. This is due, in part, to relatively large scatter in coda amplitudes as revealed by a resampling analysis. Modeling using Rayleigh–Born scattering theory and an exponential autocorrelation function shows that PKP coda amplitudes are not highly sensitive to the vertical distribution of heterogeneity in the mantle. To illustrate this we consider single-scattering in two extreme models of mantle heterogeneity. One allows heterogeneity just at the CMB; the other includes heterogeneity throughout the mantle. The amplitudes of precursors are tightly constrained by our stack and support our earlier conclusion that small-scale heterogeneity is uniformly distributed throughout the lower mantle. The best-fit model includes 8 km scale length heterogeneity with an rms velocity contrast throughout the mantle of 1%. 相似文献
94.
Summary . Born inverse methods give accurate and stable results when the source wavelet is impulsive. However, in many practical applications (reflection seismology) an impulsive source cannot be realized and the inversion needs to be generalized to include an arbitrary source function. In this paper, we present a Born solution to the seismic inverse problem which can accommodate an arbitrary source function and give accurate and stable results. It is shown that the form of the generalized inversion algorithm reduces to a Wiener shaping ***filter, which is solved efficiently using a Levinson recursion algorithm. Numerical examples of synthetic and real field data illustrate the validity of our method. 相似文献
95.
The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local
gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential.
The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem
of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector
(from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation
Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference
benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity
field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived
gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential
difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred
into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of
the offset of the zero point of the Iranian height datum from the geoid’s potential value W
0=62636855.8 m2/s2. According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid. 相似文献
96.
The method of extracting Green's function between stations from cross correlation has proven to be effective theoretically and experimentally.It has been widely applied to surface wave tomography of the crust and upmost mantle.However,there are still controversies about why this method works.Snieder employed stationary phase approximation in evaluating contribution to cross correlation function from scatterers in the whole space,and concluded that it is the constructive interference of waves emitted by the scatterers near the receiver line that leads to the emergence of Green's function.His derivation demonstrates that cross correlation function is just the convolution of noise power spectrum and the Green's function.However,his derivation ignores influence from the two stationary points at infinities,therefore it may fail when attenuation is absent.In order to obtain accurate noise-correlation function due to scatters over the whole space,we compute the total contribution with numerical integration in polar coordinates.Our numerical computation of cross correlation function indicates that the incomplete stationary phase approximation introduces remarkable errors to the cross correlation function,in both amplitude and phase,when the frequency is low with reasonable quality factor Q.Our results argue that the distance between stations has to be beyond several wavelengths in order to reduce the influence of this inaccuracy on the applications of ambient noise method,and only the station pairs whose distances are above several (5) wavelengths can be used. 相似文献
97.
An integrated wavelet concept of physical geodesy 总被引:3,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
98.
99.
顶点覆盖问题是经典的NP完全问题,在排序、计算机网络等现实生活中有许多的应用.近几年来,许多研究者开始探究它的推广形式——顶点Pk覆盖(VCPk)问题,即寻找一个顶点子集,从拓扑结构图中删除后使得剩下的顶点导出的子图不包含Pk路,其中Pk是指包含k个顶点的路.本文简单介绍了VCPk问题的应用背景,归纳了它在近似算法、精确算法、参数化算法3个方面的主要研究进展,并分析了一些主要的方法和技巧.在此基础上,对VCPk问题及其相关问题的研究前景进行了展望. 相似文献
100.