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561.
Additive models in mining and exploration 总被引:2,自引:0,他引:2
Konrad Wälder 《Natural Resources Research》1997,6(1):11-25
In this paper we present the use of additive models (AMs) for geostatistical applications. AMs are generalizations of linear
regression models which hold the central place in the toolbox of applied statisticians. Generally speaking, the linear relationship
between response and predictors is replaced with a general functional form. Recently such models were introduced in geostatistics.
Especially, we give an approach for binary data. In this case we get generalized additive models (GAMs). Logistic regression
is quite popular in medical and biological research. Using logit links also in GAMs we get so called additive logistic models.
An application for geostatistical data is introduced. In a second approach we use AMs for spatial prediction and surface modelling.
In both cases an advantage of multivariate data can be taken. The proposed applications can be used in the development of
exploration strategies, especially in the early stage of exploration 相似文献
562.
严谨的线性判别函数与判别面的理论 ,适用于线性阈值 (MP模型 )神经元分类行为分析。本文将此理论扩展到非线性 sigmoid神经元 ,分析了用来解决模式分类问题的、由 sigmoid神经元构成的单隐层 MLP(多层感知机 )的内部行为 ;并通过一系列近似推理与实验验证 ,提出了将隐层权重矢量初始值均匀地分布在权重空间的一个圆 (超球面 )上的方法。针对几个困难的分类问题的实验表明 ,该方法抓住了 MLP分类器内部行为的重要特征 ,它使 MLP分类器跨越了可能存在的学习难点 ,把学习起点放在达到目标较简便的路经上。此方法在理论上简单直接 ,应用上方便有效 ,具有一定的普遍性。 相似文献
563.
Sample schemes used in geostatistical surveys must be suitable for both variogram estimation and kriging. Previously schemes
have been optimized for one of these steps in isolation. Ordinary kriging generally requires the sampling locations to be
evenly dispersed over the region. Variogram estimation requires a more irregular pattern of sampling locations since comparisons
must be made between measurements separated by all lags up to and beyond the range of spatial correlation. Previous studies
have not considered how to combine these optimized schemes into a single survey and how to decide what proportion of sampling
effort should be devoted to variogram estimation and what proportion devoted to kriging
An expression for the total error in a geostatistical survey accounting for uncertainty due to both ordinary kriging and variogram
uncertainty is derived. In the same manner as the kriging variance, this expression is a function of the variogram but not
of the sampled response data. If a particular variogram is assumed the total error in a geostatistical survey may be estimated
prior to sampling. We can therefore design an optimal sample scheme for the combined processes of variogram estimation and
ordinary kriging by minimizing this expression. The minimization is achieved by spatial simulated annealing. The resulting
sample schemes ensure that the region is fairly evenly covered but include some close pairs to analyse the spatial correlation
over short distances. The form of these optimal sample schemes is sensitive to the assumed variogram. Therefore a Bayesian
approach is adopted where, rather than assuming a single variogram, we minimize the expected total error over a distribution
of plausible variograms. This is computationally expensive so a strategy is suggested to reduce the number of computations
required 相似文献
564.
Steve W. Lyon Arthur J. Lembo Jr. M. Todd Walter Tammo S. Steenhuis 《Advances in water resources》2006
In humid, well-vegetated areas, such as in the northeastern US, runoff is most commonly generated from relatively small portions of the landscape becoming completely saturated, however, little is known about the spatial and temporal behavior of these saturated regions. Indicator kriging provides a way to use traditional water table data to quantify probability of saturation to evaluate predicted spatial distributions of runoff generation risk, especially for the new generation of water quality models incorporating saturation excess runoff theory. When spatial measurements of a variable are transformed to binary indicators (i.e., 1 if above a given threshold value and 0 if below) and the resulting indicator semivariogram is modeled, indicator kriging produces the probability of the measured variable to exceed the threshold value. Indicator kriging gives quantified probability of saturation or, consistent with saturation excess runoff theory, runoff generation risk with depth to water table as the variable and the threshold set near the soil surface. The probability of saturation for a 120 m × 180 m hillslope based upon 43 measurements of depth to water table is investigated with indicator semivariograms for six storm events. The indicator semivariograms show high spatial structure in saturated regions with large antecedent rainfall conditions. The temporal structure of the data is used to generate interpolated (soft) data to supplement measured (hard) data. This improved the spatial structure of the indicator semivariograms for lower antecedent rainfall conditions. Probability of saturation was evaluated through indicator kriging incorporating soft data showing, based on this preliminary study, highly connected regions of saturation as expected for the wet season (April through May) in the Catskill Mountain region of New York State. Supplementation of hard data with soft data incorporates physical hydrology of the hillslope to capture significant patterns not available when using hard data alone for indicator kriging. With the need for water quality models incorporating appropriate runoff generation risk estimates on the rise, this manner of data will lay the groundwork for future model evaluation and development. 相似文献
565.
A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers 总被引:2,自引:0,他引:2
The estimation and mapping of realistic hydraulic head fields, hence of flow paths, is a major goal of many hydrogeological studies. The most widely used method to obtain reliable head fields is the inverse approach. This approach relies on the numerical approximation of the flow equation and requires specifying boundary conditions and the transmissivity of each grid element. Boundary conditions are often unknown or poorly known, yet they impose a strong signature on the head fields obtained by inverse analysis. A simpler alternative to the inverse approach is the direct kriging of the head field using the measurements obtained at observation wells. The kriging must be modified to incorporate the available information. Use of the dual kriging formalism enables simultaneously estimating the head field, the aquifer mean transmissivity, and the regional hydraulic gradient from head data in steady or transient state conditions. In transient state conditions, an estimate of the storage coefficient can be obtained. We test the approach on simple analytical cases, on synthetic cases with solutions obtained numerically using a finite element flow simulator, and on a real aquifer. For homogeneous aquifers, infinite or bounded, the kriging estimate retrieves the exact solution of the head field, the exact hydrogeological parameters and the flow net. With heterogeneous aquifers, kriging accurately estimates the head field with prediction errors of the same magnitude as typical head measurement errors. The transmissivities are also accurately estimated by kriging. Moreover, if inversion is required, the kriged head along boundaries can be used as realistic boundary conditions for flow simulation. 相似文献
566.
Three-dimensional distribution analysis of phosphorus content of limestone through a combination of geostatistics and artificial neural network 总被引:1,自引:0,他引:1
One of the factors that determines the suitability of limestone for industrial use and its commercial value is phosphorus
(P) content, i.e., the weight percentage of phosphorus contained in small quantities of limestone. Because P content changes
locally, geostatistical techniques including semivariogram, ordinary kriging, and conditional indicator sequential simulation
were used in this study to identify the spatial correlation of P content and to estimate its three-dimensional distribution
in an open-pit mine. The P content data at 43,000 points of five different bench levels were analyzed. It was found that the
horizontal semivariograms produced by using the data at the same bench level show anisotropic behavior and are represented
by the sum of two spherical models with different ranges and sills. The twelve vertical semivariograms were also constructed
from P content in boring cores. After these semivariograms were classified into four types, a multilayered neural network
was applied to clarify the horizontal distribution of each one. One of the twelve semivariograms was assigned to an arbitrary
grid point in the study area by the criterion that its type is the same as the one estimated at the point and the borehole
site producing the semivariogram is the nearest to the point. With this technique, ordinary kriging combined with the semivariogram
of borehole data provided a proper estimation of P content in the depth direction. 相似文献
567.
Conditional Spectral Simulation with Phase Identification 总被引:2,自引:0,他引:2
Tingting Yao 《Mathematical Geology》1998,30(3):285-308
Spectral simulation is used widely in electrical engineering to generate random fields with a given covariance spectrum. The algorithms used are fast particularly when based on Fast Fourier Transform (FFT). However, because of lack of phase identification, spectral simulation only generates unconditional realizations. Local data conditioning is obtained typically by adding a simulated kriging residual. This conditioning process requires an additional kriging at each simulated node thus forfeiting the speed advantage of FFT. A new algorithm for conditioning is proposed whereby the phase values are determined iteratively to ensure approximative data reproduction while reproducing the frequency spectrum, that is, the covariance model. A case study is presented to demonstrate the algorithm. 相似文献
568.
The Second-Order Stationary Universal Kriging Model Revisited 总被引:3,自引:0,他引:3
Universal kriging originally was developed for problems of spatial interpolation if a drift seemed to be justified to model the experimental data. But its use has been questioned in relation to the bias of the estimated underlying variogram (variogram of the residuals), and furthermore universal kriging came to be considered an old-fashioned method after the theory of intrinsic random functions was developed. In this paper the model is reexamined together with methods for handling problems in the inference of parameters. The efficiency of the inference of covariance parameters is shown in terms of bias, variance, and mean square error of the sampling distribution obtained by Monte Carlo simulation for three different estimators (maximum likelihood, bias corrected maximum likelihood, and restricted maximum likelihood). It is shown that unbiased estimates for the covariance parameters may be obtained but if the number of samples is small there can be no guarantee of good estimates (estimates close to the true value) because the sampling variance usually is large. This problem is not specific to the universal kriging model but rather arises in any model where parameters are inferred from experimental data. The validity of the estimates may be evaluated statistically as a risk function as is shown in this paper. 相似文献
569.
纯时间域多元信息地质统计学 总被引:5,自引:0,他引:5
随着人们动态地认识客观世界的要求日益增加,时空域中的多元信息地质统计学技术研究受到重视。本文在时间域内对几种纯时间域克立格技术进行了研究,重点对纯时间域中的普通克立格(TOK)、简单克立格(TSK)及泛克立格(TUK)进行了论述,也对纯时间域中的协同克立格(TCOK)和指示克立格(TIK)作了简要的概括。 相似文献
570.
作为模型组合创新的一次尝试,文章通过几个实例说明,在不规则数据的特殊条件下,所组建的成矿能-克立格双模型既能保持单一模型的各自优势,又能使其功能互补,可以产生单一模型不能达到的功能和效果。 相似文献