Estimating Regional Hydraulic Conductivity Fields—A Comparative Study of Geostatistical Methods     

Delphine Patriarche  Maria Clara Castro  Pierre Goovaerts 《Mathematical Geology》2005,37(6):587-613

Geostatistical estimations of the hydraulic conductivity field (K) in the Carrizo aquifer, Texas, are performed over three regional domains of increasing extent: 1) the domain corresponding to a three-dimensional groundwater flow model previously built (model domain); 2) the area corresponding to the 10 counties encompassing the model domain (County domain), and; 3) the full extension of the Carrizo aquifer within Texas (Texas domain). Two different approaches are used: 1) an indirect approach where transmissivity (T) is estimated first and K is retrieved through division of the T estimate by the screen length of the wells, and; 2) a direct approach where K data are kriged directly. Due to preferential well screen emplacement, and scarcity of sampling in the deeper portions of the formation (> 1 km), the available data set is biased toward high values of hydraulic conductivities. Kriging combined with linear regression, simple kriging with varying local means, kriging with an external drift, and cokriging allow the incorporation of specific capacity as secondary information. Prediction performances (assessed through cross-validation) differ according to the chosen approach, the considered variable (log-transformed or back-transformed), and the scale of interest. For the indirect approach, kriging of log T with varying local means yields the best estimates for both log-transformed and back-transformed variables in the model domain. For larger regional scales (County and Texas domains), cokriging performs generally better than other kriging procedures when estimating both (log T)^∗ and T^∗. Among procedures using the direct approach, the best prediction performances are obtained using kriging of log K with an external drift. Overall, geostatistical estimation of the hydraulic conductivity field at regional scales is rendered difficult by both preferential well location and preferential emplacement of well screens in the most productive portions of the aquifer. Such bias creates unrealistic hydraulic conductivity values, in particular, in sparsely sampled areas.  相似文献   

Morphometry of upper cheek teeth of cave bears (Carnivora,Ursidae)     

Gennady F. Baryshnikov  Andrey Y. Puzachenko 《Boreas: An International Journal of Quaternary Research》2019,48(3):581-604

Univariate and multivariate statistics were applied to analyse the morphometrical variability of 4920 upper cheek teeth (P4, M1 and M2) of cave bears from 123 geographical sites (180 samples) of different Pliocene – Pleistocene ages. The analysed specimens included those belonging to the big cave bears Ursus kudarensis, U. deningeri, U. spelaeus (three subspecies) and U. kanivetz (including U. ingressus), as well as the small cave bear U. rossicus. The information‐theoretical parameters (Shannon entropy and orderliness (Von Foerster, 1960: On self‐organizing systems and their environments. In Self‐Organizing Systems, 31–50. Pergamon Press, London) were used to estimate tooth diversity in different teeth, different taxa and in selected local chrono‐populations. Multivariate allometry coefficients (Klingenberg, 1996: Multivariate allometry. In Advances in Morphometrics, 23‐49. Plenum Press, New York) were used to describe the relationships of different ‘parts’ of a tooth and to compare allometric patterns amongst species or selected local samples. A multivariate analysis showed a significant overlap of the size/shape parameter ranges in deningeroid and spelaeoid bears within morphological spaces. Within the cave bear lineage, the Deninger's bear has the greatest morphological diversity index (entropy) of all the teeth overall, and the lowest diversity is observed in the final taxon of this lineage – U. kanivetz (=ingressus). The P4 and M2 diversity showed multidirectional correlations with elevation above sea level amongst several ‘local’ populations of Late Pleistocene cave bears. The morphological disparities between the studied taxa are in close agreement with the distances in the available schemes of genetic differentiation based on ancient mitochondrial DNA. The split of U. kudarensis and U. deningeri has a good bootstrap support, which corresponds to the hypothesis about their parallel evolution. The small cave bear U. rossicus is placed between U. arctos and U. deningeri. The phylogenetic signal is more pronounced in the variability of teeth in comparison with other skeletal remains of cave bears (cranium, mandible, or metapodial bones).  相似文献   

    

Douglas M. Hawkins  Noel Cressie 《Mathematical Geology》1984,16(1):3-18

Geological data frequently have a heavy-tailed normal-in-the-middle distribution, which gives rise to grade distributions that appear to be normal except for the occurrence of a few outliers. This same situation also applies to log-transformed data to which lognormal kriging is to be applied. For such data, linear kriging is nonrobust in that (1)kriged estimates tend to infinity as the outliers do, and (2)it is also not minimum mean squared error. The more general nonlinear method of disjunctive kriging is even more nonrobust, computationally more laborious, and in the end need not produce better practical answers. We propose a robust kriging method for such nearly normal data based on linear kriging of an editing of the data. It is little more laborious than conventional linear kriging and, used in conjunction with a robust estimator of the variogram, provides good protection against the effects of data outliers. The method is also applicable to time series analysis.  相似文献   

The updated kriging variance and optimal sample design     

Haiyu Gao  Jiahua Wang  Pengda Zhao 《Mathematical Geology》1996,28(3):295-313

A number of criteria based on kriging variance calculations may be used for infill sampling design in geologic site characterization. Searching for the best new sample locations from a set of candidate locations can result in excessive computation time if these criteria and the naive rekriging are used. The relative updated kriging estimate and variance for universal kriging estimation are demonstrated as a simple kriging estimate and variance, respectively. The updated kriging variance is demonstrated as the multiplication of two kriging variances. Using these updated kriging variance equations can increase the computational speed for selecting the best new sample locations. The application results for oil rock thickness in an oilfield indicate that minimizing the average relative updated kriging variance is a useful alternative to the other criteria based on kriging variance in optimal infill sampling design for geologic site characterization.  相似文献   

Geostatistical modelling of spatial and depth variability of SPT data for Bangalore     

《Geomechanics and Geoengineering》2013,8(4):307-316

The purpose of this study is to develop a geostatistical model to evaluate the spatial and depth variability of Standard Penetration Test (SPT) data from Bangalore, India. The database consists of 766 boreholes spread over a 220 km² area, with several SPT values (N) in each of them. The geostatistical analysis is done for N corrected (N _corrected) values. The N _corrected value has been corrected for different parameters such as overburden stress, size of the bore hole, type of sampler, hammer energy and length of the connecting rod. The knowledge of the semivariogram of the SPT data is used with kriging theory to estimate the values at points in the subsurface of Bangalore where field measurements are not available. The model is used to compute the variance of estimated data. The model predicts reasonably well the SPT data. The geostatistical model provides valuable results that can be used for seismic hazard analysis, site response and liquefaction studies for the development of microzonation maps. The predicted N values from the developed model can also be used to estimate the subsurface information, allowable bearing pressure of soils and elastic modulus of soils.  相似文献   

A geostatistically based approach to the identification of aquifer transmissivities in Yolo Basin, California     

Mohamed Aboufirassi  Miguel A. Mariño 《Mathematical Geology》1984,16(2):125-137

A geostatistically based approach is developed for the identification of aquifer transmissivities in Yolo Basin, California. The approach combines weighted least-squares with universal kriging and cokriging techniques in an overall scheme that (1)considers a prioriknown information on aquifer transmissivity and specific capacities of wells, (2)considers uncertainties in water level and transmissivity data, and (3)estimates the reliability of the generated transmissivity values. Minimization of a global least-squares function that incorporates calibration and plausibility criteria leads to a transmissivity map that shows a good agreement with pumping-test results.  相似文献   

Sampling design optimization for spatial functions   总被引：4，自引：0，他引：4  

Ricardo A. Olea 《Mathematical Geology》1984,16(4):369-392

A new procedure is presented for minimizing the sampling requirements necessary to estimate a mappable spatial function at a specified level of accuracy. The technique is based on universal kriging, an estimation method within the theory of regionalized variables. Neither actual implementation of the sampling nor universal kriging estimations are necessary to make an optimal design. The average standard errorand maximum standard error of estimationover the sampling domain are used as global indices of sampling efficiency. The procedure optimally selects those parameters controlling the magnitude of the indices, including the density and spatial pattern of the sample elements and the number of nearest sample elements used in the estimation. As an illustration, the network of observation wells used to monitor the water table in the Equus Beds of Kansas is analyzed and an improved sampling pattern suggested. This example demonstrates the practical utility of the procedure, which can be applied equally well to other spatial sampling problems, as the procedure is not limited by the nature of the spatial function.  相似文献   

Some binary and ternary silicate solution models     

Y. Fei  S. K. Saxena  G. Eriksson 《Contributions to Mineralogy and Petrology》1986,94(2):221-229

Four different solution models, the two-parameter Margules, the quasi-chemical (QC), the Wilson and the non-random two-liquid (NRTL) model, have been used for fitting the calorimetric excess enthalpy of solution for the following four binary silicate systems: anorthite-albite, pyrope-grossular, diopside-enstatite and diopside-Ca-Tschermak. All models except the Wilson model yield a satisfactory fit to the data but the NRTL model generally results in the lowest residuals. The use of NRTL and QC facilitates the study of the configurational and non-configurational parts of the excess entropy of mixing.Three different methods, namely those of Kohler, Wohl, and Hillert, have been used to combine binary solution properties to predict ternary solution properties. Comparison of computed excess free energy of mixing in a hypothetical solution shows that all the three methods are viable but the Kohler and Wohl methods are similar to each other and are significantly different from the Hillert method. The Kohler method with one or a combination of different binary models is recommended for predicting multicomponent solution properties.Abbreviations G ^ex excess free energy of mixing - H ^ex excess enthalpy of mixing - S ^ex total excess entropy of mixing - S _ex ^c configurational excess entropy of mixing - W _ij interaction energy parameter between speciesi andj - X _i mole fraction of speciesi - QC quasi-chemical - NRTL non-random two-liquid - M Margules formulation - W Wohl's formulation - RK Redlich-Kister - K Bertrand-Kohler - H Hillert - Di diopside (CaMgSi₂O₆) - En enstatite (Mg₂Si₂O₆) - Py pyrope (MgAl_2/3SiO₄) - Gr grossular (CaAl_2/3SiO₄) - CaTs Ca-Tschermak (CaAl₂SiO₆) - Ab albite (NaAlSi₃O₈) - An anorthite (CaAl₂Si₂O₈)  相似文献   

Kriging with strings of data   总被引：1，自引：0，他引：1  

Clayton V. Deutsch 《Mathematical Geology》1994,26(5):623-638

The concept of a random function and, consequently, the application of kriging cells for the implicit assumption that the data locations are embedded within an infinite domain. An implication of this assumption is that, all else being equal, outlying data locations will receive greater weight because they are seen as less redundant, hence, more informative of the infinite domain. A two- step kriging procedure is proposed for correcting this siring effect. The first step is to establish the total kriging weight attributable to each string. The distribution of that total weight to the samples in the string is accomplished by a second stage of kriging. In the second stage, a spatial redundancy measure r_(n) is used in place of the covariance measure in the data-data kriging matrix. This measure is constructed such that each datum has the same redundancy with the (n)data of the string to which it belongs. This paper documents the problem of kriging with strings of data, develops the redundancy measure r_(n),and presents a number of examples.  相似文献   

On the equivalence of kriging and maximum entropy estimators     

Yuh-Ming Lee  J. Hugh Ellis 《Mathematical Geology》1997,29(1):131-152

This study compares kriging and maximum entropy estimators for spatial estimation and monitoring network design. For second-order stationary random fields (a subset of Gaussian fields) the estimators and their associated interpolation error variances are identical. Simple lognormal kriging differs from the lognormal maximum entropy estimator, however, in both mathematical formulation and estimation error variances. Two numerical examples are described that compare the two estimators. Simple lognormal kriging yields systematically higher estimates and smoother interpolation surfaces compared to those produced by the lognormal maximum entropy estimator. The second empirical comparison applies kriging and entropy-based models to the problem of optimizing groundwater monitoring network design, using six alternative objective functions. The maximum entropy-based sampling design approach is shown to be the more computationally efficient of the two.  相似文献   

Factorial kriging with external drift: a case study on the Penedono Region,Portugal     

《Applied Geochemistry》2001,16(7-8):921-929

Factorial kriging has been used in geochemical exploration for the estimation and cartography of the spatial components of the variables, helping with the identification and interpretation of geochemical anomalies. Those spatial components appear by the decomposition of the variables in its several structural components, given by the variograms. In this paper a new form of factorial kriging is introduced, by using the geologic information as an external drift. This was achieved considering as an external variable (external drift) sample co-ordinates on the first axis resultant from a principal component analysis (PCA), interpreted as a lithological factor. With this type of geostatistical technique each point appears in the resultant maps as a combination of geochemical and geological information, attending the geographic localization of the samples. This technique was tested on a set of 2450 sediment samples collected on a 640 km² area, between the Trás-os-Montes e Alto Douro and the Beira Alta regions. From the 34 initial elements analyzed (10 major elements P₂O₅, SiO₂, Al₂O₃, Fe₂O₃, MgO, CaO, Na₂O, K₂O, TiO₂ and MnO expressed in oxide percentage and 24 elements expressed in ppm As, Bi, Ag, Sb, W, B, Cu, Pb, Zn, Sn, Nb, Li, Be, Zr, Y, La, Ba, Cd, Mo, V, Cr, Co, Ni and Sr) only the results obtained for 2 of them are presented in this work. The first was Sn, which is associated with some mineralisation in this region and the other one was Zn, which shows similar behavior in the whole area, with the exception of a small region.  相似文献   

地质统计学及其在第四纪研究中的应用          下载免费PDF全文

侯景儒 《第四纪研究》1993,13(3):203-213

地质统计学是数学地质领域最为活跃而实用的分支,它是以区域化变量理论为基础,以变异函数为基本工具,研究那些在空间分布上既具有随机性又具有结构性的自然现象的科学。在第四纪研究中的很多特征(变量)均可看成区域化变量进行地质统计学分析。作者在讨论了经典概率论及数理统计方法简单地应用于第四纪研究可能出现的问题后,着重介绍了用于第四纪研究中的若干地质统计学方法及基本理论,同时,对地质统计学方法应用于第四纪研究中的前景进行了分析。  相似文献   

Crowdsourcing photograph locations for debris flow hot spot mapping     

Hone-Jay Chu  Yi-Chin Chen 《Natural Hazards》2018,90(3):1259-1276

This study shows the feasibility of obtaining hazardous hot spot information on landslide and debris flow from crowdsourced data. Historical hazard or disaster photographs were voluntarily uploaded by the public to a Web photograph album. A total of 2245 hazard photographs from 1973 to 2015 were crowdsourced, and each photograph was tagged with geographical coordinates. After the removal of outliers, 96% of the photograph points were found within the 4 km potential debris flow buffer of existing databases, and none was found along the steep slopes with a mean of 14°. The photograph hot spot analysis using local Moran’s I or G _i * was identified statistically significant without subjective judgment. The DBSCAN model was also used to detect hot spot clusters effectively. The model parameters were nearly automatically generated on the basis of the count plot and the nearest neighbor distance graph. The results of these approaches were generally consistent with the hazardous hot spot maps and strongly related to central and southern Taiwan from the crowdsourced photograph data. Results reveal that the hot spot areas are found in areas with faults and near the potentially weak and fractured rocky regions. The majority of the landslides occur near the fault line because the strong ground motions triggered by an earthquake propagated along the fault rupture plane. Hot spot mapping using crowdsourced data can be used to estimate where debris flow will frequently occur and show how large the debris flow will be. Potentially hazardous areas can be effectively determined by the hot spot analysis of crowdsourced data.  相似文献   

Synthetic light curves of close binaries in a cool-disk model. The “hot line” and “hot spot” as visual indicators of interaction between the flow and disk     

T. S. Khruzina 《Astronomy Reports》2011,55(5):425-436

We present a “combined” model taking into account visual manifestations of the interaction between the gas flow and the accretion disk in a close binary system in the form of a “hot line” and a “hot spot.” The binary consists of a red dwarf that fills its Roche lobe and a compact spherical star (a white dwarf or neutron star) surrounded with a thick ellipsoidal accretion disk of a complex shape. The disk thickness is not large near the compact star but increases according to a parabolic law towards its outer edge. The oblique collision of the gaseous flow with matter of the cool, rotating disk, whose outer edge has a temperature <10 000 K, creates an extended region of enhanced energy release. In the combined model, this region is represented with a hot line that coincides with the optically opaque part of the flow and is located outside the disk, together with a hot spot at the outer surface of the disk, on the leeward side of the flow. The synthetic light curves for the combinedmodel and a hot-line model demonstrate that both models are able to fairly accurately reproduce the shapes of both classical and atypical light curves of cataclysmic variables in quiescence. Our determination of the parameters of the cataclysmic variable OY Car from an analysis of its light curves using the two models shows that the basic characteristics of the close binary, such as the component mass ratio q = M ₁/M ₂, orbital inclination i, effective temperatures of the red dwarf (T ₂) and white dwarf (T ₁), and orientation of the disk α _e , remain the same within the errors. The parameters describing the size of the slightly elliptical disk and the radiation flux from the disk differ by several percent (∼ 2–8%). A more significant difference is detected in the parameters of the hot line, due to the different shape and alignment of the flow and the presence of an additional radiation source—the hot spot—on the disk.  相似文献   

Comparison of 230Th-238U disequilibrium systematics in lavas from three hot spot regions: Hawaii,Prince Edward and Samoa     

S Newman  R.C Finkel  J.D Macdougall 《Geochimica et cosmochimica acta》1984,48(2):315-324

²³⁰Th-²³⁸U disequilibrium systematics reveal several important characteristics of the mantle source regions and petrogenesis of volcanic rocks in the presumed hot spots of Hawaii, Marion Island (Prince Edward hot spot), and Samoa. The (${}^{230}\text{Th}{}^{232}\text{Th}$) activity ratios of lavas from these three hot spots (1.06 ± 0.07, 1.04 ± 0.08, and 0.81 ± 0.06, respectively) imply that the source regions are each nearly homogeneous with $\text{Th}\text{U}$ weight ratios of 2.9, 3.0, and 3.8. For Marion Island and Mauna Kea, Hawaii, negligible secular variation occurs in the (${}^{230}\text{Th}{}^{232}\text{Th}$) initial ratios. This supports other evidence for very short transfer time between source and surface. Significant residence time at depth prior to eruption cannot be ruled out for the Samoan lavas we have studied; however, the data for one of these flows deviate from the proposed (${}^{230}\text{Th}{}^{232}\text{Th}$)-${}^{87}\text{Sr}{}^{86}\text{Sr}$ correlation (Condomineset al., 1981a) in the opposite sense from that expected for such residence. If it is assumed that the measured (${}^{230}\text{Th}{}^{232}\text{Th}$) ratios of the young lavas reflect $\text{Th}\text{U}$ in their mantle sources, then the observed variations among these three hot spots, combined with those reported by other workers for Iceland, the Azores and Tristan de Cunha, suggest that these sources are characterized by $\text{Th}\text{U}$ ratios ranging from values similar to that of MORB source (~2.5) to values similar to those of bulk earth (~3.8). Mixing of different proportions of depleted and enriched mantle may be responsible for the observed range.  相似文献   

Application of universal kriging to geochemical prospecting data     

Yujiu Song  Pengfei Ding  Yuanming Cheng  Guangdao Hu  Renduo Wang 《Mathematical Geology》1992,24(6):609-629

In the 1:50,000 mineral-resource assessments for regions of different rock types, the application of universal kriging to process geochemical prospecting data, obtained from different sampling media, can provide much useful information for evaluating mineralization potential. The method has succeeded in effectively separating local anomalies from the regional background, objectively extracting useful information, and improving the analysis of the metallogenic and ore-controlling factors, thereby playing an important role in qualitative and quantitative predictions. In 1:50,000 mineral-resource assessment it is advantageous to use universal kriging in the processing of geochemical prospecting data because universal kriging has many advantages compared to other oreassessment methods.  相似文献   

Determination of the uranium valence state in the brannerite structure using EELS, XPS, and EDX     

M. Colella  G. R. Lumpkin  Z. Zhang  E. C. Buck  K. L. Smith 《Physics and Chemistry of Minerals》2005,32(1):52-64

In this study, the valence states of uranium in synthetic and natural brannerite samples were studied using a combination of transmission electron microscopy-electron energy loss spectroscopy, scanning electron microscopy-energy dispersive X-ray analysis (SEM-EDX), and X-ray photoelectron spectroscopy (XPS) techniques. We used a set of five (UO₂, CaUO₄, SrCa₂UO₆, UTi₂O₆, and Y_0.5U_0.5Ti₂O₆) U standard samples, including two synthetic brannerites, to calibrate the EELS branching ratio, M₅/(M₄ +M₅), against the number of f electrons. The EELS data were collected at liquid nitrogen temperature in order to minimise the effects of electron beam reduction of U⁶⁺ and U⁵⁺. Test samples consisted of three additional synthetic brannerites (Th_0.7U_0.3Ti₂O₆, Ca_0.2U_0.8Ti₂O₆, and Th_0.55U_0.3Ca_0.15Ti₂O₆) and three natural brannerites from different localities. The natural brannerite samples are all completely amorphous, due to cumulative alpha decay events over geological time periods (24–508 Ma). Our U valence calibration results are in reasonable agreement with previous work, suggesting possibly a non-linear relationship between the branching ratio and the number of f electrons (and hence the average valence state) of U in solids. We found excellent agreement between the nominal valence states of U and the average valence states determined directly by EELS and estimated by EDX analysis (with assumptions regarding stoichiometry) in two of the three synthetic brannerite test samples. The average U oxidation states of the five synthetic brannerite samples, as derived from XPS analyses, are also in good agreement with those determined by other techniques. The average valence states of U in three amorphous (metamict) natural brannerite samples with alpha decay doses ranging from 3.6×10¹⁶ to 6.9×10¹⁷ /mg were found to be 4.4, 4.7, and 4.8, consistent with the presence of U⁵⁺ and/or U⁶⁺ as well as U⁴⁺ in these samples. These results are in general agreement with previous wet chemical analyses of natural brannerite. However, the average valence states inferred by SEM-EDX for two of the natural brannerite samples do not show satisfactory agreement with the EELS determined valence. This may be due to the occurrence of OH^– groups, cation vacancies, anion vacancies, or excess oxygen in the radiation-damaged structure of natural brannerite.  相似文献   

The Second-Order Stationary Universal Kriging Model Revisited   总被引：3，自引：0，他引：3  

E. Pardo-Igúzquiza  P. A. Dowd 《Mathematical Geology》1998,30(4):347-378

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   

High-temperature enthalpy at the orientational order-disorder transition in calcite: implications for the calcite/aragonite phase equilibrium     

S. A. T. Redfern  E. Salje  A. Navrotsky 《Contributions to Mineralogy and Petrology》1989,101(4):479-484

The enthalpy of calcite has been measured directly between 973 K and 1325 K by transposed-temperature- drop calorimetry. The excess enthalpy has been analysed in terms of Landau theory for this tricritical phase transition. The zero-point enthalpy and entropy allow estimates of the parameters a and C in the Landau expansion for free energy which expresses excess free energy G as a function of the order parameter Q and temperature T: G 1/2a(T _2c–T)Q ²+1/6CQ ⁶ with a=24 J·K·mol^-1, C = 30 kJ·mol^– T _c = 1260 ±5 K. The entropy of disorder below the transition has been formulated as a function of temperature allowing the calculation of the calcite/aragonite phase boundary when taking this extra entropy into account. There is remarkable agreement between the calculated equilibrium curve and previous experimental observations. The Landau theory predicts behaviour which fully accounts for the change in slope of the calcite/aragonite phase boundary, which is thus wholly due to the R¯3c –R¯3m transition in calcite.  相似文献   

Solving the kriging problem by using the Gram-Schmidt orthogonalization     

Marek Kacewicz 《Mathematical Geology》1991,23(1):111-118

This paper presents an approach to solve the kriging problem, defined in terms of projections, by using Gram-Schmidt orthogonalization. The Gram-Schmidt orthogonalization allows us to find an optimal approximationY* in then-dimensional subspaceH _n of any vectorY element of a Hilbert spaceH. This approach requiresO(n ³) multiplication operations to obtain an orthogonal basis, andO(n ²) multiplications needed to calculate kriging solution for a given point.  相似文献