sh=Fdk
sh=1/cFs
where F and c are coefficients that depend on local conditions.The expressions obtained are characterized by acceptable to good values for correlation coefficient r (|0.74|≤r≤|0.87|) and standard deviation of residuals ε (0.01≤ε≤0.22).The s vs. d regression law confirms previous results of regression analysis on data from granite outcrops in an area to the north of this case study, and this can therefore be regarded as a first step towards finding a generally applicable regression law.  相似文献   

3.
Transfer functions under no-analog conditions: Experiments with Indian Ocean planktonic Foraminifera     
William Halsey Hutson 《Quaternary Research》1977,8(3):355-367
This paper documents and investigates an important source of inaccuracy when paleoecological equations calibrated on modern biological data are applied downcore: fossil assemblages for which there are no modern analogs. Algebraic experiments with five calibration techniques are used to evaluate the sensitivity of the methods with respect to no-analog conditions. The five techniques are: species regression; principal-components regression [e.g., Imbrie, J., and Kipp, N. G. (1971). In “The Late Cenozoic Ages,” 71–181]; distance-index regression [Hecht, A. D. (1973). Micropaleontology19, 68–77]; diversity-index regression (Williams, D. F., and Johnson, W. C. (1975). Quaternary Research5, 237–250]; weighted-average method [Jones, J. I. (1964). Unpublished Ph. D. Thesis, Univ. of Wisconsin]. The experiments indicate that the four regression techniques extrapolate under no-analog conditions, yielding erroneous estimates. The weighted-average technique, however, does not extrapolate under no-analog conditions and consequently is more accurate than the other techniques. Methods for recognizing no-analog conditions downcore are discussed, and ways to minimize inaccuracy are suggested. Using several equations based on different calibration techniques is recommended. Divergent estimates suggest that no-analog conditions occur and that estimates are unreliable. The value determined by the weighted-average technique, however, may well be the most accurate.  相似文献   

4.
Pollen percentages,tree abundances and the Fagerlind effect     
I. C. Prentice  T. Webb 《第四纪科学杂志》1986,1(1):35-43
Pollen diagrams traditionally are read as if pollen percentages were linearly related to relative tree abundances, although the slopes and intercepts of these relationships are accepted to differ among taxa. Corresponding map patterns of modern pollen and tree percentages support this assumption of linearity, which also underlies the use of linear regression on percentage data for pollen-tree calibration. Fagerlind, however, showed that the theoretical relationship need not be linear and may be confounded by interdependencies among taxa. Regressions and scatter plots of modern pollen and tree percentages are here compared with results of extended R-value (ERV) models, which correct for the ‘Fagerlind effect’. Three data sets from Wisconsin and Michigan, USA illustrate that regression coefficients provide a first approximation to their ERV equivalents, but scatter plots derived from the ERV analyses show reduced scatter about linearised relationships.  相似文献   

5.
Multiple regression with correlated independent variables     
Thomas A. Jones 《Mathematical Geology》1972,4(3):203-218
Multiple linear regression analysis may be used to describe the relation of one geologic variable to a number of other (independent) variables, and also may be used to fit a trend surface to geographically distributed variables. The leastsquares estimates of the regression coefficients differ unpredictably from the true coefficients if the independent variables are correlated. The estimates can be too large in absolute value, and may have the wrong sign. Also, the least-squares solution may be unstable in that replicate samples can give widely differing values of the regression coefficients. Ridgeregression analysis is a technique for removing the effect of correlations from the regression analysis. The procedure involves addition of a small constant K to the diagonal elements of the standardized covariance matrix. The estimates obtained are biased but have smaller sums of squared deviations between the coefficients and their estimates. The ridge trace, a plot of the coefficients versus K, helps determine the value of K that stabilizes the estimates. Correlations between geologic variables are common, and regression coefficients based on these data may be suspect. In trendsurface analysis, correlations between the geographic coordinates may differ widely, and extreme correlations may be introduced if higher order terms are used in the trend. Ridgeregression analysis serves to guide the geologist to a more reliable interpretation of the results of multiple regression if the independent variables are correlated.  相似文献   

6.
The HMX mixing calculation program     
D. Stöckelmann  W. U. Reimold 《Mathematical Geology》1989,21(8):853-860
The HMX (harmonic mixing) mixing calculation program, originally developed to solve geological problems, provides a solution fora posteriori multicomponent mixing problems, i.e., for computations of the proportions of components contributing to a mixture in such cases where the compositions of components and mixture are known. Naturally, these problematics are not restricted to geosciences, but occur throughout all disciplines of natural sciences. The method applied is a harmonic least-squares regression analysis in combination with an optimization technique known as the variable metric method. This procedure guarantees a least-squares regression solution for those real mixing problems, where all data treated are subject to error. In these cases, the application of graphical or least-squares methods for linear regression, as they were used previously, will give significantly different, probably distorted, results.  相似文献   

7.
Nonlinear regression for dependent variables     
Richard B. McCammon 《Mathematical Geology》1973,5(4):365-375
Nonlinear regression methods can be used to fit functions for two related variables where both variables are subject to error. A computer program for nonlinear estimation described previously has been modified to fit such functions for a given set of data. A numerical example is provided for a second-degree equation in xand y.A closer fit to an observed set of data is possible if the error structure for the variables is specified.  相似文献   

8.
近20年三江平原地表蒸散发时空特征及驱动因素分析   总被引:1,自引:0,他引:1       下载免费PDF全文
林楠  姜然哲  刘强  郭晓东  杨航  陈思 《中国地质》2021,48(5):1392-1407
分析地表蒸散发时空变化规律及驱动因素,对促进区域水资源的科学分配、做好生态系统水源保护具有重要意义。本文基于MOD16蒸散发遥感数据产品,采用趋势分析及显著性检验法,深入分析了近20年三江平原地表蒸散量的时空变化特征,根据Penman-Monteith公式选取与地表蒸散量(ET)相关的驱动因子,分析各驱动因子对地表蒸散量变化的影响,并构建岭回归统计模型,分析研究地表蒸散量变化的主要驱动因子及其相对贡献率。结果表明:近20年三江平原地表蒸散发(ET)年际起伏特征明显,整体呈上升趋势;研究区内91.53%的地区ET呈增加趋势,且ET分布的地域差异逐年缩小;年内ET呈单峰型周期性变化,季节差异性明显;研究区坡度对ET有正向影响,高程和风速对ET有负向影响;气温、日照时数、降水量及NDVIET均呈正相关性,其中降水量与ET相关性最为显著;构建岭回归驱动分析模型的决定系数R2为0.823,能够有效解释各驱动因素与ET的关系。模型计算结果表明:降水量和植被覆盖度对三江平原地表蒸散量影响较大,是影响地表蒸散量变化的主要驱动力。  相似文献   

9.
Sedimentation Rates, Observation Span, and the Problem of Spurious Correlation     
W. Schlager  D. Marsal  P. A. G. van der Geest  A. Sprenger 《Mathematical Geology》1998,30(5):547-556
Plots of sedimentation rates vs. time span of observation are routinely used to demonstrate that sedimentation rates decrease if one averages over longer time spans. However, these plots are suspect because they plot a variable, time, against its inverse. It has been shown that even random numbers may yield correlation coefficients of 0.7 or higher under these circumstances. We have circumvented this problem by splitting observed sedimentation rates into time classes and performing regression on the primary variables, thickness and time, separately in each class. An alternative is weighted regression that corrects for the effect of spurious correlation. Regression on the primary variables has been performed on real data from siliciclastic and carbonate rocks. Data were sorted into time classes of 10 –110 2 yr, 10 210 5 yr, and 10 510 8 yr. Sedimentation rates decrease systematically as the time windows increase. The experiment indicates that the decrease of sedimentation rates with increase of time is not simply an effect of the mathematical transformation. It is a physical phenomenon, probably related to the fact that sedimentation is an episodic process and that the sediment record is riddled with hiatuses on all scales.  相似文献   

10.
The distribution of salt marsh foraminifera at Little Dipper Harbour New Brunswick, Canada: implications for development of widely applicable transfer functions in sea-level research     
R. Timothy Patterson  W. Roland Gehrels  Daniel F. Belknap  A.P.Andrew P. Dalby 《Quaternary International》2004,120(1):185
A stepwise linear regression analysis was carried out on both 0–1 and 0–10 cm surface samples from a transect across the marsh at Little Dipper Harbour, New Brunswick. Only the 0–1 cm surface samples produce statistically reliable results (R2=0.705; R2=0.609). These results are in sharp contrast to those obtained from British Columbia marshes where infaunal habitat and taphonomic biasing result in 0–10 cm samples producing the best results using stepwise linear regression. The fundamental difference in the apparent preferred habitats of marsh foraminifera in these areas pose difficulties for researchers attempting to develop transfer function training sets that can be applied over wide areas in paleo-sea-level research.  相似文献   

11.
Nonlinear genetic-based simulation of soil shear strength parameters     
SEYYED MOHAMMAD MOUSAVI  AMIR HOSSEIN ALAVI  AMIR HOSSEIN GANDOMI  ALI MOLLAHASANI 《Journal of Earth System Science》2011,120(6):1001-1022
New nonlinear solutions were developed to estimate the soil shear strength parameters utilizing linear genetic programming (LGP). The soil cohesion intercept (c) and angle of shearing resistance (ϕ) were formulated in terms of the basic soil physical properties. The best models were selected after developing and controlling several models with different combinations of influencing parameters. Comprehensive experimental database used for developing the models was established upon a series of unconsolidated, undrained, and unsaturated triaxial tests conducted in this study. Further, sensitivity and parametric analyses were carried out. c and ϕ were found to be mostly influenced by the soil unit weight and liquid limit. In order to benchmark the proposed models, a multiple least squares regression (MLSR) analysis was performed. The validity of the models was proved on portions of laboratory results that were not included in the modelling process. The developed models are able to effectively learn the complex relationship between the soil strength parameters and their contributing factors. The LGP models provide a significantly better prediction performance than the regression models.  相似文献   

12.
Least‐square support vector machine applied to settlement of shallow foundations on cohesionless soils     
Pijush Samui  T. G. Sitharam 《国际地质力学数值与分析法杂志》2008,32(17):2033-2043
This paper examines the potential of least‐square support vector machine (LSVVM) in the prediction of settlement of shallow foundation on cohesionless soil. In LSSVM, Vapnik's ε‐insensitive loss function has been replaced by a cost function that corresponds to a form of ridge regression. The LSSVM involves equality instead of inequality constraints and works with a least‐squares cost function. The five input variables used for the LSSVM for the prediction of settlement are footing width (B), footing length (L), footing net applied pressure (P), average standard penetration test value (N) and footing embedment depth (d). Comparison between LSSVM and some of the traditional interpretation methods are also presented. LSSVM has been used to compute error bar. The results presented in this paper clearly highlight that the LSSVM is a robust tool for prediction of settlement of shallow foundation on cohesionless soil. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

13.
A new empirical estimator of coseismic landslide displacement for Zagros Mountain region (Iran)     
Ali M. Rajabi  Mohammad R. Mahdavifar  M. Khamehchiyan  V. Del Gaudio 《Natural Hazards》2011,59(2):1189-1203
Earthquake-induced landslides are responsible worldwide for significant socioeconomic losses and historically have a prominent position in the list of natural hazards affecting the Iran plateau. As a step toward the development of tools for the assessment and the management of this kind of hazard at regional scale, an empirical estimator of coseismic displacements along potential sliding surfaces was obtained through a regression analysis for the Zagros region, a mountainous Iranian region subjected to earthquake-induced landslides. This estimator, based on the Newmark’s model, allows to evaluate the expected permanent displacement (named “Newmark displacement”) induced by seismic shaking of defined energy on potential sliding surface characterized by a given critical acceleration. To produce regression models for Newmark displacement estimators, a data set was constructed for different critical acceleration values on the basis of 108 accelerometric recordings from 80 Iranian earthquakes with moment magnitudes between 3.6 and 7. The empirical estimator has a general form, proposed by Jibson (Eng Geol 91:209–218, 2007), relating Newmark displacement to Arias intensity (as parameter representing the energy of the seismic forces) and to critical acceleration (as parameter representing the dynamic shear resistance of the sliding mass). As an example of application, this relation was employed to provide a basic document for earthquake-induced landslide hazard assessment at regional scale, according to a method proposed by Del Gaudio et al. (Bull Seismol Soc Am 93:557–569, 2003), applied to the whole Iranian territory, including Zagros region. This method consists in evaluating the shear resistance required to slopes to limit the occurrence of seismically induced failures, on the basis of the Newmark’s model. The obtained results show that the exposure to landslide seismic induction is maximum in the Alborz Mountains region, where critical accelerations up to ~0.1 g are required to limit the probability of seismic triggering of coherent type landslides within 10% in 50 years.  相似文献   

14.
The New “York” Regression: Application of an Improved Statistical Method to Geochemistry     
《International Geology Review》2012,54(4):293-303
York's (1969) method of regression, determining the best-fit line to data with errors in both variables using a least-squares solution, has become an integral part of isotope geochemistry. Although other methods agree with York's best-fit line (e.g., maximum likelihood), there is little agreement on the standard-error estimates for slope and intercept values. The reasons for this are differing levels of approximation used to compute the standard error, doubts concerning procedures for determining a confidence interval once the standard error has been estimated, and a typographical error in the original publication. This paper examines York's method of regression and standard errors of the parameters of a best-fit line. A very accurate method for determining the standard error in slope and intercept values is introduced, which eliminates the need to multiply the standard-error estimate by the goodness-of-fit parameter known as MSWD. In addition, a derivation of a fixed-intercept method of regression is introduced, and interpretations of MSWD and use of the t-adjustment in confidence intervals are discussed. The accuracy of the standard-error computations is determined by comparing the results to slope and intercept statistics generated from several thousand Monte Carlo regressions using synthetic 40Ar/39Ar inverse isochron data.  相似文献   

15.
Comparison of approaches to spatial estimation in a bivariate context   总被引:6,自引:0,他引:6  
Mustapha Asli  Denis Marcotte 《Mathematical Geology》1995,27(5):641-658
The problem of estimating a regionalized variable in the presence of other secondary variables is encountered in spatial investigations. Given a context in which the secondary variable is known everywhere (or can be estimated with great precision), different estimation methods are compared: regression, regression with residual simple kriging, kriging, simple kriging with a mean obtained by regression, kriging with an external drift, and cokriging. The study focuses on 19 pairs of regionalized variables from five different datasets representing different domains (geochemical, environmental, geotechnical). The methods are compared by cross-validation using the mean absolute error as criterion. For correlations between the principal and secondary variable under 0.4, similar results are obtained using kriging and cokriging, and these methods are superior slightly to the other approaches in terms of minimizing estimation error. For correlations greater than 0.4, cokriging generally performs better than other methods, with a reduction in mean absolute errors that can reach 46% when there is a high degree of correlation between the variables. Kriging with an external drift or kriging the residuals of a regression (SKR) are almost as precise as cokriging.  相似文献   

16.
Application of statistical learning algorithms to ultimate bearing capacity of shallow foundation on cohesionless soil     
Pijush Samui 《国际地质力学数值与分析法杂志》2012,36(1):100-110
This study employs two statistical learning algorithms (Support Vector Machine (SVM) and Relevance Vector Machine (RVM)) for the determination of ultimate bearing capacity (qu) of shallow foundation on cohesionless soil. SVM is firmly based on the theory of statistical learning, uses regression technique by introducing varepsilon‐insensitive loss function. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. It also gives variance of predicted data. The inputs of models are width of footing (B), depth of footing (D), footing geometry (L/B), unit weight of sand (γ) and angle of shearing resistance (?). Equations have been developed for the determination of qu of shallow foundation on cohesionless soil based on the SVM and RVM models. Sensitivity analysis has also been carried out to determine the effect of each input parameter. This study shows that the developed SVM and RVM are robust models for the prediction of qu of shallow foundation on cohesionless soil. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

17.
Cyclic characteristics of sediments in the Moon Island Beach Subgroup, Newcastle Coal Measures, New South Wales     
K. R. Johnson  A. C. Cook 《Mathematical Geology》1973,5(1):91-110
Cyclic characteristics of a sequence of Permian coal-measure sediments have been studied using Markov chain analysis on borehole data. Fining-upwards and oscillating sequences can be distinguished, and depositional regimes are proposed to explain the observed sequences. However, there is no clearly defined relationship of sequence type to tectonosedimentary environment. The relationship of the number of coal-defined and fining-upwards cycles to total thickness and mean cycle thickness is examined using linear regression. The relationships for coal-defined and fining-upwards cycles are essentially the same. Significant positive correlations are present between the number of cycles and total thickness and significant inverse relationships are present for the number of cycles and the mean cycle thickness.  相似文献   

18.
Dependence of radon concentration in natural gas on the geological and physical parameters of the gas reservoir     
Walter Kolb  Marcin Wojcik 《Mathematical Geology》1987,19(4):309-317
Pressure of natural gas in its rock reservoir determines the final radon concentration in this gas after its decompression to normal conditions. In this investigation, radon contents of 62 natural gas samples were measured and a simple physical model of the gas reservoir was applied. The model takes into account an additional dependence of radon concentration on the natural gas pressure and on the porosity of the rock reservoir. The influence of the gas pressure on the value of the radon emanating power is discussed. The mean 226 Ra content in the source rock needed for generation of 222 Rn concentrations observed in gas is also calculated. The calculations are made with the help of regression analysis.  相似文献   

19.
On the resolution of mixed frequency distributions into normal components     
E. Mundry 《Mathematical Geology》1972,4(1):55-60
The resolution of mixed frequency distributions into normal components may be accomplished graphically on probability paper. By means of nonlinear regression, a method for such a resolution in the probability net is given and exemplified. It is based on the observed cumulative frequencies.  相似文献   

20.
岩体特性和岩体应力推算的回归分析          下载免费PDF全文
黄建安  王思敬 《地质科学》1984,(2):173-185
岩体的开挖改变了岩体的边界条件,扰动了岩体的原始应力场,并使岩体产生变形。岩体的这种变形综合地反映了岩体的结构和地质构造环境,变形的量值及其变化规律直观地反映了岩体的稳定性。量测分析岩体的变形对监视预测岩体的失稳和不支护安全运营的期限、确定岩体加固处理的方法等都有重要的意义。因此,岩体变形的量测在地下洞室、边坡等岩体工程的勘探、施工和运营中都广泛地开展着。  相似文献   

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1.
This paper presents a methodological framework for inter‐instrument comparison of different particle‐size analysers. The framework consists of: (i) quantifying the difference between complete particle‐size distributions; (ii) identifying the best regression model for homogenizing data sets of particle‐size distributions measured by different instruments; (iii) quantifying the precision of a range of particle‐size analysers; and (iv) identifying the most appropriate instrument for analysing a given set of samples. The log‐ratio transform is applied to particle‐size distributions throughout this study to avoid the pitfalls of analysing percentage‐frequency data in ‘closed‐space’. A Normalized Distance statistic is used to quantify the difference between particle‐size distributions and assess the performance of log‐ratio regression models. Forty‐six different regression models are applied to sediment samples measured by both sieve‐pipette and laser analysis. Interactive quadratic regression models offer the best means of homogenizing data sets of particle‐size distributions measured by different instruments into a comparable format. However, quadratic interactive log‐ratio regression models require a large number of training samples (n > 80) to achieve optimal performance compared to linear regression models (n = 50). The precision of ten particle‐size analysis instruments was assessed using a data set of ten replicate measurements made of four previously published silty sediment samples. Instrument precision is quantified as the median Normalized Difference measured between the ten replicate measurements made for each sediment sample. The Differentiation Power statistic is introduced to assess the ability of each instrument to detect differences between the four sediment samples. Differentiation Power scores show that instruments based on laser diffraction principles are able to differentiate most effectively between the samples of silty sediment at a 95% confidence level. Instruments applying the principles of sedimentation offer the next most precise approach.  相似文献   

2.
In order to investigate how the apparent separation of jointing varies according to the distance from faults, and how the mechanical properties of rock masses depend on this distance and jointing density, a number of regression analysis were performed on the variables s (apparent joint separation), d (distance from major fault), and sh (rebound value of Schmidt hammer).The variables were measured at 380 stations distributed over a wide study area located in the Aspromonte range in Calabria, Southern Italy.The most significant results of simple regression analysis are expressed by the formulas:
s=c+Fd05
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