Additive models in mining and exploration

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     

THE EFFECT OF MEAN CENTERING ON PREDICTION IN MULTIVARIATE CALIBRATION

Traditionally,one form of preprocessing in multivariate calibration methods such as principal componentregression and partial least squares is mean centering the independent variables(responses)and thedependent variables(concentrations).However,upon examination of the statistical issue of errorpropagation in multivariate calibration,it was found that mean centering is not advised for some datastructures.In this paper it is shown that for response data which(i)vary linearly with concentration,(ii)have no baseline(when there is a component with a non-zero response that does not change inconcentration)and(iii)have no closure in the concentrations(for each sample the concentrations of allcomponents add to a constant,e.g.100%)it is better not to mean center the calibration data.That is,the prediction errors as evaluated by a root mean square error statistic will be smaller for a model madewith the raw data than a model made with mean-centered data.With simulated data relativeimprovements ranging from 1% to 13% were observed depending on the amount of error in thecalibration concentrations and responses.     

COMPUTER-GENERATED MULTICOMPONENT CALIBRATION DESIGNS FOR OPTIMAL ANALYSIS SAMPLE PREDICTIONS

This paper utilizes variable step size generalized simulated annealing(VSGSA)to design multicomponentcalibration samples for spectroscopic data.VSGSA is an optimization procedure which is capable ofconverging to exact positions of global optima located on multidimensional continuous functions.On thebasis of analysis sample response vectors,optimally designed calibration concentration matrices areobtained assuming knowledge of components present.The complexity of response surfaces establishedby the optimization criteria is described.     

DISCRIMINANT PRINCIPAL COMPONENTS ANALYSIS

When the number of variables exceeds the number of samples, one method of multivariate discriminationis to use principal components analysis to reduce the dimensionality and then to perform canonicalvariates analysis (PC-CVA). This paper proposes an alternative approach in which discriminant analysisis carried out by a weighted principal component analysis of the group means (DPCA). This method doesnot require prior data reduction and produces discriminant factors that are orthogonal in the original dataspace. The theory and performance of the two methods are compared. Although the individual factors ofDPCA are found to be less discriminating than PC-CVA, the overall discrimination, calculated bymultivariate analysis of variance, and the predictive value, estimated by the leaving-one-out error rate,are broadly comparable.     

Enhancement and Mapping of Weak Multivariate Stream Sediment Geochemical Anomalies in Ahar Area,NW Iran

In this study, stream sediment geochemical data have been subjected to robust principal components analysis (RPCA) and singularity mapping (SM) to enhance and map significant multivariate geochemical anomalies (i.e., mineralization-related) in Ahar area, NW Iran. The RPCA was applied to (a) account for the compositional nature of stream sediment geochemical data using suitable log-ratio transformation, (b) modulate the effect of outliers in component estimation and (c) derive a multivariate geochemical footprint of mineralization. The SM was applied to extract anomalous patterns of the multivariate geochemical footprint of mineralization. The exploration targets were then delineated using Student’s t-statistics analysis. The correlations of mapped exploration targets with the known mineral occurrences and mineralization-related patterns were further evaluated using normalized density index and overall accuracy analyses.     

Long-period seismic source inversions using global tomographic models

We investigate the effect of laterally varying earth structure on centroid moment tensor inversions using fundamental mode mantle waves. Theoretical seismograms are calculated using a full formulation of surface wave ray theory. Calculations are made using a variety of global tomographic earth models. Results are compared with those obtained using the so-called great-circle approximation, which assumes that phase corrections are given in terms of mean phase slowness along the great circle, and which neglects amplitude effects of heterogeneity. Synthetic tests suggest that even source parameters which fit the data very well may have large errors due to incomplete knowledge of lateral heterogeneity. The method is applied to 31 shallow, large earthquakes. For a given earthquake, the focal mechanisms calculated using different earth models and different forward modelling techniques can significantly vary. We provide a range of selected solutions based on the fit to the data, rather than one single solution. Difficulties in constraining the dip-slip components of the seismic moment tensor often produce overestimates of seismic moment, leading to near vertical dip-slip mechanisms. This happens more commonly for earth models not fitting the data well, confirming that more accurate modelling of lateral heterogeneity can help to constrain the dip-slip components of the seismic moment tensor.     

主成分分析法在新疆兵团经济可持续发展能力评价中的应用

采用多元统计主成分分析方法对新疆兵团13个师1991～2006年的各师农场职工家庭人均纯收入、人均农业增加值、人均工业增加值、人均第二产业增加值、人均GDP等11个经济指标进行分析计算并且对各师的综合经济可持续能力进行比较。结果表明：从原始数据中提出占总方差86．6％的4个因子来反映各师的经济可持续发展程度,经分析发现影响各师的4个主成分因子：（1）人均GDP、人均工业增加值（包括第二产业、第三产业的增加值）的因子控制;（2）人均新增固定资产、人均固定资产投资等反映人均资产投入的综合指标;（3）反映人均耕地面积、人均利润、人均社会消费品零售总额的综合指标。（4）反映人均农业增加值、人均固定资产投入及人均社会消费品零售总额的综合指标。然后将各主成分得分结合主成分权重进行计算得出各师经济可持续能力值,其中农一师排在第一。从总体上看1992～2006年各师经济可持续发展的综合指标趋势是逐渐上升的,发展具有可持续性。,     

Diatom-based total phosphorus (TP) and pH transfer functions for the Irish Ecoregion

A 72-lake diatom training set was developed for the Irish Ecoregion to examine the response of surface sediment diatom assemblages to measured environmental variables. A variety of multivariate data analyses was used to investigate environmental and biological data structure and their inter-relationships. Of the variables used in determining a typology for lakes in the Irish Ecoregion, alkalinity was the only one found to have a significant effect on diatom assemblages. A total of 602 diatom taxa were identified, with 233 recorded at three or more sites with abundances ≥1%. Generally diatom data displayed a high degree of heterogeneity at the species level and non-linear ecological responses. Both pH and total phosphorus (TP) (in the ranges of 5.1–8.5 and 4.0–142.3 μg l⁻¹ respectively) were shown to be the most significant variables in determining the surface sediment diatom assemblages. The calibration models for pH and TP were developed using the weighted averaging (WA) method; data manipulation showed strong influences on model performances. The optima WA models based on 70 lakes produced a jack-knifed coefficient of determination (r ² _jack) of 0.89 with a root mean squared error (RMSEP) of 0.32 for pH and r ² _jack of 0.74 and RMSEP of 0.21 (log₁₀ μg l⁻¹) for TP. Both models showed strong performances in comparison with existing models for Ireland and elsewhere. Application of the pH and TP transfer functions developed here will enable the generation of quantitative water quality data from the expanding number of palaeolimnological records available for the Irish Ecoregion, and thus facilitate the use of palaeolimnological approaches in the reconstruction of past lake water quality, ecological assessment and restoration.     

QUADRATIC PLS REGRESSION

We treat here an extension of linear PLS regression to include regression on quadratic PLS components.The quadratic regression can be viewed as a natural extension of linear PLS regression to quadratic PLSaccording to the H-principle of mathematical modelling.The numerical implementation is treated indetail.It is shown that this approach can be used for models with large numbers of variables.Somemodelling strategies are discussed depending on the purpose of the modelling.Applications of thisapproach are treated.     

LATE QUATERNARY AEOLIAN GEOMORPHOLOGY OF THE DALE LAKE SAND SHEET,SOUTHERN MOJAVE DESERT,CALIFORNIA

Geomorphological and sedimentological analysis of aeolian deposits, combined with scanning electron microscopy (SEM) of quartz-grain surface characteristics, suggest six dune-building episodes during late Quaternary time in the southern Mojave Desert, California. The aeolian units accumulated largely in response to the lowering of water levels in lake basins and a consequent increase in fine sediment availability, and to stronger and more persistent winds, associated with rapidly changing environmental conditions. Peak dune deposition is believed to have taken place during the middle Holocene Altithermal between around 7.5 and 5 ka, a period characterized by greater aridity than the present. SEM analysis of the quartz surface textures indicates that mechanical and especially chemical weathering processes play a significant role in the post-depositional modification of aeolian sediments. Such evidence permits paleoenvironmental reconstruction during and since deposition, and a basis for the relative dating of aeolian sequences. Discriminant analysis using grain-size parameters, combined with principal components analysis of the SEM data from quartz-grain surfaces, is an effective analytical tool for distinguishing between spatially and temporally distributed aeolian deposits. [Key words: aeolian geomorphology, granulometry, quartz grain surface microfeatures, scanning electron microscopy, multivariate statistical analysis.]     

Linear correlations between Florida Current volume transport and surface speed with Miami sea-level and weather during 1964-70

Summary. The 1964-70 Florida Current data of Niiler & Richardson are examined for linear correlation with observed sea-level and weather, because their data provide an independent test of similar correlations reported in Maul et al. Seventy-five values of directly measured volume transport and 67 values of surface speed from Niiler & Richardson's unevenly spaced data are correlated with available daily mean values of Miami Beach sea-level, Bimini sea-level, Bimini-Miami Beach sea-level difference, and Miami weather (barometric pressure, air temperature, and north and east components of wind speed). Statistical frequency distribution of transport and of surface speed suggest variability that is not dominated by annual and/or semiannual cycles. Volume transport is most highly correlated with Bimini minus Miami Beach sea-level difference, and surface speed is most highly correlated with inverted Miami Beach sea-level. Including certain weather variables results in statistically significant improvements in linear multivariate modelling of transport and surface speed from sea-level; the standard errors are ± 2.6 sverdrup and ±10 cms⁻¹ respectively. Linear correlation coefficients and multivariate regression parameters from Niiler & Richardson's data are in agreement with those from Maul et al. , except that the standard error of estimating volume transport from sea-level is smaller in Maul et al. , apparently because of smaller errors in the direct measurements.     

Modelling patterned ground distribution in Finnish Lapland: an integration of topographical, ground and remote sensing information

New data technologies and modelling methods have gained more attention in the field of periglacial geomorphology during the last decade. In this paper we present a new modelling approach that integrates topographical, ground and remote sensing information in predictive geomorphological mapping using generalized additive modelling (GAM) . First, we explored the roles of different environmental variable groups in determining the occurrence of non‐sorted and sorted patterned ground in a fell region of 100 km2 at the resolution of 1 ha in northern Finland. Second, we compared the predictive accuracy of ground‐topography‐ and remote‐sensing‐based models. The results indicate that non‐sorted patterned ground is more common at lower altitudes where the ground moisture and vegetation abundance is relatively high, whereas sorted patterned ground is dominant at higher altitudes with relatively high slope angle and sparse vegetation cover. All modelling results were from good to excellent in model evaluation data using the area under the curve (AUC) values, derived from receiver operating characteristic (ROC) plots. Generally, models built with remotely sensed data were better than ground‐topography‐based models and combination of all environmental variables improved the predictive ability of the models. This paper confirms the potential utility of remote sensing information for modelling patterned ground distribution in subarctic landscapes.     

DETECTING AND ADJUSTING FOR NON-LINEARITIES IN CALIBRATION OF NEAR-INFRARED DATA USING PRINCIPAL COMPONENTS

A new regression method for non-linear near-infrared spectroscopic data is proposed.The technique isbased on a model which is linear in the principal components and simple functions(squares and products)of them.Added variable plots are used to determine which squares and products to incorporate into themodel.The regression coefficients are estimated by a Stein estimate which shrinks towards the estimatedetermined by the first several principal components and the selected non-linear terms.The technique isnot computationally intensive and is appropriate for routine predictions of chemical concentrations.Themethod is tested on three data sets and in all cases gives more accurate predictions than does linearprincipal components regression.     

Wide-angle seismic velocities in heterogeneous crust

Seismic velocities measured by wide-angle surveys are commonly used to constrain material composition in the deep crust. Therefore, it is important to understand how these velocities are affected by the presence of multiscale heterogeneities. The effects may be characterised by the scale of the heterogeneity relative to the dominant seismic wavelength (λ); what is clear is that heterogeneities of all scales and strengths bias wide-angle velocities to some degree. Waveform modelling was used to investigate the apparent wide-angle P -wave velocities of different heterogeneous lower crusts. A constant composition (50 per cent felsic and 50 per cent ultramafic) was formed into a variety of 1- and 2-D heterogeneous arrangements and the resulting wide-angle seismic velocity was estimated. Elastic, 1-D models produced the largest velocity shift relative to the true average velocity of the medium (which is the velocity of an isotropic mixture of the two components). Thick (width > λ) horizontal layers, as a result of Fermat's Principle, provided the largest increase in velocity; thin (width ≪λ) vertical layers produced the largest decrease in velocity. Acoustic 2-D algorithms were shown to be inadequate for modelling the kinematics of waves in bodies with multiscale heterogeneities. Elastic, 2-D modelling found velocity shifts (both positive and negative) that were of a smaller magnitude than those produced by 1-D models. The key to the magnitude of the velocity shift appears to be the connectivity of the fast (and/or slow) components. Thus, the models with the highest apparent levels of connectivity between the fast phases, the 1-D layers, produced the highest-magnitude velocity shifts. To understand the relationship between measured seismic velocities and petrology in the deep crust it is clear that high-resolution structural information (which describes such connectivity) must be included in any modelling.     

Use of GIS for a spatial and temporal analysis of Kenyan wildlife with generalised linear modelling

This paper applies generalised linear statistical techniques in a GIS to analyse wildlife data from a Kenyan wildlife reserve and its surrounding areas. Attention focuses on the spatial distribution of elephant during nine successive surveys, analysing their temporal and spatial relationship to 12 environmental covariates. A principal component analysis identifies five major determining factors, thereby reducing dimensionality in the data, while a simple spatial analysis procedure, suitable for wildlife data obtained from airborne surveys, quantfies clustering for different animal species. The number of explanatory variables appearing in abundance models is found to be subject to large variations during successive surveys with a minimum and maximum of four and eight variables, respectively. Species from highly clustered populations are found to have over 20 times more observations within short distances compared to the rest. The study concludes that a combination of generalised linear modelling and GIS gives deeper insight into the dynamics of wildlife species in and around well-defined nature reserves.     

Spherical prism magnetic effects by Gauss–Legendre quadrature integration

Regional spherical coordinate observations of the Earth's crustal magnetic field components are becoming increasingly available from shipborne, airborne, and satellite surveys. In assessing the geological significance of these data, theoretical anomalous magnetic fields from geologic models in spherical coordinates need to be evaluated. This study explicitly develops the elegant Gauss–Legendre quadrature formulation for numerically modelling the complete magnetic effects (i.e. potential, vector and tensor gradient fields) of the spherical prism. We also use these results to demonstrate the magnetic effects for the crustal prism and to investigate the crustal magnetic effects at satellite altitudes for a large region of the Middle East centred on Iran.     

Soil erodibility and processes of water erosion on hillslope

The importance of the inherent resistance of soil to erosional processes, or soil erodibility, is generally recognized in hillslope and fluvial geomorphology, but the full implications of the dynamic soil properties that affect erodibility are seldom considered. In Canada, a wide spectrum of soils and erosional processes has stimulated much research related to soil erodibility. This paper aims to place this work in an international framework of research on water erosion processes, and to identify critical emerging research questions. It focuses particularly on experimental research on rill and interrill erosion using simulated rainfall and recently developed techniques that provide data at appropriate temporal and spatial scales, essential for event-based soil erosion prediction. Results show that many components of erosional response, such as partitioning between rill and interrill or surface and subsurface processes, threshold hydraulic conditions for rill incision, rill network configuration and hillslope sediment delivery, are strongly affected by spatially variable and temporally dynamic soil properties. This agrees with other recent studies, but contrasts markedly with long-held concepts of soil credibility as an essentially constant property for any soil type. Properties that determine erodibility, such as soil aggregation and shear strength, are strongly affected by climatic factors such as rainfall distribution and frost action, and show systematic seasonal variation. They can also change significantly over much shorter time scales with subtle variations in soil water conditions, organic composition, microbiological activity, age-hardening and the structural effect of applied stresses. Property changes between and during rainstorms can dramatically affect the incidence and intensity of rill and interrill erosion and, therefore, both short and long-term hillslope erosional response. Similar property changes, linked to climatic conditions, may also significantly influence the stability and resilience of plant species and vegetation systems. Full understanding of such changes is essential if current event-based soil erosion models such as WEPP and EUROSEM are to attain their full potential predictive precision. The complexity of the interacting processes involved may, however, ultimately make stochastic modelling more effective than physically based modelling in predicting hillslope response to erodibility dynamics.