MULTIVARIATE RESPONSE SURFACE MODELLING BY PRINCIPAL COMPONENTS ANALYSIS

Analysis of multivariate response data by modelling the principal components of the response has beenapplied to two sets of data. In both cases principal components analysis revealed the relationships amongthe response variables and exploited them to simplify the problem of modelling and optimizing themultivariate response. The models and optima obtained from the principal components comparedfavourably with the individual models and simultaneous optima.     

The delesse relation in a concentrically zoned sphere. I. The section-number bias

Zonal areas of a randomly chosen section through a concentrically zoned sphere yield an estimate of the (volumetric) amount of the outer zone which is subject to a large positive bias that decreases rapidly with increase in the number of sections on which the estimate is based. It will not exceed 3% of the amount present if an analysis is based on as many as 8 sections and will be less than 1% if 32 sections are used.     

Deposit modeling of a nickel belt in Finland

Data from 34 Ni−Cu deposits of the 315^c-striking, 420-km long, and 10–40-km wide Kotalahtinickel belt have been recorded in the previously described system of the Ore Data File of Finland. For comparison data from four Ni−Cu deposits outside the belt have been collected. The statistical treatment of the data begins with cluster analysis and four classes are distinguished on the basis of 303 data elements. These classes form eight groups within the linear belt. Two groups containing the largest deposits, Hitura and Kotalahti, are processed by characteristic analysis, and factor analysis is applied to test the interdependence of the characteristics. This paper was presented at the International Geological Correlation Program (IGCP) Project 98: “Standards for Computer Applications in Resource Studies” held at Taita Hills, Kenya, November 8–15, 1977.     

Sensitivity analysis of geologic computer models: A formal procedure based on Latin hypercube sampling

Mathematical models in which a response variableY is calculated, usually via a computer program, as a function of input variablesX ₁ ,X ₂, ...,X _k are encountered frequently in earth sciences literature. In many cases, uncertainty in the knowledge of the correct values of the input variables exists, leading to uncertainty in the correct value of the response. Sensitivity analysis procedures can be used to identify which input variable uncertainties contribute most to uncertainty in the response variable.This paper presents the technique of Latin hypercube sampling, a structured, formal sampling process used in the sensitivity analysis procedure. Output resulting from the sample is analyzed using stepwise regression analysis, leading to identification of key input variables. Future data gathering activities can then be done efficiently, focusing on these variables. The technique is applied to a model, developed by Sudicky and Frind, which represents the flow of a contaminant through a porous media.     

Spatial pattern recognition by decomposition

The decomposition problem—the assignment of sample observations to component populations—is studied in a spatial context. The observations are spatially located and the assignment to component populations takes into account the value of each observation as well as the values of neighboring observations. Both parameter estimation and assignment rules use a new method that integrates a standard multivariate decomposition algorithm with nonlinear regression. The method is illustrated and tested with artificial data. The distribution of the trace component Cr₂O₃ in recent Lake Michigan sediments is, then, analyzed by the method. It yields a pattern of component populations that is correlated with the Lake's bottom structure and depositional environments. Study carried out as visiting scholar at the Department of Geological Sciences, Northwestern University, Evanston, Illinois U.S.A.     

Bias in estimating fractal dimension with the rescaled-range (R/S) technique

Fractal geostatistics are being applied to subsurface geological data as a way of predicting the spatial distribution of hydrocarbon reservoir properties. The fractal dimension is the controlling parameter in stochastic methods to produce random fields of porosity and permeability. Rescaled range (R/S)analysis has become a popular way of estimating the fractal dimension, via determination of the Hurst exponent (H). A systematic investigation has been undertaken of the bias to be expected due to a range of factors commonly inherent in borehole data, particularly downhole wireline logs. The results are integrated with a review of previous work in this area. Small datasets. overlapping samples, drift and nonstationariry of means can produce a very large bias, and convergence of estimates of H around 0.85–0.90 regardless of original fractal dimension. Nonstationarity can also account for H>1, which has been reported in the literature but which is theoretically impossible for fractal time series. These results call into question the validity of fractal stochastic models built using fractal dimensions estimated with the R/Smethod.     

SHORT COMMUNICATION APPLICATION OF THE POWELL METHOD TO THE OPTIMIZATION OF FLOW INJECTION SYSTEMS

This paper describes the application of the Powell algorithm to the optimization of a flow injectionsystem configuration.The performance of this algorithm has been compared with the modified simplexmethod.The system studied is the determination of ammonia,based on the indophenol blue reaction.Alinear combination of sensitivity and sample throughput is used as the objective function because of itssimultaneous optimization capability.Results obtained show that the proposed method may reach theoptimal conditions with a lower number of experimental evaluations.