MODELING THE SPATIAL DISTRIBUTION OF MINERAL DEPOSITS USING NEURAL NETWORKS

ABSTRACT. In the context of Geographic Information Systems (GIS), mineral potential mapping can be seen as a process whereby a set of input maps, each representing a distinct geoscientific variable, are combined to produce a single map which ranks areas according to their potential to host deposits of a particular type. However, unlike many spatial classification tasks, the objective is not to assign a pixel to some class, but to assign to each pixel a continuous value representing its mineralization potential. Logistic regression provides one method of modeling conditional probabilities on data in which the target values are binary, e.g., deposit present/deposit absent; however, logistic regression limits the output to be a logistic transformation of the inputs and hence may not be able to capture complex relationships among the input variables. This paper reports on the application of multilayer perceptrons (MLPs) to mapping reef gold mineralization potential in the Castlemaine region of Victoria, Australia. We show that the ability of MLPs to predict the presence of hold‐out test deposits is significantly better than that for logistic regression. We also show that a Bayesian learning approach can be used to automatically select an appropriate value for the weight regularization coefficient without the need of using a cross‐validation procedure. This means that all available data can be used for weight optimization, thus eliminating any sensitivity of the final map to the particular training/validation set partition used. This paper was presented at the 2004 Research Modeling Association World Conference on Natural Resource Modeling in Melbourne, Australia.     

Upper-Branch Instability of Flow in Pipes of Large Aspect Ratio with Three-Dimensional Nonlinear Viscous Critical Layers

We consider the upper-branch neutral stability of flow in pipesof large aspect ratio, basically extending the work of F. T.Smith to the nonlinear regime. The inclusion of weak nonlinearityleads to an eigenproblem whose solution depends on the propertiesof three-dimensional nonlinear critical layers. Two specialcases are considered. The first is for very small amplitude perturbations, where R is a Reynolds numberbased on the height of the tube and which is assumed large.Then a fully analytical solution of the three-dimensional criticallayers is possible, from which the linear results of Smith maybe deduced. The second case studied is that of flow in a rectangularpipe, where a solution of the nonlinear critical layer problemcan be obtained. Further analysis of neutral modes in this lattercase suggests the possible existence, inter alia, of neutralmodes for finite aspect ratio tubes. These modes depend on thescaled amplitude and have O(1) wavespeeds.     

Weakly Nonlinear Lower-Branch Stability of Fully Developed and Developing Free-Surface Flows

We examine the weakly nonlinear stability of both fully developedand of developing liquid layers. The study of these free-surfaceflows is more complicated than that of many other flows owingto the fully nonlinear boundary conditions present. The scalingsused for the two problems follow from the work of J. S. B. Gajjar,who described their linear stability properties. We use thetechnique given by F. T. Smith to derive amplitude equationsof the type presented by J. T. Stuart and J. Watson. Both flowsare found to be supercritically stable in general and a varietyof asymptotic cases are considered.     

Convergence Results for an Analytical Trial Free-Boundary Method

We consider a free-boundary problem, in two dimensions, involvingan ideal fluid flow with constant pressure on the free boundary.(A three-dimensional generalization is also considered.) Forthis problem, we give a novel definition for the iterationsof an analytical trial free-boundary method for approximatingthe solution. We then show that the successive approximationsdo converge to the solution, and we derive an error estimate.     

Energy shifts and forbidden transitions in H+ 2 due to electronic g/u symmetry breaking

A full account is given of calculations and measurements of transition frequencies and intensities of the forbidden pure rotation transition (v = 19, N = 1)-(v = 19, N = 0) in the ground electronic state (1sσ_g) of H⁺ ₂. The transition has measurable intensity because of ortho-paru mixing that arises from electronic g/u symmetry breaking caused by the Fermi contact hyper-fine interaction. Measurements of the transition were made in both single and double resonance using a fast ion beam/microwave spectrometer. The transition frequency was determined to be at 14961.7 ± 1.1 MHz (95% confidence, 5 measurements), in excellent agreement with the theoretical prediction of 14960 ± 3 MHz. The intensity of the transition relative to the allowed 1sσ_g (v = 19, N = 1)-2pσ_u,(v = 0, N = 2) transition was estimated from the available measurements to be 8000, in reasonable agreement with the theoretically predicted value of ?3000.