This paper essentially introduces a new statistical technique of data analysis together with a practical application. The technique is Correspondence Analysis and it is designed to extract the maximum information from a two dimensional array of positive numbers, such as the concentrations of various elements in several samples. It combines the advantages of R– and Q–mode analysis and also considerably reduces the problems encountered in the practical application of these techniques: Scaling problems and computer costs. The diagrams, which are produced by projecting at the same time samples and variables on the same plane with proper scaling, aid the interpretation of geological processes. The example that is discussed concerns the Bourlamaque batholith, where igneous differentiation and metamorphism have been clearly identified as the major factors controlling its geochemistry. The complete mathematical formulation is given since it has apparently never been published in the geological literature of North America.

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Fully three-dimensional numerical solutions can quantify exterior seismic or acoustic propagation throughout complex geologic or atmospheric domains. Results from impulsive sources typically reveal propagating waves plus reverberations typical of multi-path scattering and wave-guide behavior, with decay toward quiescent motions as the dominant wave energy moves out of the domain. Because such computations are expensive and yield large data sets, it is advantageous to make the data reusable and reducible for both direct and reciprocal simulations. Our objective is efficient time-domain simulation of the wave-field response to sources with arbitrary time series. For this purpose we developed a practical and robust technique for superstable model identification. A superstable model has the form of a state-space model, but the output matrix contains the system dynamics. It simulates propagation with the fidelity of the pulse response calculated for the numerical system. Our development of the superstable technique was motivated by our initial application of the Eigensystem Realization Algorithm to wave-field systems from high-performance-computing analyses, where we recognized exterior propagation features allowing superstable model assignment. Most importantly the pulse response and its decay over the domain are captured in a finite duration, and decay to zero beyond a finite number of time steps implies a system with zero eigenvalues. We demonstrate propagationsystem identification with pulse response data derived from supercomputer analysis, and conclude that, using superstable-identified systems, we are able to create reusable and reducible propagation-system models that accurately simulate the wave field using a fraction of the original computational resources.