INTERFERENCE IMAGING: This phenomenon depends on the fundamental equation of light interferometry (Steel, 1983): OP(Optical Path) = RI(Refractive Index) x t(thickness or distance). The OP is determined by the order of interference, and, if either RI or t is held constant then the other may be obtained. Thus we may determine RI distribution within a transparent sample and/or micro-relief of an etched surface. Both RI and susceptibility to etching may be a function of the important parameters: major element composition (Ca, Na in plagioclase) and structural state (maskelynite, for example, is a glassy state of plagioclase produced by hyperbaric shock waves generated by meteorite impact).

How do these new techniques compare with older ones? They give a new type of information but are entirely complementary to existing techniques. For example, the spatial resolution of laser interferometry is limited by the resolution of the light microscopy (0.4 microns) and is 5 to 10 times that of the electron microscope (approx. 2.8 to 4.3 microns for Ca and Na, respectively, Reed, 1975) while analytical precision is about the same (Pearce, 1984c). This spatial resolution is important in studies of detailed zoning patterns in which unit zones may be only a few microns wide. Because of the ability of interference imaging to obtain an "instant snapshot" of the detailed distribution of phases, it is an ideal complement to the electron microprobe.

The Nomarski technique in reflected light depends on the subtle relief of the etched surface which alters the phase front of the reflected light beam thus enhancing the image of the topography produced by the microscope (Anderson, 1983).

Interferogram of plagioclase from Mt St. Helens (750 microns long).Inner core of calcitic
plagioclase surrounded my oligoclase. Photographed in coherent red, green, and blue laser light.

PLAGIOCLASE is probably the most important mineral (volumetrically and probably chemically) in the crusts of both the Earth and the Moon (especially in its original anorthositic crust). It is the most common mineral in the oceanic crust of the Earth and a major constituent of continental crust. Furthermore, the coupled substitution (Al + Ca = Si + Na) between the Ca- rich anorthite and Na-rich albite which form the plagioclase solid solution series does not proceed rapidly even at magmatic temperatures of 1200/ C. Thus plagioclase both records and retains its history of growth for geologically significant periods of time (thousands to millions of years). Changes in composition during growth resemble "tree rings" and are interpreted in a somewhat similar manner (although the periods of growth resulting in zones are not, of course, annual). Plagioclase is probably the most valuable mineral for recording details of growth history. Thus the ability to decipher its growth patterns is of great theoretical significance in igneous petrology.

NEURAL NETWORKS are computer applications modeled on a simplified concept of how the brain works, and which attempt to mimic the brain's process for problem solving. A neural network takes previously solved samples to build a system of "neurons" that makes new decisions. Neural networks look for patterns in training sets of data and develop the "ability" to classify new patterns or to make forecasts and predictions. Since the 1980's, neural nets have been successfully applied to an astonishing variety of problems, for example: likelihood of credit card fraud, failure of complex electrical systems, and probability of coronary disease. It is a measure of the power of this technique that, with changes of parameters, the same application can be used to predict gold prices and to predict the vegetable mixes necessary to maintain a consistent taste in canned vegetable soup.

At present, I have some preliminary results on two general types of problem, namely, classification of data sets, and, prediction of spatial-temporal dynamical data. For the classification problem, a data set of igneous and hydrothermal melanite garnets (courtesy of J. K. Russell, U. B. C.) were classified by Probabilistic Neural Networks (P.N.N.) and Kohonen unsupervised Networks. The P.N.N. nets performed exceptionally, recording accuracies in excess of 99% (even up to 100%). Kohonen nets were somewhat less accurate but still better than 86% accuracy. An attempt to classify 150 granites according to S-, A-, and I-types was equally successful, again recording accuracies of up to 100% (in training and test data sets).

The second problem involves identifying the presence of deterministic order in chaotic pseudo-random data obtained from the discrete logistic equation (c= 3.98). Initially, a backpropagation neural net was trained on a set of 200 pseudo-random points and was successful in predicting the next value of a "time sequence" following a series of 4 numbers with accuracies exceeding 86%. Further work has improved the accuracy to >96% with an average error of 0.9%. This work suggests that neural nets might be useful in identifying and assessing chaotic data, an otherwise difficult task.

This research shows promising and, even unexpected results which will assist more traditional techniques.

They work especially well in situations with numerical data and where variables are unknown or numerous (an obvious implication in the Earth Sciences). The writer is one of very few earth scientists working in this new field (there should be more, - how about you?).

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