John C. Butler

Mineralogy and Petrology of Coarse Particulate Material from Lunar Surface at Tranquillity Base

Five grams of coarse fines (10085,11) contains 1227 grains, mostly mafic holocrystalline rock fragments, microbreccia, and glass spatter and agglomerates with less abundant anorthosite fragments and regularly shaped glass. The crystalline lithic fragments in the coarse fines and microbreccias represent a closely related suite of gabbroid igneous rocks that have a wider range of modal analyses and textures than seen in the larger crystalline rock samples returned by Apollo 11. Petrographic evidence of shock metamorphism is common, and the abundant glass is almost all shock-produced. None of the glass observed is similar to tektite glass.

The effects of closure on the moments of a distribution

When percentages are formed from uncorrelated, normally distributed parent variables the moments of the percentage distribution may differ considerably from those of the parents. Equations can be derived which enable the approximation of the moments of a percentage variable in terms of the moments of the parent distribution, the row sum statistics, and the correlation between a part of a sum and the sum (the part-whole correlation). If the part-whole correlation is negative the mean and variance of the percentage are increased (relative to the means and variances of those variables with a positive part-whole correlation) and the percentage variable will exhibit a positive skewness. If the part-whole correlation is positive the percentage variable will be negatively skewed if, and only if, the part-whole correlation is greater than the ratio of the coefficient of variation of the row sum (T) to the coefficient of variation of the parent variable. The kurtosis of the percentage variable must be greater than that of the parent variable regardless of the sign of the part-whole correlation. It is obvious that the interpretation or explanation of the distribution of a percentage variable must include an assessment of the effects of percentage formation. However, at the present time the isolation of the percentage effect appears to be impossible unless the parent data set is available.

Effect of various transformations on the analysis of percentage data

Proper analysis of transformed data arrays (such as percentages) requires paying special attention to the effects of the transformation process itself. Effects of several commonly used transformations (including percentage formation, row and column normalization, and the square root transformation) have been examined with emphasis placed on changes in the statistical and geometrical properties of column vectors that accompany the application of the transformation. Even though many transformations, including taking the square root, “open up” the percentage array, this does not allow one to ignore the fact that percentage formation may have considerably modified the statistical and geometrical properties of the columns of the matrix. In preparing to analyze percentages one should give serious consideration to using the row normalized form of the data matrix. The individual elements in such a matrix are the direction cosines of the vector in M-dimensional space, the row vectors are of unit length, and the row normalized matrix computed from the closed array is equal to the row normalized, open matrix that is unobservable. Application of a column transformation (such as range restriction and proportion of the maximum) destroys the equality of the open and percentage row normalized matrices. Despite repeated claims to the contrary, one can not deduce the statistical and geometrical properties of the open matrix given only the statistical and geometrical properties of the closed matrix.

Principal components analysis using the hypothetical closed array

The application of R-mode principal components analysis to a set of closed chemical data is described using previously published chemical analyses of rocks from Gough Island. Different measures of similarity have been used and the results compared by calculating the correlation coefficients between each of the elements of the extracted eigenvectors and each of the original variables. These correlations provide a convenient measure of the contribution of each variable to each of the principal components. The choice of similarity measure (variance-covariance or correlation coefficient)should reflect the nature of the data and the view of the investigator as to which is the proper weighting of the variables—according to their sample variance or equally. If the data are appropriate for principal components analysis, then the Chayes and Kruskal concept of the hypothetical open and closed arrays and the expected closure correlations would seem to be useful in defining the structure to be expected in the absence of significant departures from randomness. If the data are not multivariate normally distributed, then it is possible that the principal components will not be independent. This may result in significant nonzero covariances between various pairs of principal components.

Petrology of Rattlesnake Mountain Sill, Big Bend National Park, Texas

The Rattlesnake Mountain intrusion in the Big Bend region of Texas is an early Tertiary analcime-bearing monzonite sill about 80 m thick that was injected at shallow depth and underwent differentiation in place. It contains sheets, lamellae, cylindroidal masses, and ocelli of syenite that show systematic distribution within the monzonite. Lamellae occur in the contact rocks, cylinders are confined to the lower central zone, and sheets are concentrated in the upper central zone. Ocelli are found only in a narrow zone near the top of the sill. All rocks of the sill display similar mineral assemblages with strong compositional zonation of individual mineral species. In particular, feldspars range from intermediate plagioclase, through anorthoclase, to Na-rich sanidine, and finally, to albite plus K-feldspar. Pyroxenes show a general trend from essentially normal augite to increasingly iron-plus-sodium–enriched varieties. Over-all crystal settling did not cause formation of syenitic rocks, but the central zone of the sill contains a relatively mafic monzonite that is complementary in composition and amount to the enclosed bodies of syenite. Border zones have little syenite (1 percent), and the monzonite composition is the same as a mixture of the more mafic central monzonite and enclosed syenitic rocks in the proportions in which they occur in the central zone. Crystal fractionation played a dominant role in generating syenitic rest liquids that could be aggregated into the structures found in the sill; rifting of a partially solid crystal mesh explains the formation of lamellae and many sheets, but the cylindroidal masses and ocelli are more enigmatic. The rocks of the Rattlesnake Mountain sill, as well as others of Big Bend, show distinct chemical similarities to alkalic oceanic suites such as those of the Azores. The syenite of the sill is typical of the undersaturated felsic rocks found in many shallow mafic intrusions in Big Bend, and it is in contrast to oversaturated quartz-bearing microsyenite, microgranite, and extrusive equivalents that occur as separate masses unconnected with more mafic rocks. There appear to be two differentiation trends related, perhaps, to undersaturated and saturated basaltic lava flows known in the area and possibly also affected by depth at which differentiation occurred.

Is the Internet helping to create learning environments

An environment in which learning is facilitated is multidimensional. On one axis is the content producer/deliverer and on another is a learner. Regardless of the other axes, a learning environment requires a set of interactions between the former and the latter and the flow of information can be in either direction. What do the producers/deliverers need in order to use Internet‐based resources as part of their “bag of tricks” to build a learning environment? What are the expectations, skill sets and experiences of the learners? This note reflects the author’s experiences over a four‐year time span in attempting to answer the question raised in the title.

Complete subcompositional independence testing of closed arrays

Abstract The problem of testing for correlations in closed data, where all components sum to a constant, has undermined confidence in many inferences concerning geologic data. By their nature, much data of geologic interest are closed. Fortunately, significant progress has occurred recently in the rigorous treatment of closed data. The program documented here exploits these advances to provide a test for complete subcompositional independence. If the hypothesis of complete subcompositional independence can be demonstrated, then no nonoverlapping subvectors of the data display correlations beyond those induced solely through closure.

A classification of lunar rock and glass samples using theG-mode central method

We have used theG-mode central method to classify sets of major oxide chemical data of lunar rocks (163 averages) and lunar glasses (921 separate analyses). These data were selected from the Lunar Data Base using the following criteria: (1) the amount of SiO2, Al2O3, TiO2, FeO, MgO, CaO, Na2O, and K2O were measured by the same group of investigators and (2) the sum of these 8 major oxides was in the range 97.0–103.0 wt.% for the rocks and 99.0–101.0 for the glasses.TheG-mode central method attempts to recognize homogeneous sets or groups of samples within a raw data matrix. The original multivariate distribution is reduced to a set ofG values which follow a ‘quasi-Gaussian univariate’ distribution. Each of the homogenous groups consists of those samples that can be described by a specific normal distribution of the computedG values. We have followed previous suggestions and have not yet experimented with the effects of variations in estimates of precision, the nature of the distribution(s), or the influence of percentage formation on the recognition of homogenous groups.Fifteen groups of lunar rocks have been recognized but three of these groups are very small and certainly not homogeneous. All eight variables contribute to the recognition of the 12 retained groups (151 averages) with TiO2−Al2O3−FeO being the most effective ternary subset for the recognition and definition of these groups. A combination ofQ-mode cluster analysis (using all 8 major oxides and cos θ as the measure of similarity) and spatial position in the TiO2−Al2O3−FeO ternary allowed recognition of five families of the 151 retained lunar rock averages. Oxide wt.% and cation normative mean vectors are given for each of the 12 groups. We have assigned names to each of the families on the basis of comparisons with published information but these names are to be considered as descriptive andnot genetic.A total of 8 families and 16 groups of lunar glasses have been recognized and vector means for the oxide wt.% and cation percentage normative components are given along with the number of samples in each group and the percentage of the total number of retained samples (885) accounted for by each group. Again, names used to describe each group should not be considered as having genetic significance.

An introduction to geoscience education resources on the Internet

Abstract There is an abundance of material on the Internet which is of potential interest to individuals involved in higher education in the geosciences. The challenge is how to make judicious use of the material and how to help develop this skill for students. Experiments conducted during the fall semester 1994, lead to the conclusion that structured assignments are preferred as opposed to encouraging Internet “surfing”.

A virtual geosciences professor

Abstract Many universities are considering how best to meet the challenges of changing student characteristics (older students, more females, and increasing numbers of under-represented students) and changing fiscal climate (insufficient funding to sustain existing initiatives and develop new ones). Many are exploring the potential of Internet-based resources as an element in both synchronous courses (everyone in the same place at the same time) and asynchronous courses (where members of the class could be in many different places at different times). Simply using the Internet to broadcast course content (where information flow is primarily from the instructor to the class) fails to take advantage of its distributed nature. Perhaps the greatest contribution of “new technologies” will be a rethinking of what is required for learning to occur. The Internet itself is the best place for finding out how these resources are being incorporated into formal courses. Approximately half of the Geosciences Departments in the United States and Canada have Internet home pages. More than 200 geosciences courses, produced by more than 70 of these academic departments have Internet-based home pages. An increasing number of field trips, course exercises, tours, reference materials, poster sessions, and student projects are appearing which can be incorporated into new courses.