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A.T. Miesch

Publications and source records attributed to A.T. Miesch.

At least 19 recordsLinked to original sources
USGS1981

Estimation of the geochemical threshold and its statistical significance

A statistic is proposed for estimating the geochemical threshold and its statistical significance, or it may be used to identify a group of extreme values that can be tested for significance by other means. The statistic is the maximum gap between adjacent values in an ordered array after each gap has been adjusted for the expected frequency. The values in the ordered array are geochemical values transformed by either ln( χ - α ) or ln( α - χ ) and then standardized so that the mean is zero and the variance is unity. The expected frequency is taken from a fitted normal curve with unit area. The midpoint of an adjusted gap that exceeds the corresponding critical value may be taken as an estimate of the geochemical threshold, and the associated probability indicates the likelihood that the threshold separates two geochemical populations. The adjusted gap test may fail to identify threshold values if the variation tends to be continuous from background values to the higher values that reflect mineralized ground. However, the test will serve to identify other anomalies that may be too subtle to have been noted by other means.

Journal of Geochemical Exploration↗
USGS1981

Petrogenetic modeling of a potential uranium source rock, Granite Mountains, Wyoming

Previous studies of the granite of Lankin Dome have led to the conclusion that this granite was a source for the sandstone-type uranium deposits in the basins that surround the Granite Mountains, Wyo. Q-mode factor analysis of 29 samples of this granite shows that five bulk compositions are required to explain the observed variances of 33 constituents in these samples. Models presented in this paper show that the origin of the granite can be accounted for by the mixing of a starting liquid with two ranges of solid compositions such that all five compositions are granitic. There are several features of the granite of Lankin Dome that suggest derivation by partial melting and, because the proposed source region was inhomogeneous, that more than one of the five end members may have been a liquid. Data for the granite are compatible with derivation from rocks similar to those of the metamorphic complex that the granite intrudes. Evidence for crustal derivation by partial melting includes a strongly peraluminous nature, extremely high differentiation indices, high contents of incompatible elements, generally large negative Eu anomalies, and high initial lead and strontium isotopic ratios. If the granite of Lankin Dome originated by partial melting of a heterogeneous metamorphic complex, the initial magma could reasonably have been composed of a range of granitic liquids. Five variables were not well accounted for by a five-end-member model. Water, CO 2 , and U0 2 contents and the oxidation state of iron are all subject to variations caused by near-surface processes. The Q-mode factor analysis suggests that these four variables have a distribution determined by postmagmatic processes. The reason for failure of Cs0 2 to vary systematically with the other 33 variables is not known. Other granites that have lost large amounts of uranium possibly can be identified by Q-mode factor analysis.

Professional Paper↗
USGS1980

Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data

The dominant feature distinguishing one method of principal components analysis from another is the manner in which the original data are transformed prior to the other computations. The only other distinguishing feature of any importance is whether the eigenvectors of the inner product-moment of the transformed data matrix are taken directly as the Q-mode scores or scaled by the square roots of their associated eigenvalues and called the R-mode loadings. If the eigenvectors are extracted from the product-moment correlation matrix, the variables, in effect, were transformed by column standardization (zero means and unit variances), and the sum of the p-largest eigenvalues divided by the sum of all the eigenvalues indicates the degree to which a model containing p components will account for the total variance in the original data. However, if the data were transformed in any manner other than column standardization, the eigenvalues cannot be used in this manner, but can only be used to determine the degree to which the model will account for the transformed data. Regardless of the type of principal components analysis that is performed-even whether it is R or Q-mode-the goodness-of-fit of the model to the original data is given better by the eigenvalues of the correlation matrix than by those of the matrix that was actually factored. ?? 1980 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1979

Vector analysis of chemical variation in the lavas of Parícutin volcano, Mexico

Compositional variations in the lavas of Parícutin volcano, Mexico, have been examined by an extended method of Q-mode factor analysis. Each sample composition is treated as a vector projected from an original eight-dimensional space into a vector system of three dimensions. The compositions represented by the vectors after projection are closely similar to the original compositions except for Na2O and Fe2O3. The vectors in the three-dimensional system cluster about three different planes that represent three stages of compositional change in the Parícutin lavas. Because chemical data on the compositions of the minerals in the lavas are presently lacking, interpretations of the mineral phases that may have been involved in fractional crystallization are based on CIPW norm calculations. Changes during the first stage are attributed largely to the fractional crystallization of plagioclase and olivine. Changes during the second stage can be explained by the separation of plagioclase and pyroxene. Changes during the final stage may have resulted mostly from the assimilation of a granitic material, as previously proposed by R. E. Wilcox.

Journal of the International Association for Mathe↗
USGS1977

The U.S. geological survey rass-statpac system for management and statistical reduction of geochemical data

RASS is an acronym for Rock Analysis Storage System and STATPAC, for Statistical Package. The RASS and STATPAC computer programs are integrated into the RASS-STATPAC system for the management and statistical reduction of geochemical data. The system, in its present form, has been in use for more than 9 yr by scores of U.S. Geological Survey geologists, geochemists, and other scientists engaged in a broad range of geologic and geochemical investigations. The principal advantage of the system is the flexibility afforded the user both in data searches and retrievals and in the manner of statistical treatment of data. The statistical programs provide for most types of statistical reduction normally used in geochemistry and petrology, but also contain bridges to other program systems for statistical processing and automatic plotting. ?? 1977.

Computers & Geosciences↗
USGS1977

Chemical variability in the Lakeview Mountains pluton, southern California batholith: A comparison of the methods of correspondence analysis and extended Q-mode factor analysis

An extended method of Q -mode factor analysis that has been described previously offers a number of important advantages over conventional Q -mode factor analysis and correspondence analysis when applied to compositional data. Among these are the ability to compute the compositions, in the original units of the data, represented by the reference axes. The only special requirement of the data is that the values for each observation sum to a constant. Mathematically derived reference axes, such as the principal-components and varimax axes, commonly represent compositions that are partly negative. Even where no negative values are present, these compositions are comparatively difficult to interpret in petrologic terms and impossible or inappropriate to include in petrogenetic models. A model has been developed for the Lakeview Mountains pluton which employs vectors representing the compositions of melanocratic schlieren, leucocratic schlieren, and inclusions as the reference axes. When the effect of the inclusions is removed, the compositional zoning in the pluton is like that found in otherwise similar plutons in the Sierra Nevada batholith. The genetic implication of the model is that the inclusions were separated from the magma at least in its marginal parts. In the central part of the pluton, the inclusions were either separated to a lesser extent than in the marginal parts, or were reincorporated into the magma.

California↗
USGS1976

Q-mode factor analysis of compositional data

An extended form of the method of Q-mode factor analysis may be used if the rows of the data matrix sum to a constant. The constant row-sum provides a means for scaling the factor model to conform to the units of the original data in such forms as proportions, percentages, or parts per million. The scale factors for an m-factor model are used to derive composition scores and loadings, which lead to the same reproduced data regardless of the choice of reference axes (end-members). Factor-variance diagrams may be constructed to show the proportion of the variance that will be accounted for in each compositional variable by models containing various numbers of end-members. The method may be used to develop a petrologic mixing model by searching for end-members that are geologically plausible. ?? 1976.

Computers & Geosciences↗
USGS1976

Extended cabfac and Qmodel computer programs for Q-mode factor analysis of compositional data

The computer program CABFAC for Q-mode factor analysis of geologic data has been extended for use with data having constant row-sums. Another program, QMODEL, reads an output file from CABFAC and can be used to develop a variety of Q-mode models. The models serve to reproduce estimates of the original data rather than of the data in normalized form. ?? 1976.

Computers & Geosciences↗