Transfer and exchange equilibria in a portion of the pyroxene quadrilateral as deduced from natural and experimental data

Differences in the chemical composition of metamorphic and igneous pyroxene minerals may be attributed to a transfer reaction, which determines the Ca content of the minerals, and an exchange reaction, which determines the relative Mg:Fe²⁺ ratios. Natural data for associated Ca pyroxene (Cpx) and orthopyroxene (Opx) or pigeonite are combined with experimental data for Fe-free pyroxenes, to produce the following equations for the Cpx slope of the solvus surface: $\text{> 1080°C: T =}\text{1000}\text{(0.468 + 0.246X}{}^{\mathrm{Cpx}}\text{? 0.123 ln (1–2 [Ca]))}$$\text{< 1080°C: T =}\text{1000}\text{(0.054 + 0.608X}{}^{\mathrm{Cpx}}\text{? 0.304 ln (1–2 [Ca]))}$, and the following equation for the temperature-dependence of the Mg-Fe distribution coefficient: $\text{T =}\text{1130}\text{(}\text{ln}\text{K}{}_{\mathrm{p}}\text{+ 0.505)}$, where T is absolute temperature, X is $\text{Fe}{}^{\mathrm{2+}}\text{(Mg + Fe}{}^{\mathrm{2+}}\text{))}$, [Ca] is $\text{Ca}\text{(Ca + Mg + Fe}{}^{\mathrm{2+}}\text{)}$ in Cpx, and K_D is the distribution coefficient, defined as $\text{X}{}^{\mathrm{Opx}}\text{/(1 ? X}{}^{\mathrm{Opx}}\text{) ÷ X}{}_{\mathrm{Cpx}}\text{/(1 ?}{}^{\mathrm{Cpx}}\text{)}$.The transfer and exchange equations form useful temperature indicators, and when applied to 9 sets of well-studied rocks, yield pairs of temperatures that are in good agreement. For example, temperatures obtained for the Bushveld Complex are 1020°C (solvus equation) and 980°C (exchange equation), based on 7 specimens. The uncertainty in these numbers, due to precision and accuracy errors, is estimated to be ±60°.     

A petrologic method of analysis of nonmaceral microstructures in coal

The petrographic maceral composition and vitrinoid reflectance of bituminous coals have been correlated with their carbonization characteristics and are widely used to predict how coals will perform in the coking process and to calculate the strength of the resulting coke. As a result, there is a growing dependence on coal petrographic data in characterizing coals for cokemaking. In addition, there is a growing awareness that there are other nonmaceral microstructures in coal such as material size, shape, association, fracturing, and weathering which should permit better characterization of coals when properly interpreted. These nonmaceral microstructures also give an insight into the metamorphic history and changes due to burial and exhumanation.To expand the use of coal petrologic and petrographic data, a new analytical procedure has been developed that requires the microscopic determination of such nonmaceral microstructures as normal coal, coal fines, pseudovitrinoids, microbrecciation, oxidation, coarse mineral matter, miscellaneous materials, and contamination. The occurrence of one or more of these microstructures in coal, depending on their kind and abundance, may have a significant effect on the coal performance in various processes. This work has resulted in formulation of a technique for determining the nonmaceral microstructures in coal and, if applied as a supplement to the routine maceral analysis of coals, should help in explaining the anomalous behavior of some coals.     

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1°-averaged surface free-air gravity anomalies and POGO satellite magnetometer data for the United States, Mexico and Central America illustrate the capabilities of the method.     

Assessing the spatial variability of the ~3 μm OH/H2O absorption feature in CM2 carbonaceous chondrites

H₂O and OH are readily detected in hydrated minerals in CM chondrites via reflectance spectroscopy due to their characteristic vibration absorptions at infrared wavelengths. Previous spectroscopic work on bulk powdered CM chondrites has shown that spectral parameters, like the wavelength position of the “3 μm absorption feature,” vary systematically with the extent to which the samples have been aqueously altered. However, it is yet unclear how these spectral features may vary across an intact meteorite chip when measured at spatial scales smaller than that of the individual components of the meteorite. Here, we explore the spatial variability of this spectral feature and others on intact CM2 chips which, unlike powders, retain their petrologic and textural characteristics. We also model the modal mineralogy of the bulk meteorite powders and correlate this with key spectral features, demonstrating that microscope Fourier transform infrared spectroscopic mapping provides a powerful, rapid, and non-destructive technique for assessing compositional diversity and variations in water–rock interactions in chondritic planetary materials. In all CM2 chondrites studied here, we find that variations in the position, shape, and strength of the 3 μm absorption feature reveal a single chondrite can exhibit as much spectral variation as the entire suite of CM2 chondrites. The observed variations in the position and shape of the 3 μm feature within individual CM2 chondrite chips suggest a range of alteration products (e.g., Mg-rich to Fe-rich phyllosilicates) are present and record sub-mm scale variations in the amount and/or chemistry of the altering fluids. The samples having experienced the most progressive aqueous alteration show the least amount of variability in features like the 3 μm absorption band minimum position, whereas the least altered samples exhibit the most variability. We also find that the bulk spectral signatures in the least altered samples appear to be biased toward the spectral signatures of clasts versus matrix. By extension, asteroid reflectance spectra exhibiting 3 μm absorption features consistent with those measured here may be interpreted in a similar framework in which the spectrum of what may appear to be the least altered asteroids represents an average that belies the true diversity of mineralogy and chemistry of the body.     

Finite-element method in modeling geologic transport processes

Deterministic mathematical modeling of complex geologic transport processes may require the use of odd boundary shapes, time dependency, and two or three dimensions. Under these circumstances the governing transport equations must be solved by numerical methods. For a number of transport phenomena a general form of the convective-dispersion equation can be employed. The solution of this equation for complicated problems can be solved readily by the finite-element method. Using quadrilateral isoparametric elements or triangular elements and a computational algorithm based on Galerkin's procedure, solutions to unsteady heat flux from a dike and seawater intrusion in an aquifer have been obtained. These examples illustrate that the finite-element numerical procedure is well suited for solving boundary-value problems resulting from modeling of complex physical phenomena.