Timothy M. Lutz

INCLUSIVE CHEMICAL CHARACTERIZATION OF TOURMALINE : MOSSBAUER STUDY OF FE VALENCE AND SITE OCCUPANCY

Abstract We report here the results of a series of inclusive chemical characterizations, including all elements except oxygen, for a suite of 54 tourmaline samples. A combination of analytical techniques was used to analyze for major and light elements (electron microprobe), Fe3+ and Fe2+ (Mossbauer spectroscopy), H (U extraction), and B, Li, and F (ion microprobe, or SIMS). The B content of the tourmalines studied ranges from 2.86 to 3.26 B per formula unit (pfu) with 31 anions; excess boron is believed to reside in the Si site. Li ranges from 0.0 to 1.44 Li pfu and F contents are 0.0-0.91 pfu. H contents range from nearly anhydrous up to 3.76 H pfu and do not correlate simply with Fe3+ content. Mössbauer results show that tourmaline exhibits the entire range of Fe3+∑Fe from 0.0-1.0. Fe2+ is represented in the spectra by three doublets, with occupancy in at least three distinct types of Y sites (with different types of nearest and next nearest neighbors). Fe3+ was found in 26 of the 54 samples studied. Although Mössbauer data do not allow the distinction between [Y]Fe3+ and [Z]Fe3+ site occupancies to be made, XRD data on these samples suggest that the majority of Fe3+ is also in Y. Of the samples studied, [4]Fe3+ occurs in nine; five of those were either olenite or uvite with extensive Na substitution. A mixed valence doublet corresponding to delocalized electrons shared between adjacent octahedra was observed in 14 of the samples studied. Projection pursuit regression analysis shows that distribution of Fe among doublets is a function (albeit a complex one) of bulk composition of the tourmaline and supports the interpretation of doublets representing different populations of neighbors. Variations in Fe3+/ Fe2+ ratio cannot be directly related to variations in charge in any single site of the structure. Fe3+/Fe2+ ratio is probably controlled by the prevailing oxidation state in the bulk rock assemblage, rather than by any particular crystal chemical substitution.

An inverse method of modeling thermal histories from apatite fission-track data

Abstract Apatite fission-track (FT) ages and track length distributions are important sources of information about the thermal histories of rocks. Recent advances in the understanding of track annealing in apatite provide a solution to the forward problem of predicting FT ages and track length distributions that result from a given thermal history. In this paper, a method is presented to address the inverse problem—estimation of the thermal history from FT data. The inverse method uses an iterative approach (the downhill simplex) to systematically modify a starting thermal history to achieve satisfactory statistical agreement between the predicted and observed FT age and track length distribution. However, because of analytical uncertainties, a unique thermal history does not exist. Monte Carlo simulations are used to take into account the uncertainties in the data and yield a spectrum of possible thermal histories. The results are based on the isothermal annealing model of Laslett et al. ([1], Chem. Geol. Isot. Geosci. Sect., Vol. 65) but because the method uses forward predictions and not an analytical formula specific to a single annealing model, alternative annealing models could be used within the same framework. This method is an improvement in interpreting fission-track data because the range of thermal histories permitted by the data can be evaluated. To demonstrate the method, it is applied to several sets of test data created by forward modeling of idealized thermal histories. The results show that the age at which the sample cooled through its closure temperature and the most general features of the thermal history are revealed. However, data from partially annealed samples have wide spectra that reflect large uncertainties in the form of the thermal history. For such samples, FT data alone are not likely to provide strong tests of geologic hypotheses. Conversely, geologic information may play a crucial role in constraining the thermal history spectrum. In application to uplift-related cooling, this inverse method can provide much more realistic assessments of the cooling rate and its uncertainty than are otherwise possible.

Apatite fission-track evidence for Laramide and post-Laramide uplift and anomalous thermal regime at the Beartooth overthrust, Montana-Wyoming

The crystalline rocks of the Beartooth overthrust in southwest Montana and northwest Wyoming were uplifted and thrust over the northwest margin of the Bighorn basin during the Laramide orogeny. The timing and geometry of that event is well documented in the synorogenic Paleocene and early Eocene sedimentary rocks that were deposited ahead of the rising Beartooth basement block and partially over-ridden as the block advanced. The absence of post-Laramide sedimentary rocks on the block and in the adjacent Bighorn Basin has, however, precluded the reconstruction of the post-orogenic tectonothermal history of this region. We report here the results of fission-track analysis of apatite from the three components of the Beartooth over-thrust with the aim of reconstructing the Laramide and post-Laramide tectono-thermal history of the southeast margin of the Beartooth Mountains. Apatite fission-track ages and corresponding horizontal confined track length distributions (HCTLDs) from Precambrian basement rocks constituting the upper plate of the Beartooth overthrust indicate that from 7 to 12 km of uplift of the Red Lodge corner of the Beartooth block has occurred since early Paleocene time. This amount of uplift occurred in two stages, with an intervening mid-Tertiary period of tectonic quiescence. The latter was a period of either (1) Oligocene and/or Miocene deposition or (2) tectonic quiescence. Uplift of 4 to 8 km occurred during the first phase of cooling, which lasted from early Paleocene time (∼61 Ma) to early Eocene time (∼52 Ma). During the second phase, which began in late Miocene-early Pliocene time and continues to the present day, about 4 km of uplift occurred. Our fission-track data suggest that the thermal regime in rocks above the Beartooth overthrust was relatively stable during Tertiary time. The maximum geothermal gradient permitted by model thermal histories generated from our observed fission-track data during post-Laramide time is 17 °C/km. This value is the same as that of the present-day geothermal gradient measured in the Amoco Beartooth well and suggests that a low geothermal gradient prevailed throughout Tertiary time. Apatite fission-track ages and HCTLDs from Jurassic and Cretaceous sedimentary rocks beneath the Beartooth overthrust indicate that these rocks have remained 10-20 °C cooler than overlying rocks in the shear zone and the lowermost part of the upper plate since ∼61 Ma, an observation that is not consistent with the stratigraphic position of these rocks. We interpret this temperature to be the result of a persistent thermal regime in which ground water circulating through the sedimentary rocks of the lower plate cooled them and insulated them from conductive heat transfer from hotter overlying rocks; this ground-water circulation may have been responsible for flushing hydrocarbons out of the rock column explored by the Beartooth well. Shear-zone rocks experienced a higher temperature during Cenozoic time than did rocks of the upper and lower plates; this condition was maintained by flow through the shear zone of ground water heated to higher temperatures at deeper levels along the thrust.

Fractal geometry of ammonoid sutures

Interior chamber walls of ammonites range from smoothly undulating surfaces in some taxa to complex surfaces, corrugated on many scales, in others. The ammonite suture, which is the expression of the intersection of these walls on the exterior of the shell, has been used to assess anatomical complexity. We used the fractal dimension to measure sutural complexity and to inves- tigate complexity over evolutionary time and showed that the range of variation in sutural com- plexity increased through time. In this paper we extend our analyses and consider two new param- eters that measure the range of scales over which fractal geometry is a satisfactory metric of a suture. We use a principal components analysis of these parameters and the fractal dimension to establish a two-dimensional morphospace in which the shapes of sutures can be plotted and in which variations and evolution of suture morphology can be investigated. Our results show that mor- phospace coordinates of ammonitic sutures correspond to visually perceptible differences in suture shape. However, three main classes of sutures (goniatitic, ceratitic, and ammonitic) are not unam- biguously discriminated in this morphospace. Interestingly, ammonitic sutures occupy a smaller morphospace than other suture types (roughly one-half of the morphospace of goniatitic and ceratitic sutures combined), and the space they occupied did not change dimensions from the Jurassic to the late Cretaceous. We also compare two methods commonly used to measure the fractal dimension of linear features: the Box method and the Richardson (or divider) method. Both methods yield comparable results for ammonitic sutures but the Richardson method yields more precise results for less complex sutures.

The role of residual melt migration in producing compositional diversity in a suite of granitic rocks

Abstract We present a quantitative model for in situ crystallization within a solidification zone (or boundary layer) based on the trace and major element compositions of plutonic igneous rocks and related geochemical data. We developed the model to account for the characteristics of a suite of granitic rocks: nearly uniform mineral compositions in rocks that range widely in bulk composition (e.g., 58–76 wt.% SiO 2 ); linear variation and correlation of all major and trace elements analyzed except Ba; large and apparently random variations in Ba concentration. These characteristics cannot be explained by any standard petrogenetic model involving fractionation, mixing, or restite unmixing, but are successfully reproduced by our model of residual melt migration. We do not attempt to model the entire crystallization history of a pluton but, rather, only that interval during which melt migration processes have recognizable geochemical effects. For the granitic suite, the chemical signature of residual melt migration resulted from the change in Ba compatibility with the onset of orthoclase crystallization at a granite minimum. Our results demonstrate that plutonic rocks can develop large compositional variations, comparable to those expected to result from extreme differentiation within a large magma body, over short distances by melt migration under conditions of high permeability or slow crystallization rate within the solidification zone. Melt migration is probably a common process that could be overlooked in large plutons if sampling is sparse and if variations in some components that appear random are not considered. Our model equations yield estimates for parameters that describe the proportions of residual melt that crystallize within and migrate out of the solidification zone. Values of these parameters can be used to infer information about permeability and melt mobility within the solidification zone. The model parameters derived for the granitic suite have a roughly concentric spatial pattern in the pluton, suggesting that residual melt was trapped near the margins, accumulated in the interior, with a zone of enhanced melt mobility and possibly compositional convection in between. Our model may be of general usefulness because it requires no assumptions about magma chamber geometry or magma dynamics, it is applicable to magmas of any composition, and the equations could be formulated to include those variables best constrained by a particular suite of plutonic igneous rocks.

Trace element and isotopic zoning in minerals: Models of compositional fractionation by mineral separation procedures

Abstract Data on compositional zoning of minerals are required to apply thermodynamic models to mineral ,chemistry and to constrain kinetic models of diffusion and grain growth. Trace elements and isotopes have not been utilized fully in these applications because in situ methods of analysis (e.g. SIMS and PIXE) have not become routine. Trace element and isotopic compositions of minerals are usually determined from mineral separates. However, routine mineral separation procedures are not designed to detect and characterize zoning. Mineral separates are formed by segregating simple (monomineralic) particles of a mineral from other minerals and compound particles. Models of the formation of simple and compound particles during rock comminution show how the size and shape of mineral grains and the size of the particles formed affect the constitution of the separates. The interior portions of minerals are strongly over-represented in mineral separates, while the margins of the grains are preferentially included in compound particles. The particle size/grain size ratio is the dominant factor in the segregation of the rims of minerals from the cores. The particle size/grain size ratio can be controlled through regulation of rock comminution and sieving procedures. Separation protocols are suggested to gain information about the nature of chemical and isotopic heterogeneities in minerals. In particular, chemical and isotopic effects associated with thin zones near grain boundaries can be investigated effectively.

Enhancing Students' Understanding of Risk and Geologic Hazards Using a Dartboard Model.

Magnitude-frequency relationships of natural hazards can be expressed in a visual form through a dartboard model. The rings of the dartboard can be drawn to represent magnitude, exceedance probability, average recurrence interval, or any other relevant statistic. Dartboards can be constructed from magnitude-frequency functions or from historical data, making it possible to model a wide variety of hazards. The dartboards can be used to engage students at different levels of preparation, in different contexts, and for different lengths of time: “playing” the dart game may consist of conducting a thought experiment, actually throwing at a physical dartboard, or simulating events based on a computer program. Playing the dart game helps students to understand how a magnitude-frequency relationship results from a sequence of events. Dartboards mitigate the misconception that processes occur periodically (e.g., “the 100-year flood”) by emphasizing the random nature of hazards. The dart game also helps students to visualize the long-term consequences of living in a hazardous location. Dart games provide a context in which geoscience students can learn about statistics, simulations, and the testing of models against data.

Patterns of cooling in basement rocks — A bootstrap method to measure anomalous spatial dispersion of zircon fission-track ages

Abstract Thermochronology depends on isotopic systems for which the age is related to the time that a specified mineral cooled through its closure temperature. In tectonic studies, it is often of interest to examine regional variations in cooling age. When the variation in age within a data set exceeds the analytical errors on the age determinations, many options are available to model the spatial variation in age and to correlate it with other data or with the predictions of hypotheses. For example, trend surfaces [e.g. Davis J.C. (1986) Statistics and Data Analysis in Geology , 2nd edn. Wiley, New York] could be used to explain the variation that exceeds experimental error. In the case of interest in this study it may appear that the variations in age originate entirely from random analytical error. We show how geologically significant patterns that may be present in such apparently random data can be detected. Our analysis is based on characterizing how the extreme ages (oldest and youngest) are distributed among the sample localities. In particular, we explore whether the extremes are more dispersed or more clustered than could be expected from a random assignment of ages to the localities, as deduced from bootstrap simulations. This mode of analysis is non-parametric and requires no assumptions about the distributional form of the errors or the ages. The proposed analysis is applied to 34 zircon fission-track ages from the central Appalachian Piedmont, eastern U.S.A. Our results show that the older ages are concentrated near the center of the sample region and are surrounded by younger ages. This age pattern suggests that rocks now at the surface in the central part of the study area cooled first, followed by rocks located toward the periphery of the area.