Thermometers and Barometers for Volcanic Systems (2025)

Journal of Petrology, 2000

The use of the popular Merzbacher & Eggler (1984, Geology INTRODUCTION 12, 587-590) experimental geohygrometer for calcalkaline andesites The importance of magmatic water in the evolution and and dacites is critically evaluated and two pitfalls are found. First, eruption of magmas is well established and it is considered calculation of the correct projection parameters is problematic because the most important volatile by far in volcanic processes two endmember calculation schemes are found in the literature; Baker involving silicic magmas. It strongly controls phase equi

Realistic propagation of uncertainties in geologic thermobarometry

Two of the most significant sources of uncertainty in geologic thermobarometry are analytical imprecision and the systematic error associated with experimental calibration techniques. Analytical uncertainties are sample-specific and dictate the precision of a P-T estimate. Calibration uncertainties are reaction-specific and effectively limit the accuracy of an estimate. We describe a systematic method of propagating both types of uncertainty through thermobarometric calculations in order to place realistic confidence limits on P-Z estimates. As an example, we evaluate the accuracy and precision of garnet-biotite, garnetplagioclase-kyanite-quartz, and garnet-rutile-kyanite-ilmenite-quartz thermobarometry for a pelitic sample from the Funeral Mountains of southeastern California. Calibration and analytical uncertainties together propagate into absolute pressure and temperature un@rtainties (950/o confidence level) of several hundred megapascals and more than 100 K. Analytical imprecision accounts for only l0-20o/o of the pressure uncertainty and less than 300/o of the temperature uncertainty. Our capacity to confidently calculate equilibration pressures and temperatures for geologic samples seems rather limited, but it can be improved significantly through additional careful experimental work. Comparative thermobarometry, which involves applying a single set of thermobarometers to different samples in order to calculate dffirences in P-T conditions, eliminates the systematic error associated with experimental calibrations. Through careful analytical work, it is possible to confidently resolve P-7 differences ofas little as a few tens ofdegrees and a few tens of megapascals.

A re-evaluation of the olivine-spinel geothermometer: Discussion

Contributions to Mineralogy and Petrology, 1980

The recent contribution on the olivine-spinel geothermometer by contains several noteworthy inconsistencies that result in what we consider misleading conclusions. The paper fails to present an up-to-date "reevaluation" of the geothermometer. We note the following points: (1) The criteria of geological reasonableness used by Roeder et al. to evaluate previously proposed versions of the geothermometer are not applied to their own revised model. (2) The experimental results presented are (a) of questionable quality as equilibrium data, and (b) if anything, more supportive of other published calibrations than of the revised thermometer put forward by the authors. (3) Despite the repeated acknowledgment by Roeder et al. of the problems inherent in formulating a thermodynamic model of the geothermometer based on a set of (independently gathered) free-energy data for the spinel end-members, the authors do just that. We conclude that the thermometric Eq. ( ) derived by Roeder et al. does not give meaningful temperatures. Reconciliation of their isotherms with those inferred from suites of natural samples would suggest kinetic problems in interpreting the latter, for which there is no evidence. We do not dispute the likelihood that olivine and spinel undergo exchange re-equilibration at subsolidus temperatures in slowly-cooled intrusions. However, we believe that the suggested closure temperatures (in the range 500 ~ 800 ~ C) are inaccurate, since their proposed geothermometer yields temperature-composition relations that are entirely at odds with those indicated by metamorphic assemblages in that temperature range.

Calibration: A Conceptual Framework Applied to Scientific Practices Which Investigate Natural Phenomena by Means of Standardized Instruments

Journal for General Philosophy of Science, 2013

This paper deals with calibration in scientific practices which investigate relatively wellunderstood natural phenomena by means of already standardized instrumental devices. Calibration is a crucial topic, since it conditions the reliability of instrumental procedures in science. Yet although important, calibration is a relatively neglected topic. We think more attention should be devoted to calibration. The paper attempts to take a step in this direction. The aims are twofold: (i) to characterize calibration in a relatively simple kind of scientific practices; (ii) to provide conceptual and taxonomic tools of broader scope that help to get a better understanding of calibration in more complex cases and other kinds of scientific practices. In this purpose, indications are first provided about why a conceptual framework is needed for better understanding calibration. Second, a bibliographic survey of works dealing with calibration is attempted. Third, different tools, elaborated for a better understanding of calibration, are introduced. Fourth, we turn to the elaboration of what we call a "simple exemplar" of calibration, illustrated through the case of the calibration of an equal-arm balance. Fifth, the tools previously introduced, and the framework of the simple exemplar, are put to work on a more complex case of calibration (calibration procedures in X-ray experiments). This leads to show the work accomplished by the simple exemplar, and to emphasize features of more complex cases of calibration. Finally, we revisit and specify the nature, the status, the scope and the value of the proposed framework.

Groping Toward Linear Regression Analysis: Newton's Analysis of Hipparchus' Equinox Observations

Arxiv preprint arXiv:0810.4948, 2008

Vol.  Newton's Analysis of Hipparchus' Observations astronomers of the era (Tycho Brahe, Galileo, and Kepler) used the median. Fifty years after Newton, in , Newton's method was rediscovered and enhanced by Tobias Mayer. Remarkably, the same regression method served with distinction in the s when the founding fathers of modern cosmology, Georges Lemaître (), Edwin Hubble (), and Willem de Sitter (), employed it to derive the Hubble constant. Introduction: the dawn of regression analysis "The only thing which is surprising is that this principle [of the Least Squares], which suggests itself so readily that no particular value at all can be placed on the idea alone, was not already applied  or  years earlier by others, e.g., Euler or Lambert or Halley or Tobias Mayer, although it may very easily be that the latter, for example, has applied that sort of thing without announcing it, just as every calculator necessarily invents a collection of devices and methods which he propagates by word of mouth only as occasion offers …" Gauss to Olbers, Göttingen,  January  1. The OLS (ordinary least-squares) regression is an optimization procedure that consists of taking several derivatives of a certain quantity and setting them equal to zero to get a set of linear ('normal') equations. However, until , this procedure was not known and optimization was carried out in purely intuitive ways. In the  prize-winning -page-long memoir Recherches sur les irregularités du mouvement de Saturne et de Jupiter, published in Paris in , Leonhard Euler, then the head of the Berlin Academy, arrived at  equations with eight uknowns but only half-heartedly proceeded combining observations to form a smaller set of equations, erroneously believing that the error "would multiply" 2. In contrast, a year later, in , the German astronomer Tobias Mayer, then a cartographer at the Homann Company in Nürnberg, studied the libration of the Moon over a period of one year, performing  observations of the crater Manilius, and obtained a system of  linear equations with three unknowns 3. Splitting all the equations into three equal groups with similar characteristics and summing coefficients within each group, he arrived at a set of three linear equations, which he further solved in a standard 'Gaussian' way. Mayer's optimization procedure resulted in a system of three equations with dominant coefficients on the major diagonal, where, in Mayer's words, "the differences between the three sums are made as large as possible." The method later became known in Europe as Mayer's method or the 'method of averages' 4. Averaging lies at the heart of the analytic part of the linear-regression method, though it is not so explicit in the modern least-squares technique. Remarkably, Mayer did not stop there but proceeded with a kind of error analysis, estimating that the combined error decreases in proportion to the number of combined equations 5. Thus, Mayer's  paper Abhandlung über die Umwälzung des Monds um seine Axe und die scheinbare Bewegung der Mondsflecken (Treatise on the rotation of the Moon on its axis and the apparent motion of the Moon spots) became a precursor for what later became known as regression analysis. However, it is noteworthy that fifty years earlier than Mayer, in , Isaac Newton had carried out similar averaging. Mayer's purely algebraic averaging can be viewed geometrically as finding the centre of gravity for three separate groups of points and then drawing a plane over them. For his part, Newton kept the geometrical picture from the very beginning. After separating two

Geothermics 2004 Todesco

The Phlegrean Fields is an active caldera structure, located on the periphery of Naples (Italy). After the last eruptive event (the Monte Nuovo eruption in 1538), periodic episodes of unrest have characterized the evolution of this volcanic district, involving seismic activity and slow ground motion (bradyseism). During these episodes of unrest, some remarkable changes have also affected the composition of the hydrothermal fluids discharged at La Solfatara fumarolic field. These unrest phenomena result from the complex interaction between magma chamber, hydrothermal fluid circulation, and country rocks undergoing thermal and mechanical stresses. In order to make an effective hazard assessment in such a densely populated area as the Phlegrean Fields, we must first reach a better understanding of the mechanism driving bradyseismic activity and determine the relation between ground deformation and hydrothermal fluid circulation. In this work, we present some results of numerical modeling of both the hydrothermal fluid circulation at La Solfatara, and of its effects on rock deformation. The modeling results show that periods of intensified magmatic degassing can explain many features of the recent crises of unrest at Phlegrean Fields.

The natural calibration of 18O16O geothermometers: application to the quartz-rutile mineral pair

Chemical Geology, 1991

Published data on 180/160 fractionation between quartz, rutile and other minerals in rocks are used to calibrate the quartz-rutile geothermometer. The concordance of temperatures deduced from different geothermometers is used to check the preservation of equilibrium among the coexisting minerals. There exists a significant (at the 99% level) linear relationship between 103In (O/quartz_rutile) and the equilibrium temperature (106/T 2), showing that 180/160 fractionation between quartz and rutile is a reliable measure of the equilibrium temperature. For temperatures ranging from 450 to 800 ° C, the following thermometric equation is determined: 1031n (Ogquartz_ruti|¢) : 4.78 (+ 0.08) (106/T 2). This calibration agrees with the theoretical relationship for anhydrous mineral-mineral fractionation. In addition, it is shown that correlated errors in 1031not and (106/T 2) is favourable to the natural calibration method of the oxygen isotope geothermometers. 2. The experimental calibrations of the quartzrutile asO fractionations Addy and Garlick (1974) have experimentally calibrated the rutile-water fractionations as a function of temperature. They synthesized rutile under hydrothermal conditions:

Teaching Statistics with Data of Historic Significance: Galileo's Gravity and Motion Experiments

Journal of Statistics Education

This article demonstrates the use of two datasets as an aid in teaching polynomial and nonlinear regression. The data were gathered by Galileo during his studies of falling bodies and projectiles. In analyzing and discussing these data, students are challenged to give thought to parsimony, independent and dependent variables, and the importance of understanding the scientific nature of the experiment. The opportunities for class discussion are especially rich in this understandable and real experiment, particularly when coupled with graphical analysis.

Validation of multidisciplinary data using thermo-mechanical modelling: application to the Western and Nothern Alps

Terra Nova

An Integrated Sensitivity Analysis for the Basalt Specific Multicomponent Geothermometer for High Temperature Settings

2020

For a successful geothermal reservoir exploration, an in-situ temperature estimation is essential. Since geothermometric reservoir temperature estimations often entail high uncertainties, statistical approaches are used. The focus is on the application of sensitive analyses on a basalt specific mineral set as multicomponent geothermometer to estimate the reservoir temperatures in Krafla, high-temperature geothermal field, Iceland.