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

An improved experimental calibration of the olivine-spinel geothermometer

Chinese Journal of Geochemistry, 1995

The calibration of the olivine-spinel geothermometer by is commonly adopted by a number of petrologists. But the temperatures calculated in this way for ultramafic rocks are significantly lower than those obtained by the pyroxene geothermometers. These O1-Sp temperatures are also lower than those measured experimentally in the natural system (four-phase lherzolite). Different rates of cation diffusion cannot fully account for these differences. The temperature deviation is actually related to the inconsistencies between natural and experimental data which support the calibration. A re-evaluation of the calibration is proposed on the basis of a set of new experimental data.

Inversion of temporal gravity changes by the method of local corrections: A case study from Mayon volcano, Philippines

Journal of Volcanology and Geothermal Research, 2012

The 3D inversion method based on local corrections has been introduced by Prutkin to invert potential field data. It has been applied to gravity data inversion on local, regional, and global scales. Here we introduce the application of this method to invert temporal gravity changes. The inversion procedure is demonstrated by a case study on gravity changes observed at the Mayon stratovolcano between campaigns spanning a period of 1992-1996. Residual gravity changes are compiled from the observed ones. No significant surface deformation was observed within the accuracy of the campaign GPS measurements during the considered period. Residual gravity changes were first inverted in terms of sources represented by 3D line segments. The line segment approximation facilitates the second step of the iterative non-linear inversion based on local corrections. In the second step, the residual gravity changes were inverted in terms of 3D star-convex homogenous bodies representing sources of subsurface mass/density changes. Published geological evidence indicates a shallow magma system at Mayon. The absence of significant deformation accompanying the gravity changes indicates that this system was nearly open during 1992-1996. We hypothesize that the sources of the gravity signal represent mass transport, namely injection of magma into voids of the shallow system. Inversion results for campaign differences 3-1 and 4-1 are presented. For both epochs the inversion results in a source located at a depth of about 4.4 km (± 0.3 km) below sea level. The mass of injected magma was estimated at 0.35 (± 0.10) MU and 0.12 (± 0.04) MU for the two epochs, respectively. We also compare our results with previous interpretations of the same data.

Combined gravimetry in the observation of volcanic processes in Southern Italy

Journal of Geodynamics, 2000

High precision measurements of the gravity ®eld are currently carried out on active volcanoes of Southern Italy to single out the ascent of magmatic masses which could trigger a pre-eruptive state. Dierent aspects of the gravity ®eld are considered to improve the understanding of the volcano dynamics. The volcanoes considered in this paper are Mt. Vesuvius, in the Neapolitan area, and the isle of Vulcano (Aeolian Islands, Sicily). Both are aected by signi®cant gravity changes in time and space occurring with dierent patterns. At Mt. Vesuvius, a recording gravity station is also operating. It is aimed to monitor the time variations of the gravity ®eld and tidal parameters, possibly re¯ecting changes of the physical state of the volcano. The migrating¯uids may belong in part to an active geothermal system and in part to hydrological system which control the local level of the water table. At the isle of Vulcano, vertical gravity gradient measurements are also periodically carried out on six stations of the gravity network to detect changes of the mass occurring in shallower layers. The gravity ®eld of the isle of Vulcano is characterized by short-and long-term gravity changes, partly con®rmed by the results of repeated absolute gravity measurements. They might be attributed to the migration of uids through shallow levels of the crust, which seems to be also supported by the repeated measurements of the vertical gravity gradient. At Mt. Vesuvius, the ®eld of the gravity changes appears to be very disturbed on the short-term scale, while a quite clear geometry results on the long-term, evidencing an area with decreasing gravity values in the western and upper parts of the volcano and an area with increasing values at the southern±eastern base. The gravity changes are believed to result from the migration of¯uids probably occurring through pre-existing ®ssures. A decrease of up to 60 mGal has been observed from 1985 to 1994 as also consistently detected by absolute measurements. Continuous monitoring of the gravity indicates an increase of the amplitudes of the main tidal waves from 1987/ 1990 to 1994, which could be due to a change of the elastic properties of the medium. # : S 0 2 6 4 -3 7 0 7 ( 9 9 ) 0 0 0 7 2 -1

Separation of the long-term thermal effects from the strain measurements in the Geodynamics Laboratory of Lanzarote

Journal of Geodynamics, 2006

A 12-year series (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004) of strain measurements recorded in the Geodynamics Laboratory of Lanzarote is investigated. Through a tidal analysis the non-tidal component of the data is separated in order to use it for studying signals, useful for monitoring of the volcanic activity on the island. This component contains various perturbations of meteorological and oceanic origin, which should be eliminated in order to make the useful signals discernible. The paper is devoted to the estimation and elimination of the effect of the air temperature inside the station, which strongly dominates the strainmeter data. For solving this task, a regression model is applied, which includes a linear relation with the temperature and time-dependant polynomials. The regression includes nonlinearly a set of parameters, which are estimated by a properly applied Bayesian approach. The results obtained are: the regression coefficient of the strain data on temperature is equal to (−367.4 ± 0.8) × 10 −9 • C −1 , the curve of the non-tidal component reduced by the effect of the temperature and a polynomial approximation of the reduced curve. The technique used here can be helpful to investigators in the domain of the earthquake and volcano monitoring. However, the fundamental and extremely difficult problem of what kind of signals in the reduced curves might be useful in this field is not considered here.

Multicomponent Equilibrium Models for Testing Geothermometry Approaches

2013

Geothermometry is an important tool for estimating deep reservoir temperature from the geochemical composition of shallower and cooler waters. The underlying assumption of geothermometry is that the waters collected from shallow wells and seeps maintain a chemical signature that reflects equilibrium in the deeper reservoir. Many of the geothermometers used in practice are based on correlation between water temperatures and composition or using thermodynamic calculations based a subset (typically silica, cations or cation ratios) of the dissolved constituents. An alternative approach is to use complete water compositions and equilibrium geochemical modeling to calculate the degree of disequilibrium (saturation index) for large number of potential reservoir minerals as a function of temperature. We have constructed several “forward” geochemical models using The Geochemist’s Workbench to simulate the change in chemical composition of reservoir fluids as they migrate toward the surface....