Knowledge of temperature and pressure, however qualitative, has been central to our views of geology since at least the early 19th century. In 1822, for example, Charles Daubeny presented what may be the very first “Geological Thermometer,” comparing temperatures of various geologic processes (Torrens 2006). Daubeny (1835) may even have been the first to measure the temperature of a lava flow, by laying a thermometer on the top of a flow at Vesuvius—albeit several months following the eruption, after intervening rain (his estimate was 390°F). In any case, pressure ( P ) and temperature ( T ) estimation lie at the heart of fundamental questions: How hot is Earth, and at what rate has the planet cooled. Are volcanoes the products of thermally driven mantle plumes? Where are magmas stored, and how are they transported to the surface—and how do storage and transport relate to plate tectonics? Well-calibrated thermometers and barometers are essential tools if we are to fully appreciate the driving forces and inner workings of volcanic systems.

This chapter presents methods to estimate the P-T conditions of volcanic and other igneous processes. The coverage includes a review of existing geothermometers and geobarometers, and a presentation of approximately 30 new models, including a new plagioclase-liquid hygrometer. Our emphasis is on experimentally calibrated “thermobarometers,” based on analytic expressions using P or T as dependent variables. For numerical reasons (touched on below) such expressions will always provide the most accurate means of P-T estimation, and are also most easily employed. Analytical expressions also allow error to be ascertained; in the absence of estimates of error, P-T estimates are nearly meaningless. This chapter is intended to complement the chapters by Anderson et al. (2008), who cover granitic systems, and by Blundy and Cashman (2008) and Hansteen and Klugel (2008), who consider additional methods …

Thermometers and Barometers for Volcanic Systems

Aleutian magnesian andesites: Melts from subducted Pacific ocean crust

Thermodynamic and mathematical relations are presented to facilitate the description of an algorithm for the calculation of chemical mass transfer in magmatic systems. This algorithm extends the silicate liquid solution model of Ghiorso et al. (1983) to allow for the quantitative modelling of natural magmatic processes such as crystal fractionation, equilibrium crystallization, magma mixing and solid-phase assimilation. The algorithm incorporates a new method for determining the saturation surface of a non-ideal multicomponent solid-solution crystallizing from a melt. It utilizes a mathematical programming (optimization) approach to determine the stable heterogeneous (solids+liquid) equilibrium phase assemblage at a particular temperature and pressure in magmatic systems both closed and open to oxygen. Closed system equilibria are computed by direct minimization of the Gibbs free energy of the system. Open system equilibria are determined by minimization of the Korzhinskii potential (Thompson 1970), where oxygen is treated as a perfectly mobile component. Magmatic systems undergoing chemical mass transfer processes are modelled in a series of discrete steps in temperature, pressure or bulk composition, with each step characterized by heterogeneous solid-liquid equilibrium. A numerical implementation of the algorithm has been developed (in the form of a FORTRAN 77 computer program) and calculations demonstrating its utility are provided in an accompanying paper (Ghiorso and Carmichael 1985).

Chemical mass transfer in magmatic processes

Lasaga's (1982) Master Equation for crystal growth is solved for multicomponent systems in situations which allow for coupled diffusion of melt species. The structure of the solution is explored in some detail for the case of a constant diffusion coefficient matrix. Incorporating these results, the growth of plagioclase is modeled in undercooled tholeiitic melts by approximating interface growth rates with (1) a reduced growth rate function and with (2) calculated solid-liquid solution properties obtained from the silicate liquid solution model of Ghiorso et al. (1983; appendix of Ghiorso 1985). For this purpose algorithms are provided for estimating the liquidus temperature or the chemical affinity of a multicomponent solid solution precipitating from a complex melt of specified bulk composition. Compositional trends in initial solids produced by successive degrees of undercooling are opposite to those predicted in the binary system NaAlSi3O8-CaAl2Si2O8. Calculations suggest that the solid phase and interface melt compositions rapidly approach a “steady state” for a given degree of undercooling. Consequently, the overall isothermal growth rate of plagioclase forming from tholeiitic melts appears to be entirely diffusion controlled. In magmatic systems the multicomponent growth equations allow for the formation of oscillatory zoned crystals as a consequence of the “couplingr” between interface reaction kinetics and melt diffusion. The magnitude of this effect is largely dependent upon the asymmetry of the diffusion coefficient matrix. Methods are described to facilitate the calibration of diffusion matrices from experimental data on multicomponent penetration curves.Experimental results (Lesher and Walker 1986) on steady state Soret concentration profiles resulting from thermal diffusion in MORB and andesitic liquids are analyzed using the theory of multicomponent linear irreversible thermodynamics. Under conditions where the entropy production is minimized, a linear relationship is derived between liquid chemical potentials and temperature. This relationship is utilized to evaluate the validity of the solution model of Ghiorso et al. (1983) in melts up to 300° C above their liquidus. The results indicate that configurational entropies are accurately modeled for MORB and andesite bulk compositions. The modeling fails in two four-component systems tested. Equations are derived which allow the calibration of multicomponent regular solution parameters from steady state Soret arrays. An algorithm is demonstrated which permits the calculation of steady state Soret concentration profiles, given an overall bulk melt composition and temperature gradient. This algorithm uses the liquid solution properties of Ghiorso et al. (1983) and constants obtained from the experimental measurements of Lesher and Walker (1986).

Chemical mass transfer in magmatic processes: III. Crystal growth, chemical diffusion and thermal diffusion in multicomponent silicate melts

Large volcanic debris avalanches: Characteristics of source areas, deposits, and associated eruptions

A working terminology of pyroc lstic deposits

Silica activity in igneous rocks

History and tectonic setting of Caribbean magmatism

A series of basaltic and andesitic lavas from three centers in the Cascades (Lassen, Medicine Lake, Mt. Shasta) have been investigated. The lavas are weakly porphyritic, containing phenocrysts of plagioclase, augite, and olivine or orthopyroxene; these phases are also found in the groundmass. Titanomagnetite is a groundmass phase in most lavas but it appears to be absent in some. A sub-calcic augite is found in the groundmass in some of the basic lavas. Orthopyroxenes are present only in the salic lavas and show an increase in calcium with increasing iron. The range in composition shown by both phenocryst and groundmass plagioclase is very similar except that the phenocrysts extend to slightly more calcic compositions. The residual glasses in many of the lavas have a rhyolitic composition. However, only those from the Shasta andesites have normative salic constituents that plot near the ternary minimum in the Ab-Or-Qtz system at 500 bars. Both chemical and mineralogical data allow the lavas of the different centers to be distinguished from one another. The most likely origin for the orogenic lavas of the Cascades is by partial melting of the upper mantle.

Quaternary lavas from the southern Cascades, western U.S.A.

St. Pierre, Martinique, was destroyed by ash-cloud surges on May 8 and 20, 1902, that developed from the tops of block and ash flows derived from Mount Pelee. The dome was small during these eruptions, and eyewitness accounts indicate that the eruptive sequence started with vertical eruption columns followed by pyroclastic flows. The flows were topographically controlled and moved down the valley of the Riviere Blanche. Their associated ash clouds expanded to several times the width of the associated flows, and it was these expanding ash clouds that overwhelmed St. Pierre on May 8 and 20. It is our conclusion that the early nuees ardentes of the 1902 eruption of Mount Pelee were formed by column collapse into the crater and not, as commonly stated, by dome collapse or directed blast. The resultant mass poured through a cleft in the southwest side of Pelee, thereby heading the flows in that direction. It was only the later nuees ardentes that appear to have been directly affected by the presence of a dome.

Alan L. Smith

Papers

A working terminology of pyroc lstic deposits

Silica activity in igneous rocks

History and tectonic setting of Caribbean magmatism

Quaternary lavas from the southern Cascades, western U.S.A.

Destruction of St. Pierre, Martinique, by ash-cloud surges, May 8 and 20, 1902