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

SUMMARY Plate motions relative to the hotspots over the past 4 to 7 Myr are investigated with a goal of determining the shortest time interval over which reliable volcanic propagation rates and segment trends can be estimated. The rate and trend uncertainties are objectively determined from the dispersion of volcano age and of volcano location and are used to test the mutual consistency of the trends and rates. Ten hotspot data sets are constructed from overlapping time intervals with various durations and starting times. Our preferred hotspot data set, HS3, consists of two volcanic propagation rates and eleven segment trends from four plates. It averages plate motion over the past ≈5.8 Myr, which is almost twice the length of time (3.2 Myr) over which the NUVEL-1A global set of relative plate angular velocities is estimated. HS3-NUVEL1A, our preferred set of angular velocities of 15 plates relative to the hotspots, was constructed from the HS3 data set while constraining the relative plate angular velocities to consistency with NUVEL-1A. No hotspots are in significant relative motion, but the 95 per cent confidence limit on motion is typically ±20 to ±40 km Myr −1 and ranges up to ±145 km Myr −1 . The uncertainties of the new angular velocities of plates relative to the hotspots are smaller than those of previously published HS2-NUVEL1 (Gripp & Gordon 1990), while being averaged over a shorter and much more uniform time interval. Nine of the fourteen HS2-NUVEL1 angular velocities lie outside the 95 per cent confidence region of the corresponding HS3NUVEL1A angular velocity, while all fourteen of the HS3-NUVEL1A angular velocities lie inside the 95 per cent confidence region of the corresponding HS2-NUVEL1 angular velocity. The HS2-NUVEL1 Pacific Plate angular velocity lies inside the 95 per cent confidence region of the HS3-NUVEL1A Pacific Plate angular velocity, but the 0 to 3 Ma Pacific Plate angular velocity of Wessel & Kroenke (1997) lies far outside the confidence region. We show that the change in trend of the Hawaiian hotspot over the past 2 to 3 Myr has no counterpart on other chains and therefore provides no basis for inferring a change in Pacific Plate motion relative to global hotspots. The current angular velocity of the Pacific Plate can be shown to differ from the average over the past 47 Myr in rate but not in orientation, with the current rotation being about 50 per cent faster (1.06 ± 0.10 deg Myr −1 ) than the average (0.70 deg Myr −1 ) since the 47-Myr-old bend in the Hawaiian‐Emperor chain.

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Young tracks of hotspots and current plate velocities

During the quadrennial term 1979–1982, major advances have been made in our knowledge of the rheology of the oceanic lithosphere by the skillful combination of experimental and theoretical rock mechanics, seismology and marine geophysics in increasingly sophisticated models for the flexure of the oceanic lithosphere at seamounts and island chains, along transform faults, and at subduction zones. The relative simplicity of plate bending geometry, thermal history, and mineralogical and chemical compositions of the oceanic plates in these settings make the geophysical observations very powerful constraints on the in situ rheology of the oceanic lithosphere. In the first part of this paper, I review the laboratory work on materials appropriate to the oceanic lithosphere with emphasis on contributions during the quadrennial period and the need for future work. The important results of flexure models incorporating realistic material properties are then summarized.

Rheology of the lithosphere

The ubiquity of dykes in the Earth's crust is evidence that the transport of magma by fluid-induced fracture of the lithosphere is an important phenomenon. Magma fracture transports melt vertically from regions of production in the mantle to surface eruptions or near-surface magma chambers and then laterally from the magma chambers in dykes and sills. In order to investigate the mechanics of magma fracture, the driving and resisting pressures in a propagating dyke are estimated and the dominant physical balances between these pressures are described. It is shown that the transport of magma in feeder dykes is characterized by a local balance between buoyancy forces and viscous pressure drop, that elastic forces play a secondary role except near the dyke tip and that the influence of the fracture resistance of crustal rocks on dyke propagation is negligible. The local nature of the force balance implies that the local density difference controls the height of magma ascent rather than the total hydrostatic head and hence that magma is emplaced at its level of neutral buoyancy (LNB) in the crust. There is a small overshoot beyond this level which is calculated to be typically a few kilometres. Magma accumulating at the LNB will be intruded in lateral dykes and sills which are directed along the LNB by buoyancy forces since the magma is in gravitational equilibrium at this level. Laboratory analogue experiments demonstrate the physical principle of buoyancy-controlled propagation to and along the LNB. The equations governing the dynamics of magma fracture are solved for the cases of lithospheric ascent and of lateral intrusion. Volatiles are predicted to be exsolved from the melt at the tips of extending fractures due to the generation of low pressures by viscous flow into the tip. Chilling of magma at the edges of a dyke inhibits cross-stream propagation and concentrates the downstream flow into a wider dyke. The family of theoretical solutions in different geometries provides simple models which describe the relation between the elastic and fluid-mechanical phenomena and from which the lengths, widths and rates of propagation can be calculated. The predicted dimensions are in broad agreement with geological observations.

Fluid‐mechanical models of crack propagation and their application to magma transport in dykes

This textbook provides a basic understanding of the formative processes of igneous and metamorphic rock through quantitative applications of simple physical and chemical principles. The book encourages a deeper comprehension of the subject by explaining the petrologic principles rather than simply presenting the student with petrologic facts and terminology. Assuming knowledge of only introductory college-level courses in physics, chemistry, and calculus, it lucidly outlines mathematical derivations fully and at an elementary level, and is ideal for intermediate and advanced courses in igneous and metamorphic petrology. The end-of-chapter quantitative problem sets facilitate student learning by working through simple applications. They also introduce several widely-used thermodynamic software programs for calculating igneous and metamorphic phase equilibria and image analysis software. With over 350 illustrations, this revised edition contains valuable new material on the structure of the Earth's mantle and core, the properties and behaviour of magmas, recent results from satellite imaging, and more.

Principles of igneous and metamorphic petrology

Interpretation of abundant seismic data suggests that Kilauea's primary conduit within the upper mantle is concentrically zoned to about 34-km depth. This zoned structure is inferred to contain a central core region of relatively higher permeability, surrounded by numerous dikes that are in intermittent hydraulic communication with each other and with the central core. During periods of relatively high magma transport, the entire cross section of the conduit is utilized. During periods of relatively low to moderate transport, however, only the central core is active. As the conduit penetrates the oceanic crust and enters the volcanic shield, it simultaneously supplies the deeper sections of the rift zones (6-to 10-km depth) and the roots of the summit reservoir with picritic magma. The rift zones at depth are inferred to be almost wholly molten and to possess a high degree of fluid continuity from Heiheiahulu in the East Rift Zone, 45 km westward through the roots of the summit magma reservoir, and well into the Southwest Rift Zone. Higher in the shield, the subcaldera magma reservoir and the shallow rift zones occupy the 2-to 4-km depth interval. Summit-differentiated olivine tholeiite (ρ ≈ 2.62 g cm−3) is periodically injected laterally along a horizon of neutral buoyancy within the rift zones, where the density of the magma is just balanced by the in situ density of the shield (Ryan, 1987a, b). Deep rift zone intrusions push seaward the deep tectonic blocks of the volcano's south flank. Shallow rift intrusions build a sheeted dike complex, inferred to be in isostatic equilibrium with the higher-density deep rift cores below. General finite element analyses are presented for the deformation and stress fields surrounding such dikes in the horizontal and vertical planes. The dike tip in two and three dimensions is surrounded by a tubular core of tensile (σ1, σ2) and shear stress (τmax). The displacement field is characterized by counterrotating cells on either side of the dike tip which, in vertical orientation, produce the characteristic subsidence above the dike complex, with uplift on either side, forming a ridge-trough-ridge structure. A finite element model of Kilauea's shield computes the displacement fields and principal stress (σ1) distributions resulting from intrusive activity on each or both of the rift zones. Within the summit region, tensile stress lobes produced by the three-dimensional upward extension of the intrusions superpose constructively to produce calderawide regimes of tensile stress, conducive to caldera development. Parametric studies of (1) intrusion in the East Rift Zone only, (2) intrusion in the Southwest Rift Zone only, and (3) intrusion in both rift zones demonstrate their unique kinematic contributions. For case 1, the caldera undergoes a counterclockwise rotation (torque up state) conducive to the development of rightstepping en echelon eruptive fissures, as exemplified by the August 14, 1971, eruption. For case 2, the caldera undergoes a clockwise rotation (torque down state) conducive to the development of left-stepping eruptive fissures, as occurred during the December 31, 1974, eruption. For case 3, the caldera substructure is driven due southward, producing the southward migration of the upper portions of the summit magma reservoir.

The Mechanics and Three‐Dimensional Internal Structure of Active Magmatic Systems: Kilauea Volcano, Hawaii

We report the results of modeling the three-dimensional internal structure of Kilauea's magmatic passageways The approach uses a clear plexiglass model containing equally-spaced levels upon which well-located seismic hypocenters are plotted Application of constraining geologic and geophysical criteria to this distributed volume of earthquakes permits the interpretation of seismic structures produced by fracturing in response to locally high fluid pressures Four magma transport and storage structures have been identified within and beneath Kilauea: (1) Primary conduit The conduit transporting magma into Kilauea's summit storage reservoir rises from the model base (146 km) to the 65 km depth level It is a zone of intense fracturing and inferred intrusion, whose horizontal sections are elliptical in planform Over its height, the average major axis of the component horizontal sections is 33 km, with an average minor axis of 17 km This yields an aspect ratio of ξ = 052 At the 146 km level, the strike of the major axis is N67°E During passage from the upper mantle through the oceanic crust, this axis rotates in a right-handed sense, until the strike is N41°W at the 65 km level (2) Magma chamber complex floor The interval from 65 to 57 km, immediately over the primary conduit, is aseismic This suggests differentially high fluid-to-rock ratios, and relatively weak pathways for further vertical transport into higher levels of the storage complex, as well as lateral leakage eastward into the Mauna Ulu staging area—for later vertical ascent beneath the upper east rift zone Seismicity within the immediately subjacent rocks that form the top of the primary conduit (at 65 km) suggests that this inferred magma-rich horizon forms the effective floor of the summit storage complex (3) Magma chamber crown Intense seismicity over the 11–19 km depth interval defines an elliptical region in plan view The top of this region has a broad apex with an average major axis of 15 km, and an average minor axis of 11 km producing an aspect ratio of ξ = 073 This region coincides with the epicentral position of summit vertical displacement maxima during inflationary deformation and is interpreted as a region of intense diking, crowning the summit storage complex (4) Upper east rift zone pipe From a depth of 57 km, a cylindrical region of seismicity rises beneath the upper east rift zone, to the 19 km level, where it merges with the subhorizontal upper east rift zone duct This pipe-like zone has a mean diameter of 14 km and a vertical axis that pierces the surface of the volcano at the intersection of the Koae fracture system and the upper east rift zone We suggest this pipe forms a principal connection between the base of the summit storage reservoir, and near-surface storage compartments and ducts in the upper east rift zone In this role, the pipe is suggested to have contributed heavily to Mauna Ulu's magma supply during 1969–1974 The model of magma transport and storage thus constructed provides a context in which other types of data (eg, ground deformation and electrical conductivity) may be interpreted as well as a means of refining petrological inferences based on lava chemistry

Modeling the three-dimensional structure of macroscopic magma transport systems: Application to Kilauea Volcano, Hawaii

The glass transition has been experimentally detected in basalt as (1) an increase in the aggregate linear thermal expansion coefficient αL, (2) an abrupt change in the temperature dependence of Young's modulus dE/dT, and (3) a change in stress relaxation behavior that effectively separates the T> TG and T TG. Collectively, the mechanical results suggest that for Hawaiian olivine tholeiite at 1-atm pressure, the principal material responses are (1) elastic (T ≤ 600°C), (2) reduced creep (600 980°C). Fracture surface morphologies developed during solidification suggest that the presence of the supercooled melt grain boundary phase may participate in the regulation of the thermal cracking process. Well-preserved fracture surfaces formed by incremental crack growth are found to be covered with striations that correspond to the inferred sequential stopping positions of the advancing fracture front. These striae may be rationalized in terms of experimental analogues that have been produced in viscoelastic polymers by cyclic tension-tension loading. The fracture surface morphology, mechanical data, and the controlled crack growth analogues suggest that thermal fracture in solidifying basalt is an incremental and cyclic process, involving three steps: (1) the accumulation of elastic strain energy in cooling rock at temperatures below that required for stress relaxation due to viscous flow in the intercrystalline liquid phase, (2) fracture at a ΔT determined primarily by the aggregate thermal expansion coefficient αυ and Young's modulus E, (3) the penetration by the advancing crack tip, of the thermal horizon capable of relaxing stress due to the creep of intercrystalline supercooled melt, producing the rough surface texture associated with the termination of a striation. Further crack growth must now await the migration of the solidus. The cycle then repeats. Striations measured in deep Hawaiian lava lakes have been compared with the crack advance increments expected in the vicinity of the glass transition, based on two tests: (1) thermal gradients measured in Kilauea Iki, combined with the mechanical properties of olivine tholeiite evaluated near TG, and (2) the crack advance required to match the recorded seismic stopping phases for prexisting cracks of the dimensions expected for Kilauea Iki. The observed versus predicted comparisons are (1) 31 versus 36 cm; and (2) 31 versus 30 cm. We envision this incremental crack growth process as contributing to the control on the downward movement of the thermal cracking front—and its associated hydrothermal circulation zone—in the upper portions of solidifying subaerial and submarine ponded basalt.

The glass transition in basalt.

Striae on the fracture surface of columnar joints in basalt may be rationalized in the light of experimental fracture mechanics. Morphologic similarity between experimentally produced and natural fracture surfaces suggests that the striae in basalt were formed during incremental crack advances accompanying cyclic stress buildup and release in the cooling body. Fracture surfaces in a Hawaiian flow (Boiling Pots) are striated by alternating smooth (∼2.5 cm wide) and rough (∼ 1.0 cm wide) zones normal to the column axis, which suggest elastic and nonelastic failure, respectively. By analogy to laboratory studies of cyclically fatigued samples, the rough band is interpreted as representing successive stopping positions of the crack tip during fracture. Seismic studies of thermal cracking in Kilauea Iki lava lake (Hawaii) indicate that thermal fracture in cooling basalt is a discrete event, characterized by a sudden period of crack advance. Comparison between cooling units shows that thin bodies have narrow striae and column faces, while thick bodies have wide striae and column faces. This suggests the importance of relative temperature gradients (that is, cooling rates) in driving the crack advance. Observations of the sense of shear on column faces [as revealed by orientations of small platelets (fracture lances) within striae] permit a kinematic interpretation of polygon development and suggest that purely tensile opening frequently is coupled with antiplane shear during crack propagation. Striations are thus a record of the crack advance in cooling basalt; not only should they provide a new tool for the field geologist, but their interpretation should lay the basis for models that examine the coupling of the thermal and mechanical behavior in subsolidus cooling basalt.

Cyclic fracture mechanisms in cooling basalt

An analytic model has been developed for the prediction of the three-dimensional deformation field generated by the withdrawal of magma from a sill-like storage compartment during an intrusion or eruption cycle. The model is based on the work of Berry and Sales (1961, 1962) and predicts the vertical displacement components over the areal plane. Model parameters are the depth of burial h, the intrusion half width a, the intrusion half length b, the thickness of the magmatic interior at the moment of melt withdrawal tm, and the planform aspect ratio ξ = a/b. The products of the model include areal deformation maps. Systematic variation in model parameters within the context of Kilauea Volcano, Hawaii, have revealed that circular and elliptical deformation patterns result from the collapse of draining rectilinear intrusions at depth. Moreover, the geometric parameters of a storage compartment may interact in complex ways to produce similar deformation patterns. The model has been applied to Kilauea Volcano for three periods of pronounced summit subsidence: (1) 1921–1927 (bracketing the steamblast eruptive phases of 1924); (2) June 1972 to December 1972, and (3) December 1972 to May 1973. Application of the model requires the simultaneous optimization of five predicted deformation features with respect to field measurements and the derivative deformation maps: (1) the vertical displacement maxima; (2) the vertical displacement gradients over the areal plane, (3) the lateral extent of the deformation field, (4) the aspect ratio of the subsidence pattern, and (5) the strike of the major axis of the deformation field. The constrained geometries and volumes of the inferred collapsed storage cavities for each period are (1) 1921–1927: depth ≅ 3 km, a ≅ 1500 m, b ≅ 4500 m, tm ≅ 20 m, V 540×106 m3, (2) June 1972 to December 1972: depth ≅ 3.3 km, a ≅ 600 m, b ≅ 2000 m, tm ≅ 1 m, V ≅ 4.8×106 m3, and (3) December 1972 to May 1973: depth ≅ 2.2 km, a ≅ 500 m, b ≅ 1612 m, tm ≅ 1 m, V ≅ 3.2×106 m3. For 2 and 3, calculated magmatic thicknesses tm happen to be in the range (3.48–0.15 m) of measurements for sill-like bodies in deeply dissected Hawaiian shield volcanoes. The fits obtained between calculated and observed deformation patterns allow quantification of the location, overall dimensions, orientation, and volume of the discrete, still molten, interior of sill-like compartments from which magma is tapped during eruption or intrusion.

Michael P. Ryan

Papers

The Mechanics and Three‐Dimensional Internal Structure of Active Magmatic Systems: Kilauea Volcano, Hawaii

Modeling the three-dimensional structure of macroscopic magma transport systems: Application to Kilauea Volcano, Hawaii

The glass transition in basalt.

Cyclic fracture mechanisms in cooling basalt

Magma reservoir subsidence mechanics: Theoretical summary and application to Kilauea Volcano, Hawaii