Chapter 2—
Pyroclastic Rocks as a Tool to Evaluate Geothermal Systems

Our approach to exploration for geothermal systems in volcanic fields is based primarily on an understanding that the volume and characteristics (both physical and chemical) of pyroclastic rocks (tephra ) are fundamental indicators of the presence, size, and location of a potential hydrothermal system. Fisher and Schmincke (1984) distinguished two primary types of tephra: those produced by expansions of magmatic gases—termed pyroclastic —and those caused by expansions of water from external sources—termed hydroclastic (or hydrovolcanic ). Where we can be certain of the difference, we will use this terminology, but where the distinction is not clear or where both processes are involved in the formation of a tephra sequence, we use pyroclastic in a general sense. In this chapter, we describe important relationships among pyroclastic rocks, their parental magma body, and the potential hydrothermal reservoir in the vicinity of the magma body. Several important issues should be considered.

· The existence of pyroclastic rocks implies that explosive eruptions have occurred. The volume of these rocks can be used to estimate the size of their parental magma chamber. Some of this explosive energy will have had important effects on fracture permeability surrounding the vent.

· Many explosive eruptions and their pyroclastic/hydroclastic products resulted from vaporization of groundwater (hydrovolcanism). This process can indicate both host rock permeability and existence of water in the thermal system below the volcano.

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· For hydrovolcanic (hydroclastic ) tephra, the deposit bedforms, particle types, and vent structures are a function of the thermodynamic state of water during eruption and therefore are indicative of the abundance of meteoric water in the vent area.

· Lithic constituents in tephra deposits can be used to reconstruct the host rock lithology and stratigraphy beneath the volcano, the location of aquifers at depth, and—through secondary mineral assemblages—the thermal regime of the country rock and the composition of hydrothermal fluids at depth.

By using the information gathered from these considerations, it is possible to make an integrated appraisal of tephra deposits and help constrain the existence, location, size, depth, and reservoir character of a potential geothermal system in a volcanic field. Topics involving pyroclastic rocks that were introduced in Chapter 1 will be discussed here with emphasis on their importance to geothermal exploration.

Explosive Eruptions and Geothermal Energy Sources

Pyroclastic rocks are the products of explosive volcanism. Many different types of volcanoes exhibit explosive behavior, as discussed by Fisher and Schmincke (1984). Table 2.1 summarizes the major types of volcanoes and their explosive behavior.

In his review of significant explosive eruptions, Wilson (1980) discussed Plinian, Strombolian, and Vulcanian models (for example, Self et al ., 1979), and showed the relationships among observed kinetics, such as ash ejecta velocity, eruptive plume over-pressure, and volatile content, by using forms of the energy equations explained in Chapter 1 of this book [Eqs. (1-5) and (1-6)].

Figure 2.1 shows an idealized Plinian eruption in which ejecta dynamics are directly related to the fragmenting magma dynamics in the throat of the volcano. The isothermal form of the energy equation is appropriate for Plinian eruptions because most

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pyroclasts are small enough to transmit their thermal energy to expanding gases within the time frame of the eruption.

where n = the weight percent of water in the magma, r = the average density of the solid and gas mixture, p_i and p_f = the initial and final (atmospheric) gas pressures, and u_f is the ejecta velocity at height (h) in the ejecta plume. Other parameters are those defined in Chapter 1 and summarized in Appendix C.

For Strombolian eruptions (Fig. 2.2), ejecta velocities are related to magma gas overpressure by an adiabatic form of the energy equation.

Fig. 2.1
Idealized Plinian eruption conduit and column. This diagram shows magma (cross hatch)
rising up the volcanic conduit, the growth of vesicles (circles) before complete disruption
(dashed line), and the ejection of gas and tephra mixture (stippled) from the vent.
The initial pressure (p_i ) and velocity (u_i ) of the gas and tephra mixture within the vent,
which are primarily functions of the gas content of the magma and the vent radius,
are related to the final pressure (p_f ) and velocity (u_f ) by an isothermal form of the
energy equation [Eq. (2-1)] because the gas draws heat from the entrained tephra and
maintains a nearly constant temperature during expansion. (Adapted from Wilson, 1980.)

where r _a = the air density, g = the ratio of specific heats for the gas, r_i = the vesicle radius before burst, and n @ 0.2 for erupted materials (Blackburn et al ., 1976).

In the Vulcanian mechanism (Fig. 2.3), which applies to eruptions where the expanding gas may be either or both magmatic and hydromagmatic, a motion equation can relate pressure and velocity.

Fig. 2.2
Idealized Strombolian eruption model. Individual
centimeter-to-meter size gas bubbles burst at
the surface of the magma within the vent,
propelling scoria in ballistic trajectories. An
adiabatic form of the energy equation [Eq. (2-2)]
relates ejecta velocities to the initial pressure,
temperature, and radius of the gas bubbles.
(Adapted from Wilson, 1980.)

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where A_v = the vent area, L_p = the plug thickness, p = p_i [x_s /(x_s + y_m )]g, x_s = the thickness of the steam cap for which the ratio x_s /L_p is related to weight fraction water (n) by x_s /L_p = [(r_g RT_i )/P_i ][n/(1-n)], r_g = the steam density, and C_d (the drag coefficient) @ 1, and y_m is the vertical distance over which the rock mass is moved. In Eqs. (2-1) through (2-3), our observations of ejecta velocities allow us to estimate the explosion overpressure, which we can assume is the volatile overpressure (magmatic or hydromagmatic). The thermal energy involved in the explosion (E_t ) is related to the bulk isentropic exponent g = [(C_p + m_f C_m )/(C_v + m_f C_m ] by

where r _b = the bulk density of the erupting mixture of vapor and tephra fragments, C_p and C_v = the heat capacities of the vapor at constant pressure and volume, respectively, C_m = the magma heat capacity, and m_f is the mass fraction of fragments in the mixture of vapor and ash. On the other hand, the kinetic energy (E_k ) of the eruption is some fraction (x _c ) of E_t because not all the available thermal energy is converted to the kinetic energy of cratering and ejection of tephra. The exact value of x_c , often called the thermodynamic efficiency or conversion ratio , is generally <0.1 but can vary over an order of magnitude depending upon eruption circumstances (Wohletz, 1986). E_k can be estimated from observed ejecta velocities (v_e ) as

, but often v_e is not easily measured. In those circumstances, an upper limit (u_sonic ) can be estimated from a gas dynamic sound speed (c_s = [g p/r_b ]^1/2 ) by

The above relationship between thermal energy and estimates of eruption energy

Fig. 2.3
Idealized Vulcanian eruption model, in which
magma (cross hatch) is covered by a steam
pocket of thickness x_s , which is in turn
capped by a plug of solidified lava of
thickness L_p  in a vent of area A_v . An
equation of motion [Eq. (2-3)] relates these
dimensions to the pressure and density of
the gas pocket and acceleration of the
tephra after failure of the lava plug.
(Adapted from Wilson, 1980.)

depends on observations of actual eruptions and their ejecta. In cases where necessary ejecta masses and velocities are unknown but a crater is preserved, it is possible to empirically estimate explosion energy by using explosive-testing analogs for which there is data to relate crater dimensions to explosion energies. Assuming that the cratering efficiency of high explosives is the same (within a factor of 10) as that of volcanic explosions (Wohletz, 1986), crater dimensions scale as the cube-root of explosive energy. Johnson (1971) plotted observed crater radius, depth, and volume with respect to explosive yield, as is shown in Fig. 2.4.

Subsurface Thermal Energy Estimates

The most widely applied estimates for thermal energy in magmatic systems underlying volcanic fields are based on the volume and age of the most recent volcanism associated with these systems. As discussed in Chapter 1, Smith and Shaw

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Fig. 2.4
Scaling crater dimensions and depth of burial to the explosive energy
equivalent of TNT. English units have been used for dimensions to preserve
the original logarithmic scale. For reference, TNT releases about
4.6 MJ/kg of energy, which is about four times the enthalpy released
by cooling 1 kg of magma from 1473 to 273 K. For optimum thermal
conversion efficiencies of 10% (see Fig. 1.21), a ton of erupted magma is
roughly equivalent to 0.025 tons of TNT. Comparison of the plots for
explosions in (a) dry rock and (b) soil indicates that larger craters
typically form in soils.
(Adapted from Johnson, 1971.)

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(1975; 1979), have used this approach in estimating thermal energies of magmatic systems. Volumes are inferred from caldera size, vent distribution, seismic shadows, fracture patterns, topographic uplift, geophysical anomalies, and estimates of silicic ejecta volume. If a volcano produces chemically evolved (nonbasaltic) products—especially those spanning andesite through dacitic and rhyolitic compositions—it is very likely that magma has formed a crustal magma chamber and has differentiated on its path to the surface. Because differentiation is a time-dependent process, evolved compositions can indicate prolonged residence in the crust, during which a significant amount of heat flowed from the magma into crustal rocks. The larger the magma chamber, the larger is the thermal resource, which is a measure of the amount of economically useful energy.

The thermal resource (H_tr ) of a magmatic heat source is proportional to the volume of rock (V_tr ) that exceeds the minimum temperature for economic heat extraction (q_tr )

Table 2.2 summarizes the parameters of Eq. (2-6), which outlines aspects of modeling heat flow from a crustal magma body such as the silicic caldera depicted in Fig. 2.5. The general nature of the function for V_tr in Eq. (2-6) is based on the solution of heat flow in and around the magma body—a calculation that is discussed later in this chapter.

Because numerous petrologic experiments have shown that magma-chamber temperatures range from about 900 to 1200°C, depending upon their composition, it is possible to use heat content data (Bacon, 1977) and magma-chamber volume to calculate thermal energy. Smith and Shaw (1975) based their conclusions about magma-chamber volumes on models of magma and heat transport in the earth's crust, observations of exhumed intrusive bodies, petrologic constraints on the production of evolved magmas, and geophysical studies of active igneous systems. Smith et al . (1978) and Shaw (1985) extended this approach to the study of volume-periodicity relationships for a wide variety of volcanoes; their results, along with those of Crisp (1984) and Wadge (1984), support the basic premise that extruded volumes as well as caldera areas and other geophysical measurements can be related to magma-chamber volumes. For silicic eruptions, conservative estimates of magma-

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chamber volume are ~10 times greater than those for the dense-rock equivalent (DRE) volume of silicic products erupted. For composite cones (discussed in Chapter 7), this ratio of intrusive to extrusive volumes may range from <2 to >10. In the case of basaltic volcanoes, the relationship is uncertain because these volcanoes may not have high-level crustal magma reservoirs.

Pyroclastic Rock Volumes

Pyroclastic rock volumes provide the simplest method of estimating magma-chamber volumes for eruptions of evolved magmas in many localities. Several methods can be used to calculate the volumes of pyroclastic products. Froggatt's (1982) comparison of three types of volume estimations is based on (1) mathematical models of aerial dispersal, (2) field measurements of area and volume vs thickness, and (3) measurements of crystal-to-glass ratios.

Fig. 2.5
Heat flow from a magma body beneath a silicic
caldera is modeled for situations in which the
rock is unsaturated. In such areas, the thermal
resource might be exploited by using the hot
dry rock (HDR) technology described later in
this chapter (Rowley, 1982). The light shading
denotes country rock, and the dark shading
represents caldera fill and outflow rocks
(mostly volcanic).

The first of these volume estimation methods is predicated on the general assumption that pyroclastic deposits exponentially decrease in thickness with distance from the vent if there is no significant ponding of the deposit in topographically low areas (Froggatt, 1982; Pyle, 1989). Measurements of maximum thickness (L_i ) and distance over which the deposit thickness halves (r_h ) are sufficient to characterize the volume of a deposit of circular isopach distribution.

where k_i = [ln (2)]/r_h . For deposits of elliptical distribution, one may assume a constant eccentricity (e_e ) given by e_e = (1-b_e )^1/2 , where b_e = r_y /r_x . For this case, r_h is measured along both the major and minor axes of the ellipse to give r_x and r_y , respectively, and k_i = [ln (2)]/r_y . The volume integral reflects this ratio:

The second method requires many field measurements of thickness for logarithmic plots of isopach area or volume vs thickness. These plots make it possible to extrapolate volumes of deposits for which minimum thicknesses are not exposed in the field area. For each isopach, a minimum volume is found by multiplying its thickness by its mapped area. A sum for all isopachs gives the total volume. Froggatt (1982) found that plots of log-volume vs log thickness were superior for extrapolations.

The third method was proposed by Walker (1980) to estimate eruptive volumes when a significant proportion of ash (<2-mm diameter) has been carried great distances from the vent and therefore cannot be measured in the field. This method is based on the assumptions that all crystals, being

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denser than glass, fall out near the vent and that large pumices show average magmatic ratios for glass to crystals. It is possible to calculate the proportion of vitric ash missing from the deposit by measuring the crystal abundance in both ash and pumices and then determining the difference in enrichment. Walker (1981) suggested, however, that this third method may overestimate the deposit volume.

By recalculating the volumes of volcanic products, including tephra and lavas, to DRE (V_dre@ 0.6 V for tephra and V_dre@ V for lavas) and by assuming that they represent some fraction of the magma-chamber volume (for example, 0.1 for silicic volcanic fields), it is possible to obtain a measurement of the thermal resource described in Eq. (2-6). For instance, Fig. 2.6 depicts a young, silicic pyroclastic deposit for which V = 1.0 km³ . The thermal resource (H_tr ) of the magma chamber (volume = 6.5 km³ ) is shown as a function of the kinetic energy of the eruption that emplaced the deposit. Assuming a conservative 1% recovery of the thermal resource, the potential electrical energy resource for this system is estimated by tapping 250°C fluids from the associated hydrothermal or hot dry rock system (discussed later). About 850 kJ/kg is available from the saturated vapor produced; if one allows for a conservative 14% turbine cycle efficiency for saturated vapor cooled to 50°C, then wells producing ~600 tons/hour would generate ~19 MWe (see Appendix D).

Heat-Flow Calculation

There is one important limitation of the simple thermal resource estimation described above: the volcanic products must be erupted from a crustal magma chamber that is sufficiently young to retain much of its initial heat. This limitation has been studied in detail by Smith and Shaw (1975; 1979) and applied to numerous volcanic fields where the volume and age of underlying magma chambers have been estimated from both geomorphological constraints (for example, caldera size, vent distribution, and volume of silicic pyroclastic deposits) and geophysical anomalies. Thus, for the 1.0-km³ pyroclastic deposit shown in Fig. 2.6, one can apply the cooling calculations of Smith and Shaw (1975) as shown in Fig. 1.5. Assuming that (1) the pyroclastic deposit age reflects the time over which the magma chamber has cooled from solidus temperatures, and (2) the deposit represents about one-tenth of the magma-chamber volume, then it follows that the deposit would have to be younger than ~10,000 yr for exploitable temperatures to exist in and around the magma chamber. This estimate is conservative even if the magma chamber has cooled as a result of hydrothermal convection in roof rocks above the magma chamber. If cooling were solely conductive, the age limit could be extended to nearly 20,000 yr.

In making a detailed estimation of thermal resource (H_tr ), the thermal resource volume function (V_tr ) of Eq. (2-6) can be modeled by heat flow calculations. A first-order model assumes heat flow by conduction only, which requires solution of Fick's second law of diffusion:

for which H = the heat content or enthalpy (which is directly proportional to temperature) and k_t = the rock thermal diffusion coefficient, which can be directionally and spatially dependent. Equation (2-9) can be conveniently solved with an explicit numerical procedure (Appendix E) for a variety of geometric, initial temperature, and diffusivity conditions. An approximation for convective transport is included in the numerical procedure to better estimate heat flow in areas where hydrothermal convection is important. The procedure, given in FORTRAN in Appendix E, can be adapted for personal computers. It solves thermal diffusion in two dimensions for a variety of rocks, geologic structures, and effective x and y diffusion coefficients. The problem

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Fig. 2.6
Thermal resource (total heat contained in a magma body) and tephra volume are related to explosive
energy [1 Megaton (Mt) equivalent] by the conversion efficiency (e_c ) of the magma's thermal
energy to explosive energy (kinetic) during an eruption. For this plot, it is assumed that
the tephra volume of an eruption represents 10% of the magma body volume (Smith, 1979),
the magma density (r ) = 2.5 × 10³  kg/m³ , and the magma body is young enough to have a heat
content (H) = 800 kJ/kg. This example (X) depicts a volcano that recently erupted a 1.0-km³
pyroclastic deposit (at 0.65 km³  DRE) with an explosive energy equivalent of about 24 Mt
(e_c  = 0.077), which represents a magma chamber with a thermal resource (H_tr ) of 1.3 × 10¹⁶  kJ.
Assuming about 1% of the magma chamber's thermal resource can be exploited with ~14%
conversion to electrical energy, a geothermal plant could produce
nearly 19 MWe for 30 yr by either hydrothermal or hot dry rock methods.

for this calculation is set up in a manner similar to that outlined in Eq. (2-6). The results of this calculation give a two-dimensional representation of V_tr for any time after formation of a magma chamber. One should be cautious when using this routine to model measured geothermal gradients; the case described here is considered mathematically ill-posed because solutions may not be unique.

Figure 2.7 shows results of the above heat flow calculation for a cooling, subvolcanic pluton 2.5 km wide and 4 km below the surface. The results are compared for 100 and 200 ka of cooling, with and without a convective zone above the magma chamber. At an age of 100 ka, the two-dimensional thermal resource volume (V_tr ) within the calculated area ranges from 2 to 9 km² (the latter value is for the model with convection). This result is based on a volume of rock with temperatures above 150°C within 3 km of the surface. From Fig. 2.7b, one can see from thermal gradients that V_tr would be slightly greater after 200 ka of heat flow. Although the convection model produces a higher near-surface thermal gradient than the nonconvective model does, the gradient can not be reliably projected to greater depths. Such modeled or measured geothermal gradients are an significant initial step in evaluating the geothermal potential of an area. Figure 2.8 plots several general types of thermal gradients and their general relationship to geothermal potential.

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Fig. 2.7
(a) Results of heat flow calculation for a 2.5-km-wide magma body (dark shading) at a depth
of 4.0 km below a caldera filled and surrounded by volcanic rocks (light shading). This problem is
similar to that outlined in Fig. 2.5. The top plot depicts purely conductive heat flow;
the bottom plot includes the effects of a convective region (dark shading) below one side of
the caldera. The numbers in the grid show rock temperatures (°C) and temperature contours
after 100,000 yr of cooling.

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Fig. 2.7
 (b) Plots of calculated thermal gradients at 100 and 200 ka of
cooling compare conductive and convective gradients for locations 5 km from the caldera
and within the caldera itself. Note the high gradient for convective heat flow in the upper 1.0 km;
if projected to greater depths, this gradient would give false predictions of maximum temperatures.

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Hot Dry Rock Geothermal Energy

Most of the geothermal heat associated with volcanic fields is contained in rocks some distance from zones of formation and fracture permeability. For example, the Valles caldera in New Mexico has an estimated resource base of 8,425 × 10¹⁸ J (Smith and Shaw, 1975); of that resource base, the hydrothermal component is ~90 × 10¹⁸ J. This component represents a great deal of energy, but it is only ~1% of the entire resource base (Brook et al ., 1978). In most geothermal systems associated with volcanic fields, ~95% of the thermal resource is hot dry rock; exceptions are geothermal systems in carbonate rocks where the permeability is high.

The world's very substantive hot dry rock resource can be developed if attempts to create man-made hydrothermal circulation systems are successful. The basic concept involves drilling a hole into a thermal anomaly, fracturing the rock by stimulation techniques, and drilling a second hole into the fractured rock adjacent to the first well (Smith et al ., 1975). Water is circulated down one well, percolates through the mass of hot, fractured rock, and is extracted at high temperatures from the second well. Hot dry rock experiments have been studied in several countries, but the most extensive experiments are being conducted at Fenton Hill, just outside the west rim of the Valles caldera in New Mexico. These experiments were successful with a circulation loop through fractured rock at a depth of 3 km, where the bottomhole temperature is 197°C; present experiments are testing a similar loop at a depth of 5 km in rocks with a temperature of ~320°C. New concepts being explored will develop this source of alternate energy, which is referred to as heat mining (Armstead and Tester, 1987).

If a conventional hydrothermal well penetrates high-temperature zones with no fluids, an attempt should be made to open existing pathways or create new fractures by using stimulation techniques such as pressurizing the well with pumped fluids. If this procedure does not work, a hot dry rock system can be realistically considered: the first well will have provided a great body of data about the geology and thermal regime that can be used to design a manmade geothermal system.

Water/Magma (Hydrovolcanic) Interaction: Field and Laboratory Aspects

Recognition and study of hydrovolcanic features in a volcanic field is an important step in locating and characterizing a potential geothermal resource. These features indicate not only a potential magmatic heat source but also the possible existence of groundwater. Water is generally the dominant volatile constituent in volcanic systems. It is also the chief geothermal "working fluid" because its volume changes, which occur with varying temperature and pressure, produce thermodynamic work. In this context, water is required to transfer thermal energy from the earth to the point of exploitation, whether for direct use or production of electricity. Thus, abundant groundwater is necessary for development of a geothermal resource except in cases of hot dry rock resources, where water is artificially supplied to the thermal reservoir.

Carbon dioxide is another common volatile substance in volcanic systems. Like water, it may interact with magma, but because of its phase relationships, it cannot be considered a condensible gas in most geological environments, and thus its heat-transfer qualities must be addressed separately. The presence of carbon dioxide can greatly alter water/magma interaction and the heat convection to the earth's surface.

In Chapter 1, we introduced hydromagmatism and hydrovolcanism as general terms to describe the physical and chemical

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Fig. 2.8
Temperature-depth diagram depicting several thermal gradients and their corresponding influence
on geothermal gradients at the earth's surface. This diagram shows the range of typically observed
steam fields (hatched) and the near-surface perturbations of geothermal gradients that are caused
by groundwater and aquifers.
(Adapted from Rowley, 1982.)

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processes that develop where magma and magmatic heat interact with ground or surface water in magmatic and volcanic environments, respectively. There are many geologic terms that refer to specific aspects of these processes, such as hydrothermal, phreatic, phreatomagmatic , and hydroclastic (see Glossary, Appendix G). In addition, the text of Fisher and Schmincke (1984) explains in detail various terms that relate to the interaction between water and magma, magmatic heat, and lava. In the following discussions, we will review the aspects of hydrovolcanism that greatly affect development of a geothermal reservoir. Hydrovolcanism, recognized for over a century, has recently been more widely acknowledged in field relationships and as a theoretical basis for interpretation of volcanic activity.

Basic Concept

Initial ideas about the role of ground and surface water in volcanism developed during the last century. These perceptions were formed particularly through observations of unusually explosive periods of Hawaiian volcanism, during which ground-water entered rifts along which normal lava fountaining had occurred (Jaggar, 1949), as well as through examination of fragmental basalts found where lava had entered water (Fuller, 1931). Three well-documented eruptions during the late 1950s and early 1960s brought an increased awareness of hydrovolcanism: Capelihnos, Azores (Tazieff, 1958; Servicos Geologicos de Portugal, 1959), Surtsey, Iceland (Thorarinsson, 1964), and Taal, Philippines (Moore et al ., 1966). Fisher and Waters (1970), Waters and Fisher (1971), and Heiken (1971) expanded the concept of phreatomagmatic eruptions characterized by steam-rich eruption columns, base surges, and typical landforms such as maars, tuff rings, and tuff cones. As a result of this work, numerous 20th century phreatomagmatic eruptions are now recognized—most of them have formed maar-like craters (for example, Self et al ., 1980). We also now realize that after cinder cones, phreatomagmatic vents (tuff rings, tuff cones, and maars) are the most abundant terrestrial volcanic landform.

An interesting paradox has emerged in studies of hydrovolcanism: interaction between magma (lava) and water can be passive, explosive, or even both in situations where all other conditions are apparently the same. This anomaly is illustrated along the southern coast of Hawaii, where in some cases lava flowing into the ocean quenched passively to form pillow lavas and in other cases it was explosively fragmented during quenching to form tephra cones along the beach (Fisher, 1968). Explanations of this paradox have benefited enormously from information derived from analog phenomena such as industrial accidents in which a molten substance such as iron has caused an explosion when it was rapidly introduced to water. This type of situation is a potential safety problem, for example at nuclear reactors (Witte and Cox, 1978). The term commonly used for the industrial analog, fuel-coolant interaction (FCI), can be applied to volcanic processes involving the interaction of two materials, one at a temperature above the boiling point of the other—where the interaction varies from passive quenching and film-boiling circumstances to explosive situations in which the two materials mix and exchange heat at catastrophic rates.

Heiken (1971) studied a number of phreatomagmatic volcanoes in southeastern Oregon and correlated the volcano morphology with abundance and depth of groundwater. As summarized in Table 2.3, characteristic volcanic landforms range from low-profiled tephra rings surrounding a wide crater to steep-sided tephra cones with relatively smaller craters. The former type are termed tuff rings (or maars if the crater extends below the level of the prevolcanic ground surface); the latter type are called tuff cones (Fig. 2.9). Sheridan and Wohletz (1981; 1983a) extended this characterization

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of hydrovolcanic landforms by recognizing that they form parts of polygenetic volcanoes, such as composite cones and calderas in which characteristic tephra accumulations of tuff cones and rings may be found (see Chapter 1).

Of the various types of tephra deposits produced by hydrovolcanism, pyroclastic surge (base surge) deposits are most distinctive (Fisher and Waters, 1970; Wohletz and Sheridan 1979). The four hydroclastic-tephra bedforms illustrated in Fig. 2.10 include (a) breccias formed at the vent by explosions or in distal regions by laharic remobilization, (b) sandwaves that show a variety of dune-like bedding structures ~1 cm thick (Crowe and Fisher, 1973; Schmincke et al ., 1973), (c) massive beds that may resemble small pyroclastic flows, and (d) planar beds. In general, these tephra bedforms are deposited by pyroclastic surges, but fallout and pyroclastic flows also contribute to deposition of hydroclastic tephra. Identification of the depositional mechanisms requires careful examination of features such as those listed in Table 2.4.

Because of the variety of possible textural features found in any hydrovolcanic deposit, it is helpful to characterize the tephra facies described in Table 2.5. Some facies relationships depend on the type of vent structure; for example, facies relationships for pyroclastic surge deposits surrounding monogenetic tuff rings (Wohletz and Sheridan, 1979) include near-vent sandwave facies, massive facies at intermediate distances from the vent, and planar facies at distal portions of the deposit. In contrast, Frazzetta

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et al . (1983) showed that Vulcano, a composite cone with relatively steep slopes, has near-vent planar facies, massive facies on cone slopes, and sandwave facies at distal portions of the deposit at and beyond the base of the cone. In most cases, the positive designation of a tephra facies in hydrovolcanic deposits will require a detailed analysis of bedform textures (Fig. 2.11). Recognition of these facies relationships can help locate a buried or exhumed vent structure, as related by Crisci et al . (1981).

Wet and Dry Facies Relationships

From field observations, we have realized a significant concept about the textural relationships of various hydrovolcanic tephra deposits. Wohletz and Sheridan (1983) discuss in detail the existence of two fundamentally different types of hydrovolcanic tephra deposits: dry and wet. This designation reflects the physical state of the tephra when it is emplaced: dry deposits show little textural evidence of the presence of moisture, and wet deposits show sedimentary, textural, and diagenetic evidence of wet emplacement. Table 2.6 summarizes the field observations that help characterize these two types of deposits.

The significance of wet and dry characterization for hydrovolcanic tephra deposits will become clear during the following discussions of field relationships, theoretical eruption and emplacement models, and the development of hydrothermal systems in country rocks surrounding vent areas.

Fig. 2.9
Hydrovolcanic landform vs geohydrological environment. In unsaturated environments, basaltic
volcanism commonly produces cinder (scoria) cones by eruptions of relatively low energy.
In areas of abundant water, eruptions vaporize the fluid, which results in explosive activity and
the formation of tuff rings and cones. In deep water, extrusions of basalt are passively
quenched and form pillow lavas.
(Adapted from Wohletz and Sheridan, 1983a.)

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Hydrovolcanic eruptions disperse tephra in clouds of steam. Where water is abundant, the expansion of steam occurs in the steam dome (a two-phase region), and an appreciable amount of condensed water is emplaced with the tephra. Where water is less abundant, the steam expands in its superheated region and is more readily separated from tephra during emplacement so the deposits remain relatively dry. Observations of the eruptions of Surtsey volcano illustrate this expansion process (Thorarinsson et al ., 1964). Tephra and high-pressure water vapor were erupted in plumes called "cock's tails" or "cypressoid" jets. The water vapor was not visible until it reached lower pressure after the jets had traveled several hundred meters from the vent. At that point, saturated steam was visible in the jets of tephra, indicating that it condensed in the steam dome. This steam was carried along with the tephra jets until their emplacement on the slopes of the emerging volcano. Some of the water vapor separated earlier from the jets as optically transparent, superheated steam. It later

Fig. 2.10
Four major textural types of hydroclastic deposits
produced by explosive hydrovolcanic eruptions.
Explosion breccias are typical of near-vent
tephra deposits, whereas sandwave (dunes),
massive, and planar bedded tephra deposits are
common to pyroclastic surges and flows (Wohletz
and Sheridan, 1979). Another textural type,
the laharic breccia, forms by liquefaction of these
deposits if there is an abundance of condensed
steam or rainfall.

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became visible as it cooled and condensed in the atmosphere, rising as billowing steam clouds above the jets.

Other observations mentioned by Wohletz and Sheridan (1983) support the hypothesis that the physical state of water/steam during eruption is determined by the mass ratio of water to magma interacting in the vent. This hypothesis has evolved as detailed studies of many hydrovolcanic vents around the world have documented the dependence of eruptive energy, tephra dispersal, and the resulting vent landform on the water:magma mass ratio (summarized earlier in Chapter 1). Figure 2.12 illustrates typical hydrovolcanic bedforms and their deduced water:magma mass ratios.

Through the interpretation of deposits, one can show that many volcanoes demonstrate cyclic eruptive behavior (Chapter 1), in which the water:magma mass ratio varies with time. Sheridan and Wohletz (1983a) noted two trends at many volcanoes. A dry trend, typically found in tuff rings, is indicated by deposits that show a decreasing abundance of interacting water with time so that final eruptions can be entirely magmatic. A wet trend is illustrated by tuff cones in which the initial eruption is magmatic and the final bursts are so wet that tephra form lahars as they are emplaced. Using the information gained from these observations, it is possible to place constraints on both the water:magma ratio during the course of an eruption and the availability of water for potential hydrothermal systems associated with the volcano.

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Fig. 2.11
Pyroclastic surge facies as designated by bedform statistics. Section S-7 represents the sandwave
facies with abundant dune bedforms; U-4 is a massive facies example showing planar, massive, and
dune bedforms; S-1 is an example of planar facies with mostly planar and massive bedforms.
Section U-8 is ambiguous; after detailed analysis of bedform transitions by Markov analysis
(Wohletz and Sheridan, 1979), it is classified as sandwave facies. Bedform types are shown as
P (planar), M (massive), or S (sandwave), as defined in Fig. 2.10. Occurrences of these types are
further numbered from the base of the deposit.
(Adapted from Wohletz and Sheridan, 1979.)

Polygenetic Volcanoes and Calderas

The phenomenon of hydrovolcanism is not associated solely with eruptions at small, monogenetic volcanoes. The following descriptions illustrate the significance of hydrovolcanic processes in (a) wide-spread tephra deposits from silicic calderas, (b) the development of wet and dry cycles at composite cones, (c) the evolution of calderas, and (d) pyroclastic episodes during the eruption of domes of intermediate to silicic composition (see Chapter 5).

Taupo

The Taupo volcanic zone of New Zealand's North Island is one of the best studied examples of silicic volcanism. An important hydrovolcanic feature of this volcanic field is the extremely widespread, fine-grained silicic tephra deposits, especially those from the Taupo volcanic center (Healy, 1962; 1964).

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Self (1983) presented an extensively documented account of the Wairakei eruption (20,000 ka), which produced the Oruanui Pumice Formation (Vucetich and Pullar, 1964) and the Wairakei Breccia, both of which are part of the Wairakei Formation. Self addressed the exceptionally fine grain size, wide dispersal, high content of accretionary lapilli (up to 33 wt%), and irregular thickness distribution—features that Self and Sparks (1978) noted as indicators of silicic, phreatomagmatic (Phreatoplinian ) volcanism. Figure 2.13 illustrates the stratigraphy of the Wairakei Formation, which consists of interbedded, fine-grained pyroclastic fall and flow deposits as well as two main phreatoplinian phases that were followed by ignimbritic phases. Member 1 has a median diameter of 4.0 f (0.064 mm) even near the source and is representative of the typical phreatomagmatic materials shown in Fig. 2.14.

Heiken and Wohletz (1985) described volcanic ash samples and their phreatomagmatic textures from this section. Through interpretation of tephra deposits, Self (1983) illustrated the eruption sequence and phreatomagmatic factors of the Taupo eruption (Fig. 2.15). More detailed descriptions of geothermal studies in the Taupo region are given in Chapter 4.

Vulcano

The Island of Vulcano in the Aeolian archipelago of Italy is a classic example of hydrovolcanic activity. The Fossa cone of Vulcano has been historically active and poses an ongoing hazard (Keller, 1980). Mercalli and Silvestri (1891) observed the most recent eruptive episode and described the eruption phenomena now termed Vulcanian . Frazzetta et al . (1983) built on the work of Sheridan et al . (1981) to interpret the detailed stratigraphy of the cone and show how hydrovolcanism contributed to the five most recent episodes of volcanism; their summary of the Fossa tephra stratigraphy is illustrated in Fig. 2.16. These authors further proposed that all five episodes of volcanism were characterized by a cyclic eruption pattern that consists of the four stages shown in Fig. 2.17.

(1) Initial quiet, fumarolic activity was stimulated by heat transfer from (possibly) two magmas of differing compositions that rose below the volcano.

(2) A triggering event initiated a mixing of the two magmas, which was followed by further rise of the mixed magma to the surface where it contacted ground-water. The resulting hydrovolcanic eruptions of pyroclastic surges

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comprised chilled, nonvesiculated tephra that progressed from wet to dry.

(3) As the groundwater source was separated from the magma by a steam envelope, the eruptions became magmatic, expelling vesiculated tephra interspersed with the chilled tephra.

(4) The cycle's final stage is marked by eruption from the pumiceous cap of the magma and, later, extrusion of an obsidian-cored lava flow. Frazzetta et al . (1983) interpreted the products of the most recent eruptive cycle with respect to water:magma ratios, as shown in Fig. 1.22.

Fig. 2.12
An idealized hydrovolcanic deposit section
illustrating typical bedding textures and
bedforms and their inferred water:magma mass
 ratios (R_m ). Initial eruptions, represented by
the  basal pumice fall, involved little or no
external water; however, in later eruptions,
the stratigraphic section records bedforms
that indicate increasing water:magma ratios.
For ratios >1.0, caused by eruptions into a
standing body of water, pillow lavas/breccias
and peperites are usual, as are lahars, which
commonly occur in eruptions of high
water:magma ratios on land.

Vesuvius

The ejecta deposits of another long-active and much-studied volcano, Vesuvius, indicate that hydrovolcanic activity is significant during its eruptive cycles (Barberi et al., 1981; Rosi and Santacroce, 1983). The AD 79 eruptions of Vesuvius are among its best documented in terms of actual observations (Pliny the Younger, 1763; Radice, 1972), deposit descriptions (Sigurdsson et al ., 1985), and interpretations of eruption mechanisms (Sheridan et al ., 1981). Figure 2.18 shows representative tephra stratigraphic sections from archaeological excavations at three Roman sites that were devastated by

Fig. 2.13
Wairakei Formation tephra stratigraphy for
locations within 20 km of the vent in Lake
Taupo, New Zealand. Members 4 and 6 (m4,m6)
were previously named the Oruanui Pumice
Breccia and Wairakei Breccia, respectively.
(Adapted from Self, 1983.)

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Fig. 2.14
Grain-size characteristics of the Wairakei Formation (Self, 1983). (a)Median diameter (Md_{f )} ) vs sorting
coefficient (s_f ) is shown for the various members (m1,m2,..) illustrated in Fig. 2.13; also noted are
textural types, including accretionary lapilli (crushed), lithic/pumice-rich ignimbrite, and base surge.
The dashed field represents pyroclastic flows. (Adapted from Wright  et al ., 1981.) (b) Grain-size
fractions for m4 and m6: the dashed field represents pyroclastic flows; coarse variant shown by
symbols. (Adapted from Walker et al., 1980.) (c) Grain diameter frequency curves for fallout products
of m2 and m6 show gradual loss of coarse products with increasing distances from the source
(curve numbers in kilometers). (d) Cumulative probability distribution of size fractions (f ) for Plinian
and phreatoplinian deposits is compared to the distribution of a representative m3 sample.
(Adapted from Carey and Sigurdsson, 1982, and Walker, 1981.)

the eruptions. Fallout deposits of white and gray pumice from early magmatic eruptions were followed by hydromagmatic products emplaced as surges, pyroclastic flows, and lahars—all containing abundant lithic ejecta derived from carbonate aquifer rocks that underline the Somma Vesuvius at a >2-km depth. Figure 2.19, the model presented by Sheridan et al . (1981), interprets the stratigraphy and illustrates the effects of hydrovolcanic activity during the devastating phases of the eruption. Accretionary lapilli, abundant in the upper portions of the tephra stratigraphy, were studied in detail by

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Fig. 2.15
Wairakei eruption model showing the sequential stages or eruption of the various
members and periods of lake water/magma interaction.
(Adapted from Self, 1983.)

Sheridan and Wohletz (1983b), who described possible mechanisms for their formation in wet eruption plumes.

Contrasting hydrovolcanic behavior is evident in the early-stage interaction with water at Vulcano and the late-stage interaction shown at Vesuvius. One general explanation for this contrast is the overall hydrologic setting of these volcanoes: Vulcano is an island edifice characterized by abundant near-surface groundwater, whereas Vesuvius is built on a sedimentary platform with a deep aquifer system. Access of water to the vent system at Vulcano gradually decreases during eruptive episodes as magma congeals along vent walls where water initially infiltrates. At Vesuvius, access of groundwater to the magma chamber and vent conduit is initially limited by thermal metamorphic rocks that have sealed fractures. However, as the conduit and chamber wall rocks are fractured by expansion of magmatic gases early in Plinian eruptive episodes, groundwater gains access to the magma, especially after overpressures in the magma body and conduit have fallen below the local thermally perturbed hydrostatic

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Fig. 2.16
Composite stratigraphic section illustrates
the hydrovolcanic cycles of the Fossa volcano
at Vulcano, Italy. The Pietre Nere, Palizzi,
Commenda, and Pietre Cotte cycles all show
a progression from hydrovolcanic eruptions to
emplacement of lava flows.
(Adapted from Frazzetta et al ., 1983.)

pressure. The behaviors exhibited at Vulcano and Vesuvius are generally termed shallow and deep hydrovolcanic eruptions, respectively; the former becomes dryer and the latter becomes wetter as eruptions progress.

Throughout the entire Latium volcanic province of Italy, hydrovolcanism has been a vital component in the development of caldera complexes such as those of Vulsini, Vico, Sabatini, Albani, and the Phlegraen Fields. Broad, low-profile calderas with widespread, fine-grained silicic tephra characterize these volcanic areas. Because of their geothermal importance, we will describe them in detail in Chapter 4.

Petrography of Hydrovolcanic Tephra Constituents

Hydrovolcanic tephra may show aspects of both magmatic and hydrovolcanic origin; in such cases, petrographic inspection is necessary to determine the relative proportions of the two endmember processes. Fisher and Schmincke (1984) used the terms pyroclastic and hydroclastic to distinguish products of magmatic and hydrovolcanic explosions, respectively. Table 2.7 reviews the salient features of hydroclastic products.

Hydroclastic tephra are generally distinguished from pyroclastic tephra by their fine grain size. However, this distinction is not always apparent, especially in hydroclastic tephra sampled at near-vent locations where fine fractions have not been deposited. Figure 2.20 shows plots of sorting vs median diameter for four characteristic tephra bedforms produced by hydrovolcanic activity. Although these statistics are often

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Fig. 2.17
This schematic model of typical Vulcanian eruption cycles at Vulcano is based upon interpretation of
stratigraphic successions shown in Fig. 2.14. Activity progresses from (a) quiet fumarolic emissions to
(b) magma vesiculation and surge eruptions caused by primitive magma intruding into older evolved
magma and interaction with groundwater. (c) The development of a steam chimney above the magma
reduces direct contact between water and the melt; steam explosions eject comminuted older lavas and
some pumice, producing surge and fallout deposits. (d) The final stage is marked by eruption of a
pumice fall and emplacement of a lava flow from the chilled zone of the magma body.
(Adapted from Frazzetta et al ., 1983.)

sufficient to characterize hydroclastic tephra, we advocate further analysis of size distributions by the techniques described by Sheridan et al . (1987) to separate subpopulations from the overall sample distribution. This method involves the detailed analysis of wet and dry sieve data and sample separation procedures described in Appendix A.

Constituents of hydroclastic tephra, including glass, crystals, and lithic fragments in various proportions, are sensitive to the emplacement mechanism and magma composition. Figure 2.21 illustrates the variety of tephra constituents that characterize tuff rings and tuff cones. One of the most distinguishing features of these tephra is the amount of glass alteration in samples of wet and dry hydrovolcanic facies. Basaltic glass readily alters to palagonite, a complex combination of zeolites and smectites; rhyolitic glass alters to hydrated glass, which can crystallize to fine-grained quartz, potash feldspar, and clays. Although such alteration generally occurs in any tephra deposit through weathering and diagenetic processes, stratigraphic

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Fig. 2.18
Representative stratigraphy of AD 79 pyroclastic deposits exposed in archaeological excavations
along the coastal side of Vesuvius; FA = pumice fallout, FL = pyroclastic flows, and S = surges.
The basal white and gray pumice fallout was from early magmatic eruptions, and the upper
pyroclastic flows and surges are products of later hydrovolcanic eruptions.
(Adapted from Sheridan et al ., 1981.)

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Fig. 2.19
Model of AD 79 Plinian eruptions at Vesuvius. This model, temporally and phenomenologically
constrained by accounts of Pliny the Younger (Radice, 1972), shows (a) the initial Plinian column
eruption, (b) the decline to intermittent magmatic and hydromagmatic explosions, and (c) the
terminal hydromagmatic phase that produced wet pyroclastic flows and surges. The beginning
of hydromagmatism, during the intermediate stage, is associated with the failure of magma
chamber walls, which added a thermally metamorphosed lithic constituent to the tephra and
allowed aquifer waters to flow into the chamber.
(Adapted from Sheridan et al ., 1981.)

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information supports the conclusion that the alteration can also result when abundant hot water vapor is emplaced with the deposit.

Weathering and diagenetic effects, including the posteruptive saturation of tephra deposits by rain or groundwater, make it difficult to evaluate the timing of palagonitization and hydration; however, pertinent stratigraphic information can be useful (Fig. 2.22). Where fresh and altered tephra appear in alternating layers above the groundwater table, a strong argument can be made that alteration took place at the time of tephra emplacement. Proximity of altered tephra to a vent or fault is indicative of postemplacement alteration by hydrothermal fluids. Diagenesis below the groundwater table can be assessed for a region by determining the lateral extent of altered tephra and the presence of alteration zones that cross bedding planes.

Wet deposits can be distinguished from dry ones by the degree of glass alteration. Figure 2.23 shows that palagonitization of basaltic tephra is a function of median grain size, but for diameters <0.1 mm, palagonitization is most prevalent in samples from wet facies bedforms. This observation is not surprising if one considers the results of experiments with palagonite formation that demonstrate a strong dependence on temperature (Fig. 2.24a). Palagonitization also has a significant effect on glass chemistry; bulk chemical analysis of partly palagonitized tephra may show that its composition is considerably different than that of its parent (Fig. 2.24b).

Analyses of clast morphology by optical and electron microscope also provide important data for classifying tephra as pyroclastic or hydroclastic (Heiken, 1971; Heiken and Wohletz, 1985). Table 2.8 summarizes clast morphologies that are useful in understanding the eruptive mechanism (grain shape), transport or emplacement process (edge modification), and water abundance (clast alteration/palagonitization). Wohletz (1987) described these features for several examples of hydrovolcanic associations.

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Fig. 2.20
Grain sizes of hydrovolcanic tephra deposits of different bedding textures are shown by plots of
sorting coefficient (s_f ) vs  median diameter (Md_f ). Whereas pyroclastic surge bedforms (sandwave,
planar, and massive) range in median diameter from 2.0 to 0.063 mm, fine-ash beds demonstrate
the intense tephra fragmentation capability of hydrovolcanism with median
diameters of 0.063 to 0.022 mm.
(Adapted from Sheridan and Wohletz, 1983a.)

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Fig. 2.21
This triangular diagram of hydrovolcanic tephra
constituents shows the relative contribution of
fresh glass, altered glass, and crystal and lithic
material. Fields for tuff rings and cones reflect
the relative proportions of these constituents in
different bedforms. The greater relative
abundance of altered glass for tuff cones
attests to the greater abundance of water in
the erupting system.

Fig. 2.22
Example of stratigraphic and structural settings for altered (palagonitized and hydrated) tephra
deposits. (a) Altered tephra (cross-hatched) may exist around a vent area as a result of hydrothermal
circulation. Such alteration is relatively insensitive to tephra bedding planes, but it does not show
lateral continuity away from the vent. (b) Palagonitization and zeolitization below a groundwater
table show lateral continuity and may cross bedding planes between tephra of different
depositional character. (c) Alteration may be structurally controlled along faults through which
hydrothermal fluids have migrated. (d) However, when tephra alteration occurs rapidly during
eruption and emplacement and before cooling, the altered tephra may be intercalated with
relatively fresh tephra layers. This alteration is relatively insensitive to
the groundwater table and initial dips of the strata.

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Experimental and Theoretical Aspects of Hydrovolcanism

Much of our qualitative and quantitative understanding of hydrovolcanic processes has developed from experimental and theoretical studies of the water/magma interaction mechanism. As a brief review, we summarize several studies that are applicable to geothermal energy exploration.

Results from Experiments

Water/magma interaction belongs to a broad class of physical and chemical processes termed fuel-coolant interaction (FCI). Our research has focused on applications of FCI theory to water/magma interactions, and we describe results of our experimental studies that bear upon interpretation of hydrovolcanic products.

In their experiments, Wohletz and McQueen (1984) and Sheridan and Wohletz (1983a) used thermite as a basaltic magma analog because it readily fit experimental requirements. The thermite reaction (Fe₃ O₄ + 8/3Al « 4/3Al₂ O₃ + 3Fe + heat) produces a molten mixture of crystals and liquid at temperatures in excess of 1000°C; the viscosity and density are similar to that of basaltic magma. The molten thermite was brought into contact with water within several different pressure vessels that were constructed in such a way that variations of

Fig. 2.23
Percent of glass palagonitized vs median grain size for hydroclastic tephra. Trends are shown for
bedforms in both tuff rings and cones. In general, there is a decrease in palagonitization with
decreasing grain size, except in the case of massive and planar bedforms in tuff rings. This trend
reflects the decrease in porosity as a function of grain size; however, anomalous tuff ring samples
point to the likelihood that massive and planar bedforms are typical of wetter eruptions.

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pressure, temperature, and interaction energy (Buxton and Benedict, 1989) could be quantified (Fig. 2.25).

The pulsating ejection of fragmental debris, which ranged from passive to explosive, was studied for a variety of water:thermite mass ratios, interaction pressures, and contact geometry. Figure 2.26 summarizes these experiments, which could be interpreted as analogs to volcanic activity. One interesting observation was that the water:magma mass ratio was a dominating factor of the interaction phenomena. By quantifying the energy of the interaction as a ratio of measured mechanical energy to initial thermal energy (Fig. 1.21), Wohletz and McQueen (1984) developed Fig. 2.27 to summarize the spectrum of hydrovolcanic activity.

Fig. 2.24
(a) Thickness of palagonite skin on basaltic glass
samples as a function of alteration time at
different temperatures. The rapid increase in
alteration with temperature argues that at high
temperatures (several hundred degrees), glass
alteration to depths of several micrometers may
take place in minutes or less.
(Adapted from Furnes, 1975, and Moore, 1966.)
(b) Chemical variations between basaltic
glass and palagonite samples are normalized
to titanium accumulation. Dashed lines
indicate idealized chemical losses expected from
passive gain of TiO₂ , which increases with
palagonite maturation. Data for glass/palagonite
pairs from submarine alteration (

) and subaerial
conditions () suggest a nearly isomolar
exchange of major element oxides
with H₂ O and K₂ O.

Grain sizes of fragmental debris from these experiments show a strong relationship to explosive energy: with more efficient interaction between water and melt, finer explosion debris (experimental tephra) is produced (Fig. 2.28). By assuming simple conductive heat transfer between the melt and water, it is possible to make some interesting predictions about hydrovolcanic activity. Figure 2.29 shows the quenching time for tephra as a function of median diameter. By assuming that conductive heat transfer in these experiments reflects the more complicated process that occurs in nature, one may infer from hydrovolcanic bedforms some aspects of the energetics of eruptions that produced the tephra. For example, tephra deposited as sandwave

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beds likely resulted from more explosive interactions than those that produced other bedforms.

Size and shape studies of experimentally produced tephra have also provided some insight into the mechanisms by which magma and water come into close contact—a necessary condition for the explosive exchange of thermal energy. Wohletz (1983) used inferences from grain-shape analysis to describe some of these mechanisms, many of which are driven by dynamic instabilities that grow at interfaces between the magma and water. These instabilities develop from differences in density, surface tension, viscosity, and the relative velocity of the water and magma. Growing instabilities, caused by rapidly fluctuating steam-film jackets at the water/magma interface, mix the two and gradually fragment the magma. This quasistable mechanism increases the contact surface area between magma and water, and the subsequent heat transfer is enhanced to rates that can sustain an explosion.

Some of the characteristic grain shapes of experimental tephra shown in Fig. 2.30, including blocky shapes, irregular and convoluted fluidal shapes, spheres, ribbons, and shell-like shards, can be used to interpret interaction and mixing mechanisms.

Because chemical alteration of tephra is a characteristic feature of hydroclastic products, Taylor and Wohletz (1985) conducted experiments to investigate the chemical processes in hydrovolcanism. An interesting but perhaps not surprising aspect of these experiments concerned oxygen isotope exchanges. Like magma, thermite is relatively rich in heavy oxygen (d¹⁸ O @ 16⁰ /₀₀ ). During interactions between thermite and water typical of the meteoric composition of groundwater (d¹⁸ O @ -12⁰ /₀₀ ), Taylor and Wohletz expected that some exchange of the oxygen isotopes would deplete the ¹⁸ O composition of the experimental tephra (based on previously measured diffusion constants of 10^-4 to 10^-9 cm² /s); however, results (shown in Fig. 2.31) revealed considerable depletion of ¹⁸ O. These results indicated an exchange of up to 30% of the oxygen in the thermite—a very dynamic chemical reaction considering the length of the experiments (several seconds or less).

As discussed by Heiken and Wohletz (1987), enhanced oxygen isotope exchange can be expected for water/magma interactions in which the surface area of the magma is increased by many orders of magnitude. The behavior of oxygen suggests that other ionic species may also diffuse at effectively high rates, rapidly altering the chemical composition of finely fragmented magma during a

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Fig. 2.25
Five experimental designs were used by Wohletz and McQueen (1984) to simulate hydrovolcanic
activity with a thermite (Al₂ O₃  + Fe) magma analog: (a) sand burial, (b) confinement, (c) water box,
(d) central vent, and (e) bottom vent (lift-off). The basic design promoted contact of molten thermite
with water within a confined vessel after the thermite melted through the aluminum partition that
initially separated the two. A burst valve, designed to fail when pressure exceeded a specified limit,
allowed venting of the high-pressure steam and fragmented thermite. Pressure transducers recorded
vapor production in the vessel, and high-speed cinematography documented
the ejection of fragmented melt through the vent.

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Fig. 2.26
In this summary of hydrovolcanic experiments, four basic interaction phenomena, consisting of melt
fountaining, unsteady blasts, steady production of steam and ejecta, and the nonexplosive quenching of
melt into globular shapes (blobs), are correlated to volcanic activities and the water:melt mass ratio (R_m ).
(Adapted from Wohletz and McQueen, 1984.)

hydrovolcanic eruption and thereby producing altered tephra deposits. Studies by Hildreth et al . (1984) and Lipman and Friedman (1975) documented such behavior in large silicic systems during caldera-related eruptions. Smith (1988) found that fresh, pumiceous samples of postcollapse rhyolite of the Long Valley caldera, California, show d¹⁸ O @ 0⁰ /₀₀ , in contrast to +6.7 to +7.4⁰ /₀₀ values for obsidian, which are typical of most unaltered volcanic rocks. This result indicates about a 33% exchange of oxygen between meteoric water and the rhyolite in the formation of pumice—a conclusion supported by field evidence of a gas-rich and relatively low-viscosity extrusion. A conclusive piece of evidence for the hydrovolcanic origin of tephra is their oxygen composition if they are not affected by weathering and diagenesis.

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Fig. 2.27
Scaled kinetic energy relative to the initial melt thermal energy is shown as a function of
water:magma mass ratio. Ranges are indicated for Strombolian, Surtseyan (hydrovolcanic), and
submarine activity as well as for corresponding landform and deposit bedforms.
(Adapted from Wohletz and McQueen, 1984.)

Predictions Based on Theory

It is evident from our experiment results that one can employ theoretical physics to make accurate predictions for hydrovolcanic explosions (for example, Buchanan, 1974). One prediction that is strongly supported by the energy measurements shown in Fig. 1.21 is the relationship of explosive energy to water:magma mass ratios. In Chapter 1, we outlined a method for quantifying explosive energy that is based on thermodynamics: the method assumes that magma and water reach thermal equilibrium before explosive expansion of the water. By using a temperature-entropy diagram (Fig. 2.32), one finds that—depending upon the temperature and entropy of the initial equilibrium point—expansion of water can follow one of several thermodynamic paths. The most complex of these paths occurs during its expansion, when water maintains a temperature similar to that of the hot magma fragments. In this case, the simple isentropic expansion of water is not followed; instead expansion has a strong isothermal component that is determined by the mass ratio of magma fragments entrained and in thermal contact with the water during expansion.

As is shown in Fig. 2.32, expansion of a high-pressure mixture of water and magma may take place in the steam dome, the

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Fig. 2.28
Log efficiency (the ratio of steam mechanical energy to melt thermal energy) as a function of the
median grain diameter in fragmented melt. Small-scale (several grams of melt) laboratory
experiments (

) from Buxton and Benedict (1979) exhibited lower efficiency [heat flux (H_q )]
and coarser grain sizes than large-scale (100 kg of melt) experiments (hatched) performed
by Wohletz and McQueen (1984). Data fall within theoretical ranges of heat flux to steam from
thermite melts (bold lines). Maximum measured laboratory heat fluxes (Buchanan, 1974) indicate
resulting grain diameters between 0.125 and 0.004 mm.

Fig. 2.29
Log reciprocal cooling time vs  grain diameter
and log specific surface area. The shaded area
represents times predicted by conductive cooling
models; the circular fields show ranges of median
grain diameters for common hydrovolcanic
bedforms: F = fallout, P = planar, M = massive,
and S = sandwaves. Median grain diameters for
magmatic eruptions are commonly in the lapilli
range, and the onset of vapor-explosion
decrepitation of grain size is idealized near grain
diameters of 1.0 mm.
(Adapted from Wohletz, 1983.)

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Fig. 2.30
Sketches of four types of grain shapes observed during experiments in hydrovolcanism. Blocky and
plate-like grains are thought to be produced by brittle failure of the melt when it is subjected to
strong stress waves. Moss-like, drop-like, and spherical grains are likely produced by fluid
instabilities at water/melt interfaces:
(Adapted from Wohletz, 1983.)

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Fig. 2.31
Oxygen isotopic ratio [Eq. (1-10)] vs R_m
(water:melt ratio) shows the strong depletion
of heavy oxygen (¹⁸ O) observed in experimental
products (

) after interaction of the melt ()
with water () in times <1 s. These results suggest
that if the oxygen isotope ratio can be confidentially
measured for hydrovolcanic materials, R_m  can be
constrained. However, the effects of
weathering and the temperature at which
isotopes are exchanged in volcanic products
can complicate isotope measurements.
(Adapted from Taylor and Wohletz, 1985.)

superheated steam field, or both. Expansion within the steam dome (saturated) results in wet-steam explosions, which are of lower energy than those in the superheated field. Wohletz (1986) showed that for saturated expansions, the steam fraction (x₂ ) of the ejected water in the eruption (which forms eruption columns and pyroclastic flows and surges) is calculated by

where x_e = the steam fraction at initial thermal equilibrium, T_e = the temperature of that equilibrium [T_e = (m_w C_vw T_w + m_m C_m T_m )/(m_w C_vw + m_m C_m )], m_w and m_m = the mass of water and magma, respectively, C_pw and C_vw = water's specific heats at constant pressure and constant volume, respectively, C_m = the magma specific heat, T₂ = 373 K (assuming saturated expansion to

Fig. 2.32
Temperature-entropy diagram for vapor expansion in hydrovolcanic eruptions. From
its initial state (

), water is heated to a higher temperature and pressure (e) where
it is in thermal equilibrium with magma. With decompression, the water expands
along one of several paths, maintaining thermal equilibrium with fragmented magma, 
to its final state () at lower temperature and 1 bar atmospheric pressure. Water's 
liquid, two-phase (2f ), and vapor fields are indicated, as are points a'[where a super-
critical water and tephra mixture expands into the two- phase (steam dome) field] and 
b' [where the mixture expands out of the two-phase field into the superheated steam 
(vapor) field]. The four expansion paths shown constrain the amount of magma heat 
converted to steam expansion work; these paths are determined by the initial water:
magma mass ratio. (Adapted from Wohletz, 1986.)

1 bar), and H_lv = the enthalpy of water vaporization. For superheated expansions, the final temperature (T₂ ) is given by

where f = (m_w C_pv + m_m C_m )/m_w R, R = the gas constant, and expansion occurs from the initial pressure of thermal equilibrium (p_e ) to p₂ = 1 bar (atmospheric) pressure.

In practice, one finds that expansion might proceed from the superheated field into the saturated field—or the reverse—making the calculation more complicated. The conversion efficiency or ratio (e_c ) of the magma's thermal energy to explosive kinetic energy (the explosive efficiency) is found by dividing

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the change in the water/magma mixture's internal energy (D U_mix ) by the magma's initial thermal energy [m_m C_m (T_m -298)], where

for superheated expansion, x_e = x₂ = 0.0 and V_lv = the volume change from liquid to vapor. This calculated value gives the maximum theoretical efficiencies for the semi-isothermal cases (Wohletz, 1986) of water expansion, in which the expanding water maintains the same temperature as the entrained pyroclasts. Figure 2.33 shows a plot of those efficiencies as a function of water:magma mass ratios (logarithmic) in which maximum explosive efficiencies are reached where ratios are between 0.1 and 1.0 (about equal volumes of water and magma). Figure 2.33 also provides a comparison of this efficiency curve in which the mass fraction of water condenses from the expanding mixture (1-x₂ ). It is apparent that for eruptions of maximum energy, all water is converted to superheated steam, but with increasing amounts of water, energy gradually decreases and saturated liquid content rises sharply. For mass ratios >2.0, eruptions are very wet and most of the high-pressure vapor condenses to liquid as pressure decreases to atmospheric levels. At that point, the erupted tephra, usually wet and sticky, forms lahars during emplacement.

Building on the theoretical arguments of Colgate and Sigurgeirsson (1973), Wohletz (1986) described how growth of what are termed Rayleigh-Taylor and Kelvin-Helmholtz instabilities controls the heat transfer rates and grain sizes of magma fragments during hydrovolcanic eruptions. The interface between water (liquid and vapor) and magma can be unstable if the lighter fluid accelerates toward or across the heavier one. In the case of Rayleigh-Taylor instabilities, when the interface becomes perturbed, wavelets grow in amplitude (h_t ) with time as h_t = cosh(n_a t), where n_a is a function of acceleration, wave number, fluid densities, surface tensions, and viscosities. This instability growth occurs only when the wavelet size is greater than a critical wavelength (l_crit ; Bellman and Pennington, 1954):

where s _s = the surface tension of the magma, a = the acceleration of the water toward the magma surface (imparted by collapse of a vapor film), and r_w and r_m = the water and magma densities, respectively. If a spectrum of l larger than l _crit grows and detaches to form magma fragments, the most abundant fragment sizes are Ö 3 l_crit , and a characteristic bell-shaped size-frequency distribution results.

After an initial period of instability during which water and magma are mixed, vapor explosion may occur by superheat vaporization (Fauske, 1973) or thermal detonation (Fauske, 1977; Board et al ., 1975; Rabie et al ., 1979). Superheated water may remain in a metastable state until it attains its spontaneous nucleation temperature at ~570 K (Reid, 1976). After heat transfer raises the water temperature to that point, homogeneous vaporization causes a spontaneous vapor explosion. In the case of thermal detonation, a shock wave propagating through the coarsely mixed magma and metastable water leaves a fine fragmentation of magma and sudden vapor expansion in its wake; this sequence of events is analogous to classical Chapman-Jouguet detonation (Courant and Friedrichs, 1948).

During thermal detonation, the shock wave differentially accelerates the water and magma phases and fragments the magma in proportion to the relative velocity (u_rel ) between the two phases. For a particular combination of density, initial magma fragment size, drag coefficient, and surface tension, the differential acceleration causes magma fragmentation in less time than is

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Fig. 2.33
Theoretically calculated condensed water fraction and maximum isothermal efficiencies  vs  R_m .
The fraction of initial water that condenses to liquid after magma/water interaction increases with
R_m,,  and at R_m  = 3.0, little or no steam remains after interaction with magma and
expansion to atmospheric pressure.

required for the two phases to reach velocity equilibrium. If this situation occurs, the detonation is sustained; however, several factors can mitigate this process, including divergence of the shock wave, mixture inhomogeneities, and reflected waves. Wohletz (1986) approximated final magma fragment sizes (r_m ) resulting from thermal detonation during water/magma interaction as

for which u_rel is predicted by Chapman-Jouguet theory (Landau and Lifshitz, 1959) and D R_m is the absolute value of the difference between the water:magma mass ratio and its optimum explosive ratio (~0.3). In general, both the fluid instability/superheating and thermal detonation theories predict the fine grain sizes observed in hydrovolcanic tephra (Fig. 2.20).

The tephra deposit textures of dry and wet surges, pyroclastic flows, and lahars strongly depend on the wetness of erupted materials. Figure 2.34 is a plot of the water volume fraction of hydroclastic deposits as a function of the initial mass ratio of water interacting with magma during the eruption. The plotted curve is based on the assumption that all condensed steam is emplaced with the tephra. Eppler (1984), Pierson (1986), and Arguden and Rodolfo (1990) recently reviewed lahar formation with specific attention to the tephra deposit water contents required. Where the pore water content of deposits increases beyond 20 to 30% by volume, tephra deposits are very cohesive and can maintain the steep bedding planes typical of wet surge deposits. If deposit water content nears saturation (within a few percent of total pore space—50 to 60% by volume), tephra deposits behave like a Bingham fluid and move as lahars (Eppler, 1984). This behavior is predicted for hydroclastic tephra that are produced by eruptions whose water:magma mass ratio is >1.0. Because a great deal of steam can separate from the tephra in the eruption plume before tephra emplacement, the R_m values on the x-axis of

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Fig. 2.34
Volume fraction of liquid water in tephra deposits of hydrovolcanic origin as a function of R_m .
Where R_m  is <0.4 deposits are dry; where R_m  is >0.4 but <1.0, deposits are wet and very cohesive;
and where R_m  is >1.0, tephra deposits can contain enough liquid water to behave like lahars.

Fig. 2.34 are the minimum required for the observed tephra deposit texture.

Because the steam formed during hydrovolcanic eruptions progressively decompresses, cools, and condenses during tephra emplacement, tephra in flows and surges become wetter with increasing runout distance (time) from the vent. Whereas most dry, superheated steam might separate from tephra during emplacement of surges and flows, saturated steam gradually condenses on individual pyroclasts; therefore, tephra emplaced with saturated steam is likely to become wet and sticky—as field observations verify. This hypothesis suggests that some hydroclastic tephra deposits might show facies changes with increasing distance from the vent: dry surges near the vent, wet surges at intermediate distances, and lahars in distal parts of the deposit. This facies distribution and the corresponding runout distance of tephra deposits should be sensitive to the wetness of the eruption and the water:magma mass ratio. At one extreme, dry eruptions are expected to produce surges and flows of dry facies types over the total runout distance; at the other extreme, very wet eruptions, such as those observed at Surtsey, might expel laharic tephra.

To evaluate this wet/dry facies hypothesis, we calculate the temporal change in water vapor density with expansion—from an initial high-pressure, high-temperature state (denoted by the subscript e in above calculations) to saturated or superheated steam at atmospheric pressures. This change in water vapor density is further promoted by the cooling that occurs as surges or flows entrain cold air. From the continuity equation, we write:

for one dimension (r) in which r_g = the water (liquid or gas) density, v_e = the ejecta

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velocity, and t = time. The approach taken to solve Eq. (2-15) is analytical to make use of as much field data as possible. We calculate the first term (the temporal derivative) on the left side of this equation by using the chain rule to evaluate four related derivatives. A solution for mass conservation is achieved when the product of these derivatives is balanced by the value of the second term (the advective derivative) in this equation.

A numerical procedure was written to calculate the solution for various initial mass ratios, erupted volumes, and runout conditions. The runout is based on energy line approximations (Sheridan, 1979; Malin and Sheridan, 1982); initial velocities are constrained by the collapse height of the erupted column or, in the case of blast eruptions, the multiphase sound speed of the steam/tephra mixture (Kieffer and Sturtevant, 1984). The partial derivatives required for the temporal term of Eq. (2-15) include

In the expressions of these derivatives, r_b and r_p = the bulk density of the pyroclastic flow (or surge) and particle densities, respectively; q_p = the particle volume fraction; the gas density = r_g = (r_b - q_pr_p )/(1 - q_p ); a and v_o = the flow acceleration and initial velocity, respectively; and r_r = the radial runout of the flow (r_f = the final runout distance), which is dependent on the flow volume (V). The flow volume is, in turn, temporally dependent upon ideal behavior of the gas, for which pVg = t = constant; g = the isentropic exponent that varies with q_p (Kieffer and Sturtevant, 1984); and p is assumed to decrease linearly with time.

Equation (2-16) models the expansion of gas as a function of q_p : the gas attains atmospheric pressure as q_p increases to a level at which grains are in continuous contact (q_p = 0.6). Equation (2-17) models the radial increase of q_p , as discussed in Wohletz and Sheridan (1979) and as numerically modeled by Valentine and Wohletz (1989). The radial runout distance of the flow is given as a function of flow volume in Eq. (2-18); r_b cannot be greater than 1.5 Mg/m³ . Finally, the flow volume shown in Eq. (2-19) is an expanded differential form of the ideal gas equation.

The product of [Eqs. (2-13) through (2-16)] can be integrated with time for solutions converging to equal -¶r_g v_e /¶ r (note: ¶r_g v_e /¶ r = ¶r_g /r_g¶ r + ¶ v_e /v_e¶ r) for continuity. The results of such an analysis are considered only semiquantitative, but they provide a conceptual model for water vapor condensation in a pyroclastic flow or surge. Figure 2.35 illustrates the results for pyroclastic flow deposits of 1 and 10 km³ volumes. This model has only been field tested qualitatively, and two important assumptions are implicit in the above analysis: (a) the bulk density of the flow or surge is always dependent upon the local water (liquid/vapor) density, which ignores depositional effects, and (b) q_p decreases from a minimum near the vent to a maximum of 0.6 at the distal reaches of the deposit.

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Fig. 2.35
Conceptual results of condensation calculations, based upon solution of Eqs. (2-16) through (2-19),
depict the runout distances of tephra deposits of 1- and 10-km³  volume from respective
vents of 0.1- and 0.5-km diameter as a function of R_m . The transitions from dry to wet to laharic
deposits occur at varying distances from the vent, depending on the amount of steam
that cools and condenses within pyroclastic flows and surges.

The preceding discussions have outlined some of the predictions theory provides for water/magma interaction. Water: magma ratios are strongly tied to the energy of hydrovolcanic eruptions and are manifested by volcanic landforms, the degree of tephra dispersal, tephra grain sizes and alteration, and textural features of deposit wetness. Quantification of these manifestations serves to constrain the thermal energy and water abundance in a volcanic system. These factors are fundamental criteria for evaluating the likelihood that a geothermal system has developed within and/or near a volcanic area. The following discussions illustrate geothermal applications of hydrovolcanic theory.

Geothermal Importance of Hydrovolcanism

Field, experimental, and theoretical aspects of hydrovolcanism profoundly influence our understanding of the development, location, and nature of geothermal reservoirs in volcanic fields. Tephra stratigraphy, bedform analysis, and grain size and textures are pertinent geological information that can be interpreted to help determine the hydrologic conditions in a volcanic field. Detailed petrographic analyses of lithic constituents in the ejecta can also reveal the nature of the stratigraphic and thermal regime below a volcano; some examples of geothermal studies in Italy provide excellent documen-

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tation of the ways pyroclastic rocks have been employed to locate hydrothermal reservoirs. Finally, with knowledge of basement stratigraphy and aquifer locations, the theory of hydraulic fracture can be developed to show how a secondary permeability developed in basement rocks allows convection to prolong the transfer of residual magmatic heat to aquifers.

Tephra Stratigraphy: Geometry and Depth of Reservoir Rocks

The availability of groundwater and its depth have significant influence on the stratigraphy of hydrovolcanic tephra deposits (Heiken, 1971; Barberi, 1985; Barberi et al ., 1988). In general, where drilling information has located aquifers in volcanic fields, the aquifer depth can be correlated to types of volcanic eruptions. Figure 2.36 shows a hypothetical basin in which the aquifer is shallow or nonexistent at its margins and located at great depth near the basin's center. Eruptions of basic magma through the shallow aquifer form monogenetic structures such as single maars or tuff rings; the aquifer is gradually depleted until eruptions are no longer explosive. The magma then tends to congeal in the conduit, which eventually stops activity. If magma intersects a deep aquifer, it interacts with water under greater pressures; this delays the formation of vapor until the mixture approaches the surface, where it forms frothy ejecta that erupts in a Plinian fashion. The deep mixing does not deplete the aquifer, so repeated eruptions can occur before the magma solidifies. The surface expression of such hydrovolcanism might be a caldera complex with numerous

Fig. 2.36
An idealized cross section of a basin in which magma has erupted through rocks of varying
saturation. Where aquifers are shallow, monogenetic landforms such as single maar craters
probably form. However, if the aquifer is deep enough to surround a magma chamber, prolonged
interaction between the magma and water produces polygenetic landforms such as calderas with
numerous tuff rings and cones. In contrast, at locations where magma erupts without interacting
with an aquifer, lava flows and cinder (scoria) cones are the usual volcanic landforms.

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tuff rings and tuff cone structures (however, we emphasize the fact that not all calderas are related to hydrovolcanism). Where erupting magma encounters no groundwater, activity is confined to lava-flow emplacement and perhaps some Strombolian scoria cone eruptions.

In shallow hydromagmatic eruptions (interaction within several hundred meters of the surface), the characteristic eruption shown schematically in Fig. 2.37 develops. The idealized stratigraphy illustrated in Fig. 2.38 reflects a gradual decrease in the amount of water interacting with the magma. With initial abundant water supplies (water:magma ratio >1.0 by mass), hydroclastic eruptions might begin with phreatic bursts that produce mud slurries, lahars, and peperite deposits. As the eruption progresses, less water feeds the rising magma (water:magma ratio @ 0.5 to 1.5), and discrete explosions of wet steam and tephra deposit cool, wet pyroclastic surges. Later the water:magma ratio reaches levels (water/magma < 0.5) appropriate for very energetic eruptions of superheated steam and tephra that produce highly inflated, hot and dry pyroclastic surges capable of depositing sandwave beds. Final eruptions deposit fallout tephra and lava flows as the water supply is cut off from the magma conduit.

Deep hydromagmatic eruptions (interaction at depths from several hundred meters to several kilometers) follow a different pattern; the one described here develops a Plinian eruption sequence. Figure 2.39 depicts a Plinian eruption conduit passing at depth through an aquifer and displaying a magma fragmentation level that is receding down the conduit with time. Barberi (1985) hypothesized that in this eruption water/magma interaction will not begin until the fragmentation level has receded below the depth of the aquifer and conduit pressure falls to values less than hydrostatic. Before this stage, overpressure in the conduit is greater than hydrostatic so aquifer water does not flow into the conduit; however, after the fragmentation level passes through

Fig. 2.37
When magma erupts through a shallow aquifer (dots), the aquifer is quickly depleted;
consequently, the eruption becomes dryer in character and forms monogenetic,
maar-tuff ring structures.

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the aquifer, pressure in the conduit may fall below hydrostatic and water/magma interaction will begin. Proof of this hypothesis depends upon whether the aquifer water is really at hydrostatic pressure and whether the erupting gas-pyroclast mixture above the fragmentation level has a pressure gradient below hydrostatic.

Delaney (1982) demonstrated that when saturated rocks are heated by nearby magma, pore pressures increase sufficiently to drive hydrologic flow in the direction of least resistance (see Table 2.9). In cases where the magma is more permeable than the aquifer, the heated pore water might be forced into the magma. This hypothesis fits many observed tephra sequences in areas where information is available from drilling (Barberi, 1985; Barberi et al ., 1981). Barberi (1985) illustrated his model for deep water/magma interaction with a series of diagrams that

Fig. 2.38
This idealized depositional sequence for a shallow hydromagmatic eruption shows tephra
deposits of decreasing water abundance; such an eruption may end in solely magmatic
eruptions of pumice, scoria, or lava.
(Adapted from Barberi, 1985.)

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Fig. 2.39
In deep hydromagmatic eruptions, strong magma interaction with a deep aquifer begins after
the fragmentation surface recedes down the conduit to the depth of the aquifer. Decreased
gas pressure in the conduit above the fragmentation surface allows pore pressures in the aquifer
to drive water into the conduit. At right, the sequence of eruption styles is correlated with
the gradual migration of the fragmentation level (expansion waves) down the conduit.
(Adapted from Barberi, 1985.)

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show the progression from a Plinian over-pressured eruption column (Kieffer, 1984a, 1984b) to a pressure-balanced eruption column to a Phreatoplinian eruption phase; during this process, the fragmentation level in the conduit has receded to the depth of the aquifer (Fig. 2.40).

Figure 2.41 illustrates the idealized tephra depositional sequence from a deep hydrovolcanic eruption. Initial tephra deposits are magmatic Plinian pumice falls that blanket topography. At the intermediate stage, the eruption enters its hydrovolcanic phase (Phreatoplinian), which is marked by surge and blast deposits filled with lithic fragments from the aquifer. The final stage is characterized by emplacement of pyroclastic flows that may show many features similar to those of wet surges (such as accretionary lapilli). It is possible for the pyroclastic flow stage to be marked by periods of dry and wet expulsions of tephra that feed the pyroclastic flows, so some parts of the deposit may show entirely dry products and others may show more influence of water/magma interaction. An example of such behavior can be interpreted from the pyroclastic flow and surge deposits of the Laacher See volcano in Germany. The repeated phreatomagmatic depositional cycles found by Fisher et al . (1983) within the pyroclastic ejecta at Laacher See are attributed to varying degrees of water/ magma interaction. The degree of water/ magma interaction in our present interpretation is a function of the fragmentation level depth in the conduit: when it fluctuates above and below an aquifer, eruptions cycle between wet and dry.

Pyroclastic rocks can be used to interpret the geometry of aquifer rock units at depth below a volcanic field, as is depicted in Fig. 2.42. In this hypothetical case, the aquifer rocks are a potential geothermal reservoir. A crescent-shaped caldera wall is exposed on one side. The caldera-forming pyroclastic flow shows two major facies: (a) a coarse-grained tuff with pumiceous and a few lithic fragments in the northern portions of the outflow sheet, and (b) a fine-grained lithic-rich phreatomagmatic (hydrovolcanic) tuff in the southern portions of the outflow sheet. Tuff ring and cone vents are found along part of the caldera wall and along fault trends that extend southeasterly out of the caldera. In addition, lava flow vents are evident outside the caldera in the outflow sheet. Using the distribution of hydrovolcanic products, it is possible to infer the geometry of a saturated basement rock unit. Apparently, the caldera erupted at the intersection of an east-west fault structure and a northwest-southeast-trending one. Ring vent eruptions to the north of the fault were dry and dispersed magmatic products northward; eruptions south of the fault must have involved water from the aquifer to produce hydrovolcanic eruptions that dispersed phreatomagmatic tephra southward. The limits of this saturated reservoir rock can be further constrained along the northwest fault trend between the smaller hydrovolcanic vents and those that extruded lavas. Examples of such interpretations from the Sabatini and Albani volcanic fields of Italy are described in the following section.

Summarizing hydrovolcanic eruption sequences and aquifer depths, Fig. 2.43 is a plot of the water:magma ratio as a function of median tephra grain size. Very fine grained tephra deposits are an earmark of hydrovolcanic activity; theoretical arguments supported by field observations have determined that the finest grain sizes correlate to water:magma rations near 1.0, which are best suited for development of economically significant hydrothermal systems. Further support for this argument is developed in the following sections, which discuss such features as country rock fractures and thermal regimes—information that can be derived from detailed analysis of the lithic fragments contained in tephra deposits.

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Fig. 2.40
Sequences of pressure gradients around the conduit for a Plinian eruption involving a deep aquifer. (a) Initial
eruptions are highly overpressured at the vent, causing blast conditions that involve both a
supersonic jet with a Mach disk structure (Kieffer, 1984b) and the eruption of ground surges.
(b) As the fragmentation level recedes down the conduit, the transition from a choked, sonic-speed flow
(M »  1) to one at supersonic speed (M > 1) occurs at depth, allowing eruption of a jet near atmospheric
pressure and development of a Plinian column that produces fallout deposits. For these first two eruption stages,
conduit pressure (dotted line) is greater than hydrostatic, which precludes the flow of much water from
the aquifer into the conduit. Wherever the conduit pressure is greater than lithostatic, conduit erosion will
add lithic fragments from that stratigraphic level to the erupted mixture. (c) When conduit pressure falls
below hydrostatic, water from the aquifer mixes with the magma to produce deep-seated hydrovolcanic
eruptions; abundant lithic fragments from the aquifer rock are emplaced in pyroclastic flows and surges from
a now-collapsing eruption column.
(Adapted from Barberi, 1985.)

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Fig. 2.41
Idealized stratigraphy of deep hydromagmatic
eruption products, showing transitions from
early magmatic eruption of pumice fallout to
intermediate stages of hydromagmatic eruptions
of surge blasts to dry or wet eruptions of
pyroclastic flows (with accretionary lapilli).
(Adapted from Barberi, 1985.)

Lithic Ejecta: An Important Geothermal Prospecting Tool

Lithic ejecta can provide information about the (a) subvolcanic stratigraphy, (b) aquifer depth and physical properties, (c) aerial extent of the fluid reservoir in a volcanic region, and (d) chemical and thermal regime of rocks at depth. An in-depth study (for example, Barberi et al ., 1988) involves the collection of tephra samples, petrographic microscopic point counts of lithic constituent abundances, comparisons of the abundances with the stratigraphic position in both the tephra deposit and the regional rocks, and x-ray analyses of alteration assemblages found in lithic fragments.

Figure 2.44 schematically illustrates a hydrovolcanic eruption upward through a varied stratigraphic section that consists of three principal rock units. The interaction of water and magma occurs in aquifer rock unit 2, and subsequent eruptions excavate rock unit 1. Through analysis of the resulting tephra deposit, depicted in Fig. 2.45, the basement stratigraphy can be reconstructed. In this case—an eruption sequence that becomes wetter with time—the lowest tephra units contain mostly lithic fragments from the upper rock unit (unit 1) because it is excavated as the crater is formed. Later magmatic pumice-fall units might contain a small percentage of lithic fragments (< 10% by volume); lithic fragments from the deepest unit (unit 3) are most abundant because that unit is fractured by magma intrusion. When the hydrovolcanic dry eruption begins, lithic abundances increase by 5 to 20 vol%; those from the aquifer unit (unit 2) nearly equal those from the other two stratigraphic units combined. Final, wet eruptions produce the greatest abundance of lithic fragments (10 to 50 vol%), most of which are from the aquifer unit.

A good example of the correlation between basement stratigraphy and lithic fragments comes from geothermal investigations on the island of Nisyros, Greece (Barberi, 1985). Figure 2.46 shows the eruptive sequence and a correlation between its lithic constituents and the basement lithology encountered in a geothermal well. The hydromagmatic phases of the eruption produced dune-bedded pyroclastic surge deposits in which lithic fragments came from deep, permeable rock units, whereas the magmatic pumice fall units have lithic fragments from units higher in the basement stratigraphy in which little permeability was found. In this case, the hydroclastic tephra provide evidence of permeable rock units at depth. In addition, the lithic constituents of the hydroclastic units show alteration mineral assemblages that indicate elevated temperatures existed in the permeable strata.

The thermal regime of basement rocks is also reflected by lithic constituents found in pyroclastic strata. By careful study of the paragenesis of alteration minerals in lithic fragments, including stable isotope variations (for example, ¹⁸ O and ¹³ C) and fluid inclusion analysis (such as Cl-, SO₄ , B, NH₄ , and SiO₂ ), it is possible to surmise not only the geochemical nature of hydrothermal fluids at depth but also their evolution with

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Fig. 2.42
Hydrothermal reservoir geometry (dotted line) inferred from a geological map showing
areas underlain by dry (pumiceous) and wet (phreatomagmatic) volcanic products.
A pyroclastic flow has been erupted from a caldera; it is pumiceous in its northern
regions but lithic-rich and fine-grained in its southern portions. Tuff ring and tuff
cone vents exist within the region underlain by the hydrothermal reservoir, whereas
lava flow vents are outside that region. The caldera lies at the intersection of two fault
systems. The east-west fault system marks the northern boundary of the hydrothermal
reservoir, presumably as an aquitard, and the southeast-northwest-trending fault
apparently localizes the aquifer along its southern extent. Because the caldera straddles
the northern boundary of aquifer rocks, eruptions from its northern side are dry,
whereas those from its southern side are of a phreatomagmatic character.

Fig. 2.43
Hypothetical water:magma mass ratio (R_m ) as
a function of the near-vent median grain size of
pyroclastic rocks. Where median grain sizes of
tephra are finest (between 0.1 and 1.0 mm),
the inferred water: magma mass ratio is
between 0.3 and 1.0. In this range of R_m ,
the hydrothermal potential—and therefore
the economic significance—is greatest.

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Fig. 2.44
Sketch of a hydromagmatic eruption through basement stratigraphy consisting of three rock types:
1 and 3 are of arbitrary lithology, and rock 2, a limestone aquifer where the water/magma interaction
occurs, is thermally metamorphosed near the volcanic conduit. The abundance of lithic fragments
carried within the ejecta are shown by rock type. Type 2 is most abundant, because of the
explosive fragmentation that occurs in the aquifer. Lithic type 1 is greater than lithic type 3
because it represents near-surface rocks eroded from the conduit walls by
the pressurized mixture of steam and tephra. Lithic type 3 is least abundant
because its deep lithology is little affected by the erosive power of upward migrating magma.

time and thermal regime. In the example from Nisyros (Fig. 2.46), the four zones of secondary minerals found in the geothermal well include—with increasing depth—argillic, argillic-phyllitic, phyllitic-propylitic, and propylitic mineral assemblages, the lowest three of which show up in lithic fragments from the tephra deposit. Figure 2.47 reviews basic hydrothermal alteration facies and equilibrium temperatures represented by the mineral assemblages that characterize each facies. Secondary mineral assemblages in volcaniclastic rocks are also good indicators of burial depth (Viereck et al ., 1982). Glass shards commonly alter during diagenesis to zeolites, feldspars, opal-ct, and quartz as well as smectite clays and consequently can indicate temperature and burial depth (Fig. 2.48).

Excellent examples of the use of hydrovolcanic tephra and lithic constituents in exploration for geothermal reservoirs are provided by studies in the Latium volcanic province of Italy. This area (shown in Fig. 2.49) includes the Vulsini (Latera) volcanic complex, Vico volcano, the Sabatini volcanic complex, and the Albani volcanic complex, all of which exhibit important hydrovolcanic features (De Rita et al ., 1983).

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Fig. 2.45
An idealized stratigraphic section produced by
the eruption illustrated in Fig. 2.44. The basement
stratigraphy is represented by lithic fragment
abundances that are sensitive to eruption
sequence. Initial, dry pumice eruptions promote
nearly equal abundances of types 1 and 3 as
a result of vent widening and the relatively
large area of contact between the magma
and type 3. Conduit pressure is too great to
allow much cavitation of rock type 2. As
eruptions become hydromagmatic, the
abundance of type 2 increases significantly.

Funiciello et al . (1976) and Funiciello and Parotto (1978) described the correlation between sedimentary lithic ejecta in pyroclastic deposits of the Albani and Sabatini regions. Figure 2.50 is a sketch geologic map of the Alban Hills south of Rome. The dominant feature of this area is the Tuscolano-Artemisio caldera and the distribution of its phreatomagmatic ejecta, which is mainly to the west of the caldera. In surrounding areas, the sedimentary basement rock, consisting of Mesozoic to Cenozoic marine rocks, is exposed and is also represented by lithic fragments in the tephra of the volcanic field. The abundance of these lithic fragments and the locations of hydrovolcanic vents allowed Funiciello and Parotto (1978) to reconstruct the substrate below the volcanic complex (Fig. 2.51). The hydrovolcanic vents are located above a structurally high block of water-saturated continental shelf and basin rocks. North-northwest faults crossing this block have contributed to fracture permeability.

A second example from Italy is the Sabatini/Cesano region described by Funiciello et al . (1976). In the eastern part of the volcanic field, the authors were able to distinguish both shallow and deep aquifers. In shallow interactions, hydrovolcanic vents were monogenetic maar craters with a diameter of 1 km or less, whereas deep interactions produced poorly defined maar structures and complex caldera structures. These caldera structures appear to represent the coalescence of several maar vents that eventually collapsed together to form a single caldera. An example of this sequence of events is the Baccano caldera, whose walls expose hydrovolcanic tephra from numerous vents (see also Fig. 4.21). Fine tephra, exposed in ridges of phreatomagmatic tephra agglomerates, have a high chloride and sulfate content that is inherited from the deep hydrothermal reservoir fluids involved in water/magma interaction. In addition, ejecta analysis by scanning electron microscopy and energy dispersive x-ray

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Fig. 2.46
An example of lithic stratigraphy determined by correlations with a geothermal well in Nisyros,
Greece. The eruptive sequence shown is a magmatic-phase pumice fallout on a paleosol
substrate that is overlain by dune- and massive-bedded hydromagmatic tephra capped
by a lava. Lithic fragments from the magmatic-phase deposits correspond to impermeable strata
that are logged in the geothermal well, whereas the lithic fragments in the hydromagmatic-phase
deposits correspond to deeper, increasingly permeable strata. Hydrothermal alteration observed in
the geothermal well increases downward from argillic (A) through argillic-phyllitic (AF),
phyllitic-propylitic (FP), and propylitic (P) to thermally metamorphosed rock (TM).
(Adapted from Barberi, 1985.)

Fig. 2.47
Review of hydrothermal alteration facies
and characteristic mineral assemblages shown
as a function of depth and temperature.

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Fig. 2.48
Burial diagenesis of zeolites and clays. (a) This flow diagram shows the development of authigenic
zeolites (shaded boxes) and silicates from silicic glass during burial diagenesis and metamorphism.
(b) In this chart of mineral assemblages in a thick section of marine silicic volcaniclastic rocks,
zones I to IV indicate increasing burial depth. Zone I is characterized by partial alteration of silicic
glass to montmorillonite and opal-A/opal-CT. Zone II shows additions of alkali zeolites formed by
reaction of silicic glass with interstitial water. The transition to Zone III (where alkali zeolites are
transformed into analcime, heulandite, and laumontite) occurs at temperatures of 84 to 91°C.
The transition to Zone IV (analcime transformed to albite) occurs at temperatures of
120 to 124°C and marks a gradation into the thermal metamorphic regime.
(Adapted from lijima, 1978.)

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analysis allowed Funiciello et al . to classify secondary mineral paragenesis and determine the most recent temperature and chemistry of deep reservoir fluids involved in the hydrovolcanic eruptions. Their schematic geologic map (Fig. 2.52) was created from lithic ejecta analyses, which show excellent agreement with geophysical studies of regional gravity, electrical resistivity, and heat flow (Fig. 2.53).

The Funiciello et al . (1976) study constitutes a major step toward the application of volcanology to geothermal prospecting. They stated that

"As a first approximation, we assume that the surface covered by products of recent phreatomagmatism, rich in ejecta from the deep sedimentary basement, delimits the minimum dimensions of a potential geothermal field. As a second approximation, the study of the sedimentary ejecta allows [us] to reconstruct the stratigraphic and structural characters of the sector where the phreatomagmatism occurred. This [study] makes it possible to interpret the paleogeographic and tectonic evolution of the area and to fit it within the regional geology."

With respect to thermal regimes, Funiciello et al . (1976) added:

"Furthermore, if a sequence of phreatomagmatic products in several layers is available, the comparative investigation of the mineralizations in the different layers supplies indicators on the evolution of the hydrothermal field in the time."

Volcanic Hydrofractures

The concept of hydraulic fracturing (hydrofracture ) was introduced to the petroleum industry as a technique to increase the fracture permeability of oil and natural gas reservoirs (Clark, 1949). Because of its successful application in the increasingly important secondary petroleum recovery from tight formation rocks, Hubbert and Willis (1957) cited the technique as a major development in petroleum engineering. Although hydrofracture is historically an artificial means of stimulating a well, there is growing geological evidence that essentially the same process happens naturally in certain geologic situations where fluid over-pressures at depth are sufficient to cause either the widening of preexisting fractures or the failure of rock in the direction of greatest principal stress. These geologic conditions can occur near sites of magma intrusion and extrusion. Such a volcanic hydrofracture is geothermally significant where it increases the effective permeability of host rocks near a heat source and thus allows significant hydrothermal circulation (Knapp and Knight, 1977; Norton, 1984).

Numerous publications have suggested that hydrofracture occurs naturally during some magma intrusions in the earth's crust. Fehler (1983), Julian and Simpkin (1985), Chouet and Julian (1985), and Chouet (1986, 1988) attributed long-period seismic events and harmonic tremor to fluid-driven fracturing. Foulger and Long (1984) observed tensile crack formation in geothermal areas of

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Fig. 2.49
Sketch geological map of the Latium volcanic area in central Italy. The sedimentary basement rocks
consist of the Latium-Abruzzi carbonate platform rocks, the Umbria-Sabina successions and Tuscan
Nappe, and the allochthonous Liguridi and Subliguridi complexes. The volcanic section includes
acidic and K-alkalic volcanic rock units and the major caldera associations of the Alban Hills,
Sabatini, Vico, and Vulsini areas. Widespread hydrovolcanic units are found in each of
these caldera areas.
(Adapted from De Rita et al ., 1983.)

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Iceland, and West et al . (1978) attributed ground tilt around La Soufrière de Guadeloupe in 1976 to hydrofracturing by pressurized phreatic fluids. Leet (1988) modeled harmonic tremor caused by the hydrothermal boiling—a source mechanism that does not require movement of magma. Thus, some geophysical evidence strongly supports the concept of volcanic hydrofracture.

Theoretical Background

Hubbert and Willis (1957) discussed the mechanism of hydraulic fracture and emphasized the importance of regional stress. Failure that results in faulting occurs at a critical relationship between the greatest and least principal stresses (s₁ and s₃ , respectively), where

s is the normal stress and t_s is the shear stress acting across a plane perpendicular to the s₁ and s₃ planes at some angle a _s to s ₃ . Using a Mohr diagram, one can then determine a combination of s and t_s at which failure occurs. Mohr envelopes of rock failure (Jaeger and Cook, 1976), given by t_s /s = tan f_f , where f_f = the internal angle of friction, must be experimentally determined; however, at lower pressures, brittle failure envelopes are approximated by

where t _o = the zero normal-stress shearing strength of the rock. Where rock pores are occupied by fluids, the effective normal stress (s _eff ) is decreased so that s_eff = s - p_p , where p_p = the pore-fluid pressure. Hubbert and Willis (1957) noted that under normal hydrostatic conditions the effective vertical stress (s_z ) is slightly more than one-half the overburden pressure (S_z = r gh). In regions experiencing normal faulting, s ₁ is nearly vertical and equal to s_z ; s₃ is horizontal and probably between one-half and one-third s_z (s₃ = n /(1-n ), where n = Poisson's ratio for rock. On the other hand, in compressed regions that are characterized by thrust faulting and folding, s₃ is vertical and equal to s_z ; s₁ is horizontal and between two and three times s_z . Hydraulic fractures generally propagate in the direction of greatest principal stress. Horizontally oriented fractures will form only where the fluid injection pressure (p_pi ) is greater than the effective vertical stress (s_z ); vertical hydrofractures can form in regions of extension where p_pi@ (S_z + 2p_p )/3.

Zoback et al . (1977) conducted laboratory experiments on hydraulic fracturing of rocks to find the breakdown pressure (p_b ) of various rocks:

The tensile strength of rock (T_s ) should equal p_b - 2s₃ for nonporous rocks, but in fact, p_b must be corrected for viscous hydrodynamic losses controlled by pressurization, flow, and leakage rates (along preexisting fractures). For example, Zoback et al . measured p_b in triaxial experiments that ranged from 27 to 54 MPa for gabbros and 20 to 34 MPa for

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Fig. 2.50
Sketch geologic map of the Alban Hills volcanic group and the Tuscolano-Artemisio caldera.
The oldest volcanic rocks are associated with a composite cone, dated at 0.5 to 0.7 Ma, which
overlies upper Pliocene to Recent sedimentary rocks, Mesozoic and Cenozoic shelf-to-basin
successions, and Mesozoic shelf-edge facies rocks. Of major interest to geothermal studies
are the phreatic craters and ejecta (peperini), which contain lithic fragments that
reveal the basement structure. The youngest volcanic rocks are lavas and
pyroclastic rocks in the caldera center, dated at 0.28 Ma.
(Adapted from Funiciello et al ., 1976.)

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Fig. 2.51
Alban Hills sedimentary basement geology was reconstructed from the distribution of sedimentary
lithic fragments observed in hydroclastic tephra. This reconstruction was useful in siting geothermal
exploration wells, which located a permeable, saturated rock strata that could contain a hydrothermal
system. Numbers refer to volcanic centers: (1) Procula-Pomezia, (2) Ciampino, (3) Albano, (4) Nemi,
(5) Vivaro, (6) Doganella, (7) Valle Marciana, (8) Prata Porci, (9) Gabi, and (10) Campidoglio.
(Adapted from Funiciello et al ., 1976.)

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Fig. 2.52
Schematic of Sabatini basement geology reconstructed from distribution of lithic fragments in
hydroclastic ejecta. The map shows a northwest-southwest-trending horst (outlined by strike and
dip symbols) of Triassic flysch bounded on both sides by Miocene sedimentary rocks.
(Adapted from Funiciello et al ., 1976.)

sandstones when the pressurization rate was varied from 0.2 to 3 MPa/s, respectively. For the sandstones, p_b increased to a range of 33 to 55 MPa when the rock was prefractured, which demonstrated the effect of fracture leaks. In all cases, fracture initiation pressures, which were measured at the onset of rock acoustic emissions, were less than p_b (Fig. 2.54).

Howard and Fast (1970) reviewed other theories of hydraulic fracture and the results of oil-field studies, including the effects of fluid viscosity and pressure, pressurization time, and injection rate on the fracture width and area around well bores (Figs. 2.55 and 2.56). Solid materials such as sand and organic materials—called proppants —are added to fracturing fluids to increase viscosity and to hold fractures open. By tunneling into fractured areas, Warpinski et al . (1981) observed the effects of proppants on hydrofractures. Contrary to theory, the fractures were neither restricted nor terminated by rock interfaces, even where Young's modulus varied by a factor of 15 for a rock contact. However, fractures did propagate away from regions of high in-situ stress such as layers of tuff that were more highly compacted and altered. When different colors of sand proppants were used in sequences of hydraulic fractures, some fractures showed bedding and cross stratification. Kern et al . (1958) experimented with the movement of sand as a proppant in fractures. They found that beds are formed as sand accumulates by cohesion on the fracture surfaces. The nature of the bedding depends on the changes in fluid velocity with time, in a manner similar to that of

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sedimentation in flume studies. Bedding sets at various orientations to the fracture wall are evidence of multiple pulses of fluid. These observations have been supported by geological studies of intrusive fracture fillings (Heiken et al ., 1988) and pyroclastic dikes (Curtis, 1954).

Knapp and Knight (1977) considered the effect of a temperature rise in saturated, porous rock around a hot pluton. Pore fluids change volume with varying temperature and pressure:

where a = the isobaric coefficient of thermal expansion and b = the isothermal coefficient of compressibility. Because the a for fluids is much greater than the a for rocks, these authors studied the effects of differential thermal expansion between pore fluids and enclosing rocks. For pores of fixed volume, the derivative of fluid pressure with respect to temperature is

a /b , termed the pressure coefficient , ranges between 1 and 3 MPa/°C for water in the earth's crust; it reaches a maximum at temperatures between 100 and 300°C at lithostatic pressures <800 MPa (Fig. 2.57). By plotting pore fluid pressure vs depth for various geothermal gradients (Fig. 2.58), one finds that s_eff may fall to values less than zero; fracturing of rock is expected if s_eff is less than the tensile strength of rock [from Eq. (2-23)]. In regions near a cooling intrusion, a zero effective pressure front will propagate away from the intrusion, which results in fracture of the host rock, increased rock permeability, and increased convective heat transport. This zone of fracturing and strong convection moves upward because of buoyancy forces, as was explained by Williams (1936) and McBirney (1959; 1963) for occurrences of breccias and tuff-breccias in and around volcanic necks and intrusions. Knapp and Knight (1977) used this

Fig. 2.53
Geophysical structure of the Sabatini area is
reflected by heat flow, gravity, and electrical
resistivity maps (Baldi et al ., 1975). These maps
demonstrate similar structural interpretations,
which support those obtained by studying
the lithic ejecta (Fig. 2.52).
(Adapted from Funiciello et al ., 1976.)

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Fig. 2.54
Graph of pressure vs  time for sample deformation
measurements during triaxial loading experiments
in which rock specimens were hydraulically
fractured. Sample deformation and acoustic
emission activity begins when the borehole
pressure reaches p_i , the initial fracture pressure;
sample breakdown occurs when the borehole
pressure reaches p_b . Acoustic emissions in
fluids correspond to the seismicity typical
during hydraulic fracturing events in the earth.
(Adapted from Zoback et al ., 1977.)

model to show how thermally induced hydraulic fracturing can produce micro-earthquakes—a characteristic feature of geothermal areas and active volcanoes.

Norton (1984), in his theory of hydrothermal systems and related rock fracturing, showed how variations in the transport properties of water can result in apparent discontinuities in the physical state of convection and secondary mineral deposition. For example, in Fig. 2.59, rapid changes are visible in the water's heat capacity, kinematic viscosity, and coefficient of thermal expansion near its critical point. Heating at this range of temperatures might result in (a) rapid solution and precipitation of various minerals, (b) oscillations in fluid heat and mass transport, and (c) rapid rock failure. Where hydrofractures occur around intrusions, as described in the theory above, convective heat transfer is augmented by the fracturing. If the fracturing front propagates away from the intrusion with time, convective hydrothermal systems manifested at or near the earth's surface may not indicate hotter, more active systems at depth. As we pointed out earlier in our discussion of heat flow, it is not possible to project to depth with confidence the thermal gradients affected by convection. Norton (1984) pointed out that behind the fracturing front/convective zone, which migrates away from the intrusion, thermal decline is accompanied by secondary mineral deposition that seals fractures. As a result of these hydrothermal processes, the last vestige of hydrothermal activity is close to the earth's surface and there is only minor activity near the intrusion.

The above discussions about pore-water pressurization and heating around an intrusion cover the long-term effects of rock fracture and subsequent development of a hydrothermal system. In contrast, when Delaney (1982) modeled the short-term effects of heat transfer to porous saturated rock, he found that pore water is not heated along a constant-volume pressure path because water diffuses more rapidly than heat does. He tabulated solutions for pore-pressure increases as a function of porosity and permeability. He also considered situations in which magma intrudes into near-surface rocks (Table 2.9); phase transitions from water to steam generally occur, the pressure increases exceed lithostatic pressure, and host rock failure is likely. Figure 2.60 depicts a case in which the magma is more permeable than the host rock. Where the magma volatile overpressure is low, the pressure gradient near the intrusion is negative and water mixes into the magma—a situation that leads to intrusion brecciation and hydrovolcanism.

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Fig. 2.55
Graph of fracture area vs fluid viscosity
predicted for an assumed set of reservoir and
hydraulic fracturing conditions, where
permeability (k ) = 10 mD, porosity (f_p ) = 20%,
pumping rate (Q_f ) = 25 BPM, total
volume = 20,000 gal.  @  75.7 m³ , fracture
clearance (W) = 0.2 in. (»  5.1 mm). Two curves
show the effects of differential pressures (D p) of
1000 psi (Curve 1) and 500 psi (Curve 2). The
fracturing fluid coefficient (C_f ) is the fluid's
temporal variation in velocity divided by the
square root of time and is a function of viscosity
and relative permeability. The use of English
units is common to petroleum literature.
(Adapted from Howard and Fast, 1970.)

Fig. 2.56
Effect of pumping rate and fracturing fluid coefficient (C_f ), as defined in Fig. 2.55, on fracture
radius. Solid curves show observed fracture radius at volume fluxes of 2.5 and 25.0 BPM
(0.0066 m³ /s and 0.066 m³ /s, respectively). Dashed curves show the percentage of fluid volume
lost to the formation. Fracturing conditions are constant for total volume of 20,000 gal. (75.7 m³ )
and fracture clearance (W) of 0.2 in. (5.1 mm).
(Adapted from Howard and Fast, 1970.)

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Fig. 2.57
Plots of pressure coefficient [a /b  = (dp/dt)_v ]
(a) over a range of water temperatures and
pressures and (b) as a function of geothermal
gradients and depth. The 

 in (a) denotes
the critical point of water and its attached
line going to lower temperatures is the two-
phase boundary curve. In (b) an + marks the
depths at which the critical value of a /b  is
reached and where effective pressure vanishes.
(Adapted from Knapp and Knight, 1977.)

In addition to brecciation and rock fracture, surface ground tilt is a well-documented phenomena in hydrofractured well bores. Studying the size of hydraulic fractures, Sun (1969) showed the relationship between surface uplift and the thickness of a grout sheet that was injected into a horizontal hydraulic fracture at depth around a well bore (Fig. 2.61). Pollard et al . (1983) examined surface deformation above near-surface intrusions and modeled the rock displacement. In Fig. 2.62, their model is compared to measured data from the Kilauea rift zone in Hawaii. The topographic expression of magma injected as dikes at depth is a surface uplift with an axial depression. Calculated contours of maximum principal stress around a buried dike (Fig. 2.63) show that the regional stress field is perturbed in such a way that s₁ is horizontally directed near the sides of the dike. This prediction explains why hydrofractures can extend horizontally from some intrusions even though the regional s₁ is vertical.

Fig. 2.58
Pore-fluid pressure vs  depth for several
geothermal gradients; the lithostatic pressure
gradient for a rock density of 2.75 Mg/m³  is
indicated by the dashed line.
(Adapted from Knapp and Knight, 1977.)

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Fig. 2.59
Variation of physical properties of water at (a) 30 MPa (300 Bars) and (b) 60 MPa (600 Bars) pressure
as a function of temperature; sharp inflections and discontinuities appear near critical temperatures.
Vertical axis is nondimensional; units of measure are shown for each curve. C_p  = heat capacity at
constant pressure, µ = kinematic viscosity, a  = isobaric coefficient of expansion, b  = isothermal
coefficient of compressibility, and a /b  = pressure coefficient [(dp/dt)_v ].
(Adapted from Norton, 1984.)

Size of Hydraulic Fractures

Using the assumption that rocks deform as linear elastic bodies, several theories have evolved for predicting the width and length of hydraulic fractures. Figure 2.64 is a schematic representation of a hydrofracture propagating from a fluid reservoir such as a well bore or a magma body. Two important aspects of fracture calculations are (a) the pressure required to overcome rock compressive stresses and rock strength and (b) the pressure losses resulting from viscous fluid flow in the fracture.

Geertsma and Haafkens (1979) calculated a simple relationship of fracture size [width (W) and length (L)] from fracturing fluid pressure (p_pi ), based on the theory of England and Green (1963):

for which W is a function of distance (x), the point where the fracture narrows into a tip at a distance L [L - x = the length of the fracture tip; a measure of fracture tip asperity is included in the last term on the right-hand

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Fig. 2.60
Solutions to transient heat flow from magma to wet sediments. Top: Illustration of fluid flow lines
(arrows) as well as thermal, pore pressure, and water density gradients for (a) a short-term thermal
pressurization flow that occurs shortly after initiation of heat transfer (a); and (b) a long-term
buoyancy flow that occurs when pressure gradients caused by gravitational forces are dominant.
Bottom: (c) pressure; and (d) normalized pressure gradients for three possible boundary conditions
between the magma and the host rock. p = pressure, p¥  = pressure at infinite distance,
p_i  = initial pressure,  a_m  = magnitude of thermal expansion, D_d  = ratio of penetration depths for
thermal (k_t ) to hydraulic (w ) diffusivities, h  = Boltzmann variable, and x = distance.
(Adapted from Delaney, 1982.)

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Fig. 2.61
Map and cross section showing vertical and aerial extent of experimental hydrofracture around well
bore. (a) Plot shows surveyed data and curve calculated by Sun (1969).

 = survey points along
northwest-southeast traverse,   = points along west-northwest traverse, and 

 = northeast-
southwest traverse. (b) Plan view of surface uplift shows contours in millimeters (dashed lines),
the extent of grout sheet injected during hydrofracturing (solid line, survey traverse points (),
and core hole locations ().
(Adapted from Sun, 1969.)

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Fig. 2.62
Calculated and measured surface deformation over buried dikes on Kilauea summit and southwest
zone. (a) Data (

) with fitted dashed curve for rifting event of August 10, 1981 is compared to
results of theoretical vertical uplift. (b) Plot of theoretical horizontal stress  vs  distance
shows regions of compression and tension. (c) Data from Duffield et al. (1976) for intrusive
event of May 15-16, 1970, showing measured stations () and contour extrapolations (), which
are projected on a trend of N37°W (solid line). Duffield calculated that the intruded
dike is 3000 m long, 0.8 m thick, 400 m high, and 400 m below the Earth's surface.
(Adapted from Pollard et al ., 1983.)

Fig. 2.63
Calculated contours of maximum principal
stress around a vertical dike that cuts a vertical
plane. The dike is 100 m high and its center is
at -75 m; it is subjected to a driving pressure
of 1 MPa under a lithostatic gradient of
0.025 MPa/m intrusion. Dashed curves are
trajectories of minimum principal stress along
which secondary fracturing might occur. At
depth, hydrofractures extending out from the
dike would propagate perpendicular to
the principal stress contours.
(Adapted from Pollard et al ., 1983.)

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side of Eq. (2-26)]. v = Poisson's ratio; µ_s = the shear modulus; and D p = p_pi - s_eff . Although this formulation is designed for vertical fractures, it also applies to horizontal fractures where s₁ is horizontally directed. However, this solution does not account for viscous losses of fluid flow in the fracture and fluid losses to the host rock—problems that require complex treatments and yield relatively small dimensional differences.

Sun (1969) solved for fracture dimensions by calculating ground surface uplift caused by hydraulically induced fractures around well bores. By assuming a thin, disk-shaped fracture and an equilibrium distribution of stresses and displacements in a semi-infinite medium, he built on Green's (1949) analysis of fracturing in an infinite medium. Using an image method to represent the boundary conditions at the free (ground) surface, Sun (1969) calculated displacements—and therefore, fracture dimensions—from general equations of equilibrium for an isotropic elastic body (Love, 1939). The resulting solutions for the relationships among fracture dimensions, fluid pressure, and host rock elastic properties are

In these equations, E = Young's modulus; v = Poisson's ratio; and Q = the fracture volume. In the analysis of fracture volumes, four unknowns (p_f , x, L, and Q) can be found by simultaneous solution of Eqs. (2-26) through (2-29), providing one can obtain the host rock properties and depth at which fractures are found (h).

Spence and Turcotte (1985) provided a more rigorous solution to a fluid-driven fracture. They considered fracture of an elastic medium, which is sensitive to the critical stress intensity at the fracture tip, as well as viscous losses of fluid flow in the fracture (approximated by lubrication theory), where the fluid viscosity is sufficiently large and the flow is laminar (Schlicting, 1979). The spatial and temporal fluid pressure distribution p_f (x,t) must be such that the faces of the fracture close smoothly at its tip (Barenblatt, 1962):

where µ_s = the shear modulus; v = Poisson's ratio; W_h = the crack half-thickness; s = a point on the crack surface a small distance from the crack's end; and

= a measure of the crack length. Assuming the elastic theory of crack propagation, p_pi increases towards the fracture tip, where it must equal the fracture resistance of the rock; this calculation requires specification of the stress intensity factor (K_i ) (Irwin, 1957):

Stress intensity factors have been tabulated for various rocks (for example, Clifton et al ., 1976, and Schmidt and Huddle, 1977). Combining expressions for fluid flux and mass conservation produces the Reynold's equation for flow in the crack:

where µ = the fluid viscosity. Spence and Sharp (1983) found solutions by using a numerical similarity technique to model the combined effects of elastic behavior and fluid flux. Spence and Turcotte (1985) found two sets of solutions, depending upon whether a nondimensional stress intensity factor (g_k ) is large or small:

where Q_f (the fluid volume flux) is expressed for two dimensions rather than three.

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Fig. 2.64
Schematic illustration of a hydrofracture includes dimensions important to hydrofracture calculations:
depth in well bore (h), well-bore radius (r_w ), fracture width as function of distance and time
[W(x,t)], fracturing fluid velocity (v_x ), and total length of fracture (L).
(Adapted from Geertsma and Haafkens, 1979.)

Figure 2.65 illustrates the fracture-tip asperity as required by specification of g_k . Large g_k corresponds to situations in which the rock's fracture resistance is large compared to the viscous resistance to fluid flow—as it is in the case of a wide elliptical crack profile. Small g_k is generally applicable to geologic systems in which the fracture resistance is negligible compared to viscous resistances—as is the case if viscous fluids are forced through a narrow crack with a sharp tip that can easily split the rock. The solutions for this latter situation, in which A_f expresses the two-dimensional, fracture-fluid flux, are

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Fig. 2.65
Fracture tip asperity as a function of the
nondimensional stress intensity factor (g_k )
depends on whether fracture resistance of the
host rock is large (g_k  >> 1) or small (g_k  <<1)
compared to viscous resistance of fluid flow
(Spence and Turcotte, 1985).

Results obtained by using the above equation set show good agreement with those obtained from Eqs. (2-26) through (2-29).

Field Examples

The relationships between hydrofracture features discussed above have been used to interpret tephra-filled fractures surrounding a buried dike that was cored near Obsidian Dome in California (Heiken et al ., 1988). Hulen and Nielson (1988) studied hydrothermal brecciation encountered in a well that was cored on the southern margin of the Valles caldera in New Mexico. These examples illustrate two different approaches to understanding volcanic/hydrothermal fracturing.

The Inyo Domes are a recent chain of rhyolitic tuff rings, phreatic pits, and domes on the edge of Long Valley caldera in eastern California (Miller, 1985). The US Continental Scientific Drilling Program explored the possibility that two of the domes, Obsidian Dome and Glass Creek flow, are connected by a buried dike. In addition to proving the dike hypothesis, the core hole intersected several sets of fractures containing juvenile magmatic fragments at various lateral distances up to 130 m from the dike (Figs. 2.66 and 2.67). The fractures, found in quartz monzonitic country rock, were filled with as much as 20% poorly vesiculated, rhyolitic shards, most of which were <1 mm in diameter. The rest of the fillings were mineral clasts and fragments of the quartz monzonite. The fractures ranged in width from millimeters to 8 cm; 0.4 cm was the average width. The ubiquitous cross bedding of clasts, the likelihood of preexisting sheet fractures, and similarly filled fractures found in bedded basalt intersected by a core hole under Obsidian Dome suggest that these fractures are horizontally oriented (Fig. 2.68).

Heiken et al . (1988) used the analysis of a stress field around a dike (Fig. 2.63), as presented by Pollard et al . (1983), and Eqs. (2-26) through (2-36) to calculate hydrofracture conditions at Obsidian Dome (Fig. 2.69). The calculated overpressures of 5 to 10 MPa and fluid viscosities of 0.20 to 0.8 Pa-s correlate with either phreatomagmatic or magmatic fragmentations that produce slurries of steam, water, and solid-particle mixtures. The overall blocky, poorly vesicular textures of the pyroclasts, their dominantly rhyolitic composition, and surface alteration features strongly support the phreatomagmatic origin: late-stage phreatomagmatic eruptions that preceded dome lava extrusion.

Hulen and Nielson (1988) found breccias at a depth of 826 to 856 m in VC-1 core hole, which is located along the intersection of the Jemez fault zone and the ring-fracture zone of the Valles caldera. The tectonic

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breccias are contorted, crushed, and sheared, unlike the hydrothermal breccias, which lack frictional textures but show matrix flow foliation and clast rounding—features characteristic of fluidization (Wolfe, 1980; Kents, 1964)—as well as intense alteration. Evidence of five stages of secondary mineral paragenesis to a quartz-illite-phengite-pyrite assemblage (typical of temperatures in excess of 200°C) and a fluid inclusion homogenization temperature of 189 to 283°C were used to model the hydrothermal brecciation.

Fig. 2.66
Map of Obsidian Dome scientific drilling project.
Rhyolite lava domes of Obsidian Dome and
Glass Creek Flow are shown in shaded pattern;
lava flow front scarps are designated by
hachured line. The dashed line connecting the
two lava domes is the projection of the dike
found by drilling to pass at depth between
the domes. Core samples and hydrofracture
calculations discussed in the text are for the
(1) dike core hole that is located between the
two domes and slanted down to intersect the
dike at depth, and (2) the conduit core hole
that is slanted down to intersect below
Obsidian Dome's central depression.
(Adapted from Heiken et al ., 1988.)

An extensional state of stress can be inferred for the formation of the VC-1 core hole breccias found along the well-studied Jemez fault zone (Aldrich and Laughlin, 1984; Dey and Kranz, 1988). Hydraulic rupture in such a case is expected where p_p exceeds s₃ by an amount equal to the rock's tensile strength, as was discussed earlier. Hubbert and Willis (1957) show that this situation can be approximated by

Assuming that p_h (hydrostatic pressure) approximates that of the boiling point at depth and that p_p = p_b (the formation break-down pressure), Hulen and Nielson (1988) estimated p_b at 7.5 MPa, which is similar to the fluid injection pressure (p_pi ) used in the hot dry rock hydraulic fracturing experiments recently conducted at nearby Fenton Hill (Murphy et al ., 1983). Figure 2.70 shows the results of this model in a plot of depth vs temperature for boiling under hydrostatic and lithostatic loads; this plot also contains the homogenization temperature of fluid inclusions. Either fluid temperature increases or a transient confining pressure decrease during fault movement might cause fluids to reach p_b .

Summary: Volcanological Interpretation

Several different but naturally related processes might stimulate fracturing of potential geothermal reservoir rocks: (a) magma intrusion, (b) hydrothermal circulation, (c) magma degassing, and (d) hydrovolcanic processes. For the hydrovolcanic (phreatomagmatic) case, the series of schematic illustrations in Fig. 2.71 depicts the formation of a hypothetical fractured geothermal reservoir underneath a volcano.

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Fig. 2.67
Cross section of dike and conduit core holes showing natural hydrofractures as wavy horizontal lines at depths of 300 to 500 m.
(Adapted from Heiken et al ., 1988.)

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Fig. 2.68
These sketches of cores containing clastic fracture fillings were made by mapping core surfaces on velum wrapped around
the core.(a) Orientation of core segments taken 5 and 1 m west of the conduit that was intersected by the conduit core hole.
The gray, cross- and convolute-bedding fillings range in thickness from 7 to 40 cm. Of the two possible orientations shown,
the lower of each set best fits the bedding texture. (b) Core maps showing fracture fill,
host quartz monzonite, obsidian clasts, and void space.
(Adapted from Heiken et al ., 1988.)

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This scenario combines aspects of all four processes listed above. The initial intrusion of a gas-rich magma moves upward along a fracture, opening the fracture with its fluid-rich top. This slow mechanism of crack propagation (termed "stress corrosion" by Anderson and Grew, 1977) is related to rock breakdown by the corrosive crack-tip fluids and rapidly varying pressure brought on by nucleate boiling along the crack walls. At some point, degassing of the magma might drive a hydrofracture into near-surface, poorly competent aquifer strata. The initial Plinian eruptions are driven by exsolving gases under high pressure. With increased fracturing, the aquifer rock fails catastrophically and allows water to mix with the magma, which results in dry phreatomagmatic eruptions. The eruptions gradually become wetter as more water is supplied by the increasingly fractured aquifer. At some stage, the extrusion of magma ceases—perhaps in response to chilling by the aquifer. By this time, hydrothermal circulation is well developed, and fluid from the aquifer continues to transfer heat from the intrusion below the volcano.

The geothermal potential of such a system has only been tested in a few areas (for example, Funiciello et al ., 1976; Barberi, 1985), and its overall importance depends upon a number of geologic controls:

· age and size of the subvolcanic intrusion,

· presence of a sufficient aquifer,

· porosity and permeability of basement rocks,

· fracture strength of basement rocks,

· tectonic regime and location of preexisting fracture systems, and

· clay content of host rocks and the degree of hydrothermal alteration.

In conclusion, we offer the simple model illustrated in Fig. 2.71 as an example of one of several different volcanic processes that develop fracture permeability in basement rocks and promote hydrothermal circulation.

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Fig. 2.69
Solutions for hydrofracture at Obsidian Dome, illustrating a model for volcanic hydraulic fracturing.
(a) Hypothetical contours of maximum principal stress (Pollard  et al ., 1983; see Fig. 2.63) indicate
the horizontal propagation of hydrofractures from the dike as they intrude into the granodiorite
(quartz monzonite) host rock. (b) Calculated values of fluid overpressure required to form
hydrofractures as a function of depth for the upper and lower set of fractures observed in the dike
core hole. (c) Calculated fracture dimensions and average observed fracture widths for several
different depths. (d) Calculated fluid viscosities required to form the observed fractures.
(e) Calculated fracture formation velocities. Fracturing may have occurred in spurts, causing the
fractures to propagate several meters at a time.

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Fig. 2.70
Hydrothermal brecciation model of Hulen and Nielson (1988). This depth  vs  temperature plot shows
the boiling point curves under hydrostatic (p_h ) and lithostatic (p_l)  pressure, as well as that
required for hydrofracture (p_b ). For hydrofracturing that begins at 515 m, path AB follows
pressure buildup and subsequent fracturing as a response to increased temperature; path AC
represents hydraulic rock rupture in response to a rapid pressure release.

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Fig. 2.71
Schematic sequence illustrating the six-phase development of a fractured geothermal reservoir under a phreatomagmatic volcano.
Phases 1 through 3 are hypothesized from the studies of Obsidian Dome discussed in the text (Heiken  et al ., 1988).
Phases 4 and 5 reflect the findings of Barberi (1985) for phreatomagmatic eruptions through a deep aquifer;
the tephra deposits record increasing water interaction as the eruption progresses, presumably as a response to the
increased fracture permeability of aquifer rocks induced by hydrofracturing. Phase 6 illustrates posteruptive
cooling of magma intruded below the volcano. Hydrothermal circulation in the aquifer around the intrusion,
greatly enhanced by the magma-induced hydrofracturing, may develop a geothermal reservoir.

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