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Time-Dependent Hydraulics of the Earth's Crust 7 AMOS NUR Stanford University JOSEPH WALDER University of Washington ABSTRACT The deceivingly simple question posed here is how deep free water extends in the Earth's crust. This question is found to be inseparable from crustal porosity, permeability, and pore pressure and most significantly their dependence on time at depth. If we assume that porosity and permeability are time independent, it follows from hydrological evidence that ambient pore pressure must be hydro- static. However, geological evidence suggest that rocks in situ rapidly seal hydraulically. To reconcile this conflict, the hypothesis is explored that crustal porosity, permeability, and hence pore pressure are in general time dependent due to the gradual closure of crustal pore space via healing, sealing, and inelastic deformation. It is found that when the hydraulic conductivity of the system is large, so that the ratio of porosity reduction rate ~ to permeability k, /k, is small, the initially porous water-saturated crustal rock mass will gradually lose its porosity and fluid, until it becomes essentially dry. Pore pressure, Pp. throughout this process will remain around hydrostatic. If on the other hand, system permea- bility is small and /k is large, the pore fluid cannot escape fast enough and pore pressure will build up. It is envisioned that when the pore pressure reaches the level of the least compressive stress in the crust, natural hydraulic fracturing takes place, leading to some fluid release, pore pressure drop, and resealing of the system. With time Pp builds up again, leading to another cycle of hydrofracturing. Analysis shows that tens to hundreds of such P cycles are possible and that the duration of one cycle may be 103 to 1os yr; the Duration of the entire dewatering process can be 106 to 107 yr. If subducted lithosphere supplies additional waters, the process may last as long as 108 yr. ~3

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114 AMOS NUR AND JOSEPH WALDER The conclusion that the crust is most likely undergoing repeated (1) cyclic episodes of pore pressure buildup to lithostatic and (2) water expulsion events associated with natural hydraulic fracturing may explain such observations as the episodic nature of some types of ore deposits and veins, the recurrence time between large earthquakes, the emplacement of foreland thrust systems, and the seismic and mechanical nature of crustal detachment zones. INTRODUCTION One of the simplest yet profound questions that can be asked about the state of the Earth's crust is the depth to which free water extends. The top of the free water zone in the crust, in the form of groundwater table, is present almost everywhere. The depth to the water table typically varies between 0 and 1000 m or so and is the subject of extensive hydrological exploration, especially in arid and semiarid regions. A much more difficult question is the depth of the bottom of the free water or groundwater in the crust (see Table 7.1~: Is groundwater limited to the top 1 to 2 km, with the crust below being dry, or does free water extend to much greater depth, for example, the depth to which the crust is brittle (~10 to 15 km), or even deeper? And if free water is present at the greater depth, how much is present or, equivalently, what is the porosity in the crust? This question in turn is found to be inseparable from what the water's ambient, or steady-state, pore pressure Pp must be (Figure 7.1~. Furthermore, as dis- cussed in this chapter, the pore pressure question is itself inseparably linked to the question of permeability at depth. In this chapter we consider the following three inter- linked questions: What is the depth in the crust of free water and its pressure? What are typical crustal porosity and permeability? Are or can these parameters be time invariant? These simple questions are actually very im- portant because their answers are keys to understanding a surprisingly wide range of geological and geophysical crustal phenomena. For example, the mechanisms by which crustal rocks deform tectonically are strongly influenced by the presence or absence of water as well as by the level of pore pressure (e.g., Carter, 1976; Brace and Kohlstedt, 1980~. Circulation of crustal water has important effects on heat flow (e.g., Sleep and Wolery, 1978; Lachenbruch and Sass, 1980; Smith and Chapman, 1983), on the distr~- bution of oxygen and hydrogen isotopes (e.g., Taylor, 1977; O'Neil and Hanks, 1980), and on the formation of TABLE 7.1 Possible Indicators for the Presence of Free Water in the Earth's Crust and Estimated Depth Values Indicator Depth range References Water table 0 to 2 km Deep wells to 12 km Reservoir induced seismicity to 12 km Bell and Nur (1978) Crustal low velocity zones 7 to 12 km Berry and Mair (1977) Feng and McEvilly (1983) Jones and Nur (1984) Crustal electrical 10 to 20 km Nekut et al. (1977) conductivity zones Shankland and Ander (1983) Oxygen isotopes to 20 km Taylor (1977) Metamorphism >20 km Fyfe et al. (1978) Crack healing and sealing ? Formation of hydrothermal >5 km ore deposits Crustal seismic attenuation 7 to 15 km zones Low stress on faults 0 to 10 km? Etheridge et al. ( 1984) Richter and Simmons (1977a,b) Sprunt and Nur (1979) Ramsay (1980) Smith and Evans (1984) Norton and Knight (1977) Cathles and Smith (1983) Hermann and Mitchell ~ 1975) Winkler and Nur (1982) Raleigh and Evernden (1982)

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TIME-DEPENDENT HYDRAULICS OF THE EARTH'S CRUST Logic/ l D - h FIGURE 7.1 Rock and water pressure in porous rock in the Earth's crust. The gradients of the two lines are proportional to rock density and water density, respectively. When pore pres- sure is equal to hydrostatic, the difference between the two pres- sures gives rise to the tendency of the pores to inelastically close with time. 800 600 0 400 200 I\ !', ll 1~` n 2 4 6 8 10 Depth (km) FIGURE 7.2 Example of the depth and time migration of earth- qualces induced by reservoir impounding (from Chung-Kang et al., 1974~. As shown by Bell and Nur (1978), this induced seismicity requires the presence of free water at the depth of these induced earthquakes prior to the formation of the reservoir. ~5 hydrothermal ore deposits (e.g.; Norton and Knight, 1977~. The role of pore pressure is also central in understanding the processes of the earthquake failure process (Byerlee, 1967), earthquake prediction (Nur, 1972), induced seismi- city (Bell and Nur, 1978) (Figure 7.2), the mechanical processes in and below the accretionary wedge in subduc- tion zones (Zhao et al., 1986), the rate and depth of mag- matic melting and volcanism associated with subduction zones (McGeary et al., 1985), the nature of deep crustal seismic reflectors (Jones and Nur, 1984), and the state of stress in the crust (Zoback et al., 1987~. Answers to the three questions posed must at present be based largely on indirect evidence. For example, in situ measurements of crustal hydrologic properties typically reach to depths of only 2 to 3 km (Brace, 1980~. However, the presence of free water to much greater depths in the 8 vp it, ' - - -~0 :-f Vo 1~--~-: ~ 1--~-: \ Lit Hydr~aP.c 1-: t ' Lithostatic HyrJros~ic FIGURE 7.3 Schematic illustration of the development of a low compressional and shear wave velocity zone due to anomalously high pore pressure, based on extensive laboratory measurements (Nur and Simmons, 1969) and some field observations. crust is suggested by isotopic studies of batholithic rocks (e.g., Taylor, 1977; Norton and Taylor, 1979), studies that indicate that meteoric water may circulate to depths of up to 20 km. Deep crustal electromagnetic soundings have revealed zones of relatively low electrical resistivity, which suggests the presence of a continuous water phase (e.g., Nekut et al., 1977; Thompson et al., 1983), as inferred from laboratory studies of the electrical properties of rocks (Olhoeft, 1 98 1; Shankland and Ander, 1 983~. Seismology has also contributed to ideas about the hydrologic character of the crust. For example, Berry and Mair (1977) argue that crustal low-velocity zones could be due to Pf locally in excess of hydrostatic. This argument is based on experimental results such as those of Nur and Simmons (1969) (Figure 7.3), who showed that even in very low porosity saturated rocks, compressional velocity

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116 i 10 _ 20 2S _ 30 _ a Trident ~'ll~sre, b ~ (III/SEC} S ~1 ~I.S 1.0 0.5 0 By; ~ _) "I ./ \ _ : . .' ,! _ at,\_ EAST or S... I ~ (4 10 ~ (by (a) \\ , .~) t{C) 2. " WEST ~ S.~.~. (5 i' ) I ~ 1 logo 1 FIGURE 7.4 Compressional low-velocity zones near the San Andreas Fault in central California. The figure is taken from Raleigh and Evernden (1982), who based it on extensive crustal reflection measurements by Feng and McEvilly (1983~. Raleigh and Evernden (1982) suggest that the (a) low-velocity zone and (b) velocity anomaly ~ are due to high pore pressure in the depth range of 5 to 10 km or so. drops markedly as Pf approaches the confining pressure Pc. Feng and McEvilly (1983) discovered a prominent low-velocity zone near the near San Andreas Fault in California, which has been interpreted to result from high pore pressure (Raleigh and Evernden, 1982; Figure 7.4~. Similarly, crustal low Q zones, such as observed by Her- mann and Mitchell (1973; Figure 7.5), are also consistent with the presence of zones with pore pressure close to lithostatic (Winkler and Nur, 1982~. Using a similar line of reasoning, Jones and Nur (1984) suggested that reflec- tions from deep crustal fault zones may be associated with elevated Pf within or below these zones. The hypothesis of elevated Pf has also been suggested by Raleigh and Evernden (1982) to explain the low deviatoric stresses thought to exist along plate boundaries such as the San Andreas Fault. Other inferences about crustal hydrology are derived from geological evidence. For example, Fyfe et al. ~1978) and Etheridge et al. (1984) have reviewed geological indi- cators for free water, with Pf often exceeding hydrostatic, being widespread during low- to medium-grade regional metamorphism. Two principal lines of evidence follow. (1) The ubiquity of mineralized fractures whose micro- structure and orientation indicate that they formed in ex- tension (Ramsey, 1980~. On the basis of commonly ac- cepted criteria for brittle failure, this requires that Pf ex AMOS NUR AND JOSEPH WALDER ceed the minimum principal confining stress at the time of fracture formation. (2) Experimentally determined phase equilibria (with Pf equal to confining pressure Pc) are consistent with natural distributions of metamorphic min- eral assemblages. Together the above arguments suggests that free water must be fairly common at upper and mid-crustal levels. Furthermore, it appears that elevated Pf directly implies that the permeability of crustal rocks must be very low. Bredehoeft and Hanshaw (1968) and Hanshaw and Brede- hoeft (1968), for example, studied simple models of crustal Pf development and concluded that, in general, mainte- nance of elevated Pf for geologically significant periods of time requires the presence of some crustal horizons with very low permeability, down to 10-2~ m2 (1 ndarcy) and lower. The evidence and arguments favoring the presence of water at great crustal depth at high Pf and the consequent implication that crustal permeability must be low are in remarkable disagreement with the conclusion of Brace (1980), who after reviewing direct and indirect estimates of crustal permeability (Figure 7.6) argued that zones with 09 ( x 1~3 ) o ~2 20 . . . , , . 2000 1000 500 Boo 200 o, FIGURE 7.5 Estimated shear wave specific attenuation versus depth obtained from surface wave measurements in the stable North American continent (from Hermann and Mitchell, 1975~.

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TIME-DEPENDENT HYDRAULICS OF THE EARTH'S CRUST 2 o -2 _4 -6 -8 -10 ., , . Mine fractures Skee' card Basalt Gabbrc, , Joints, Pikes Pk. Motsushiro Oceanic inaction crust Earthquake I | Porous preCursors I | Ifa`JI! 98uQe Nat'l flow | Rangeley 1' 11 11 11 11 11 11 11 news Required for high pore pressure Shale gas cap 1 11 11 1 ~ - | Pierre shale l FIGURE 7.6 In situ permeability inferred from venous large- scale phenomena. Numbers in parentheses refer to accompany- ing notes, which explain the calculation of k (from Brace, 1980~. permeability of about 10-~5 m2 (1 mdarcy) or higher must exist down to at least 10 km depth. Brace therefore con- cluded that Pf is very unlikely to exceed hydrostatic pres- sure in regions where crystalline rocks extend to the sur- face and that Pf above hydrostatic in crystalline rocks could be maintained only if a cover of very low permeabil- ity (e.g., argillaceous) rocks were present. Also, Jones (1983) examined the hypothesized relationship between seismically reflective zones in the crust and elevated Pf by combining simple models of Pf development with syn- thetic seismograms. Jones concluded that, although ele- vated pore pressure can significantly affect the existence and amplitudes of reflected waves, such effects persist for geologically significant periods of time "only for a per- meability lower than that generally observed in laboratory measurements on crustal rocks." Clearly, a model is needed that can reconcile the two conflicting lines of evidence regarding crustal hydrology: evidence for ubiquitous high pore pressure and hence low permeability on the one hand, and evidence for relatively fast flow and fast pore pressure dissipation on the other. We will outline such a model by considering two general cases of crustal hydraulics: (1) time-invariant crustal po- rosity (and hence permeability) and (2) time-dependent porosity, permeability, and pore pressure. ~ / TIME DEPENDENCE OF POROSITY AND PERMEABILITY The simplest model one can envision for the hydraulics of the crust is based on the assumption that porosity and, consequently, permeability remain unchanged with time or are time invariant. In that case hydraulic permeability or diffusivity inferred from in situ phenomena (Brace, 1980) directly provides an estimate of the typical steady- state or ambient crustal permeability. In fact, Brace's compilation of numerous such estimates (Figure 7.5), made for a wide variety of rock types and geological settings, results in typical values of crustal permeabilities ranging from as much as 10 to 100 darcy for shallow fractured rock masses to 10-~ to 10-5 darcy for most rocks down to 10-6 to 10-7 darcy for shales and some gneisses. As pointed out by Brace (1980), pore pressure in a crust with these rock permeabilities will generally have to be close to hydrostatic, with the water at depth thus suffi- ciently connected to the free surface of the crust, so that the pressure at any depth is simply the weight per unit area of a column of water reaching the Earth's surface. Epi- sodes or regions of overpressure will thus be special cases, transient in time and localized in space. The apparent contradiction between the indirect evi- dence for elevated crustal Pf, on the one hand, and the inferred relatively high permeability throughout the crust, on the other hand, cannot be reconciled with this model. Suppose instead that porosity, permeability, and conse- quently pore pressure can vary significantly with time rather than remain static. Such variations have been in- ferred by D. Norton (University of Arizona) and co-work- ers in communication with fluid flow and mineralization associated with magmatic intrusion in the crust. Norton (Chapter 2, this volume) suggests that the pore fluid pres- sure induced by such intrusions sufficiently exceeds lithostatic pressure to cause natural hydraulic fracturing. Ramsay (1980) described indirect evidence for repeated episodic Pf pulses in the form of composite crack filing veins, presumably episodically precipitated from solution. In this chapter we explore the feasibility of this kind of episodic Pp buildup not as limited to magmatic intrusions but as a general behavior of the crust. Such general time dependence might allow for periods of fast fluid flow, for example, during episodes of Pf equal to lithostatic, brack- eting periods of lower pore pressure, and no or little flow. Brace's geological estimates may thus represent only the periods or episodes of fast flow and not the crust in gen- eral. The immediate question that arises is: How must porosity deep in the crust decrease with time, and can this decrease be rapid enough (e.g., due to inelastic processes in porous rocks)? If so, what are the conditions under

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118 which permeability changes through time to maintain Pf well in excess of hydrostatic? Three most obvious mecha- nisms potentially responsible for time-dependent changes in porosity and pore space configuration are (1) inelastic pore deformation, leading to pore closure; (2) dissolution, including pressure solution, and redeposition of solutes in the pores; and (3) the creation of fractures, with their subsequent healing and sealing. As porosity changes due to these processes, so will permeability. Possible relationships between porosity reduction and strain can be indirectly inferred from rocks that were once at considerable depths in the crust. Porosity reduction processes in rocks such as indicated by detailed studies by optical and scanning electron microscopy (e.g., Richter and Simmons, 1977a; Sprunt and Nur, 1979; Padovani et al., 1982) clearly demonstrate that crack healing and seal- ing are quite ubiquitous in a wide variety of crustal rock types, particularly in crystalline rocks. We use the term healing for former cracks in which the mineral filling is the same as the host grain and the term sealing for cases in which the crack filling is mineralogically different from the host grain. The material source for healing is likely to be local (i.e., nearby grains), whereas sealing may require an external or more remote source of crack-filling material transported via the pore fluid. Although there has been little laboratory work on po- rosity reduction in crystalline rocks, experimental studies provide some indications that porosity reduction could be relatively fast. For example, Sprunt and Nur (1976, 1977; I6: ~2 4 8 _ in o o 0 0 1 2 Tl M E (creeks) FIGURE 7.7 Experimentally induced inelastic porosity reduc- tion in a sandstone sample, subject to an overburden pressure of 1.2 kbar and pore pressure of 0.7 kbar for a period of 2 weeks at 250C. Note the rapid porosity decrease in a period of a week or so at this temperature (from Sprunt and Nur, 1976~. -! ~ - P. = 0.7kb Pc = 1.2kb AMOS NUR AND JOSEPH WALDER Figure 7.7) measured appreciable porosity loss, presuma- bly due to local pressure solution, in sandstone samples subjected to elevated temperatures (to 250C), pressures, and macroscopic shear stress (to ~500 bars) for 2 weeks. Their results indicate that porosity reduction rates in rocks subjected to tectonically induced deviatoric stresses can be fast, suggesting that porosity reduction rates in situ may also be geologically fast. Smith and Evans (1984) examined healing of cracks in synthetic quartz under elevated pressure (Pf = Pc = 200 MPa) and temperature (200 to 600C). Morphologically, healed cracks were strikingly similar to fluid inclusions and "microtubes" commonly seen in thin sections (e.g., Richter and Simmons, 1977b). Smith and Evans found that thin cracks healed extremely rapidly (in less than 1 hr) at 400C. It is likely, therefore, that healing and sealing are quite rapid on the geologic time scale under mid- crustal conditions. Evans and co-workers also found that the sealing rate falls off very rapidly with increasing crack aperture, so thick cracks (>1 mm?) may seal or heal very slowly. As pointed out by Brace (Massachusetts Institute of Technol- ogy, private communication, 1988), we do not know the crack aperture versus depth in the crust. However, the ubiquitous occurrence of fully sealed cracks in exposed or exhumed mid-crustal rocks and the evidence for sealing by repeated episodes (Ramsey, 1980) suggest that, in general, sealing is widespread and fast enough to leave only bubble chains behind. POROSITY REDUCTION WITH TIME The discussion above implies that porosity must gener- ally tend to decrease with time. This reduction leads to two important interrelated effects (Figure 7.8~: (1) the gradual expulsion of water out of the crustal pore space (if permea- bility is high enough) and (2) the gradual buildup of pore pressure within the pore space of crustal rocks if permea- bility is sufficiently low. Accordingly, two cases (Figure 7.9) for the development of crustal porosity with time, permeability, and pore pressure can be envisioned. Case 1 To illustrate this case, consider an element of porous crust at depth, subject to overburden stress, as shown in Figure 7.8. Due to porosity reduction processes, the pore space gradually decreases with time. If a permeable path exists between the subsurface rock element and the Earth's free surface, the fluid in the pores will gradually be squeezed out. The pore fluid pressure during this process will

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TIME-DEPENDENT HYDRAULICS OF THE EARTH'S CRUST _, ~-~3 Drained/ t \Undrained Cry l .~ / - _ - 2 0 ~ Pp- Pc FIGURE 7.8 Cartoon illustrating the possible development of a porous fluid-saturated rock, initially saturated and subject to stress and undergoing irreversible porosity reduction. If fluid escape is sufficiently fast relative to the pore pressure buildup Rate (due to porosity reduction), the rock will gradually lose its porosity and hence the pore fluid. If fluid escape is slow relative to pore pressure buildup, Pp will reach lithostatic pressure and cause natural hydraulic fractures to occur. obviously depend on the rate of porosity reduction on the one hand and the resistance to flow through the permeable path to the surface. If the resistance is low or, equivalently, if the permeability is sufficiently high, Pp throughout the duration of the porosity reduction process will be only slightly higher than hydrostatic. Under these conditions a gradual, continuous process of porosity loss accompanied by gradual water loss will take place, ultimately leading to a dry, pore-free crust. For this condition to be satisfied, the initial permeability of the rock element must be high and the rate of permeability decrease with porosity dk/dt must be small enough so that drainage can occur. A process that may lead to this sort of crustal porosity and permeability reduction without major Pp buildup is crack healing, which has been investigated in the labora- tory (e.g., Smith and Evans, 1984~. In this process pro- gressive elimination of pore space in the form of cracks in crystals due to mechanical closure and the healing of the bonds across the crack surfaces takes place. Under a fairly wide range of circumstances little trapped fluid remains behind and little connected pore space remains in the form of fluid inclusions. ~9 Case 2 A drastically different development of pore pressure will take place when permeability decreases more rapidly with time than porosity due to sealing and healing (Bernabe et al., 1982; Walder and Nur, 1984), so that kik > . Consider again an element of porous crustal rock at depth, again subject to overburden stress as shown in Figure 7.8. Again we expect the porosity to decrease inelastically with time. If a permeable path does not exist between the element and the free surface of the crust or the permeabil- ity of such a path is sufficiently low, the fluid in the pores will not be squeezed out fast enough, and the pore pressure of the trapped fluid will thus rise with time. If the porosity reduction rate ~ is sufficiently large, permeability k suffi- ciently small, and their rate of change with time or with each other are such that kik > , then pore pressure must increase with time. The rate of such pore pressure buildup will depend on the rate of porosity reduction ~ and the permeability k. Eventually Pp will reach its upper possible limit the least normal stress acting on' the element plus its cohesive strength. When Pp reaches that stress level, natural hydrofracturing will occur, involving a rapid epi- sode of fluid release together with a sudden reduction in pore pressure. As soon as the pore pressure drops, the flow path through the hydrofracture will close again. Because the process of porosity reduction continues, Pp will again build up toward lithostatic, leading to another cycle of hydrofractunng, fluid release, and sealing, etc. In this case, dominated by low permeability, pore pres ~Permeable~ ~ crust J Fixed lip, K / ~ ~ = 0 ~I With porosity \ reduction 4, > 0 l PP hydrostatic I No ~With sealing / \ sealing K IN Gradual loss of H2O Dry nonporous crust Pp-Ifthostatic Natural hydrofracturing Episodic loss | of H2O FIGURE 7.9 Flow diagram illustrating the possible paths that initially permeable, fluid-saturated crustal rocks can follow, depending on permeability, porosity, and their rates of change.

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120 sure oscillates episodically between lithostatic and less than lithostatic, with each oscillation involving a pulse of fluid release and flow and a short episode of fracturing, followed by a longer period of little or no flow, pore pressure recovery, and sealing. RATES AND MAGNITUDES OF PORE VOLUME STRAIN AND PORE PRESSURE BUILDUP To determine whether the transient processes described above the draining, drying, and porosity elimination of crustal rocks are actually geologically important and whether they are gradual or episodic, we need to estimate four parameters: (1) the magnitude of the porosity reduc- tion rate 0 required for Pp buildup, (2) the permeability k and its dependence on porosity to ensure Pp buildup, (3) the time required for pore pressure buildup in relevant crustal rock masses and correspondingly the duration of the Pp cycles, and (4) the time required or duration of these processes before they cease due to the elimination of connected porosity and fluid removal in situ. Walder (1984) and Walder and Nur (1984) investigated the conditions under which lithostatic pore pressure will develop and estimated the length of time required for its buildup due to porosity reduction. By dimensional analy- sis they show that the controlling factor is the dimension- less grouping pH _ ~ ~ pkg - = 1 , (7.1) where H is depth in the crust, Ap is the difference in density between rock and fluid, ,u is fluid viscosity, ~ is porosity reduction, k is hydraulic permeability, and F is the buildup index. When F < 1, pore pressure development is largely unaffected by porosity reduction. For F ~ 1, fluid pressure is strongly affected by porosity reduction. Furthermore, because F increases as the depth H to which porosity reduction occurs increases, high pore pressure is more likely at greater depth. This may be further en- hanced by the lower permeability k that is more likely at greater depth. As an example, Walder and Nur (1984) considered a 10-km-thick section of granitic rock undergoing porosity reduction. For the decrease of permeability as ~ decreases, they assumed the following relationship: k = ho $,, ,, (7.2) to - (c where ho is the initial value of permeability, So is the initial value of porosity, (c is the percolation threshold porosity for throughflow, and n is the exponent. Also assume that AMOS NUR AND JOSEPH WALDER n = 2 and 0c = 2 x 104, which is well below porosities typically measured in crystalline rocks (Q 210-3~. Assum- ing the initial permeability of 5 x 10-2 m2 (50 ndarcy) throughout the section (Brace et al., 1968), water viscosity p=2x 104Pa,Ap= 1.7x 103 kg/m3,WalderaIldNur found that F = 1 when 0 = 4 x 10-~6/s (Figure 7.10~. In other words, if porosity reduction were to proceed throughout the 10-km-thick section at a rate higher than 4 x 10-~6/s or 1 percent per million years, excess pore pressure would be generated and maintained. The next question we need to consider is whether the time required for pore pressure to build up to lithostatic is fast enough to be geologically important. This question is difficult to answer because few details are known about the processes involved and only little relevant experimen- tal evidence is available. However, much of this evidence indicates that porosity and permeability reduction can be very rapid, geologically speaking, if temperatures are suf- ficiently high. Smith and Evans (1984) found that crack healing rates, based on a model by Evans and Charles (1977), are most likely governed by processes with activa- tion energies around 50 to 100 kJ/mol, which in turn can be used to estimate in situ rates. Smith and Evans (1984) also found in the laboratory that crack healing in quartz requires several hours at 600C and several days at 400C. At the crustal depth of interest here (5 to 12 km or so) with temperatures typically ranging from 100 to 300C, the '.ok . . 111 _ ~ 0.8 _ An Or ,,, 0.6 _ In 0 0.4 _ z ~ 0.2 n LITHEST -5xlO / ~S2Xlo-t. , // _- _ ~4~-17 l HYDROSTATIC O _; I . I . I . , O 0.2 0.4 0.6 0.8 DIMENSIONLESS DEPTH 1.0 FIGURE 7.10 Fluid pressure as a function of depth for a 10-km- thick section undergoing uniform porosity reduction for several values of porosity reduction rate ~ (in s-l). Initial permeability is 5 x 10-2 m2 (50 ndarcy). Solid lines show hydrostatic and lithostatic pressure gradients. Dashed curves show fluid pressure profiles that would develop after porosity reduction for 2500 yr at indicated rates. Note that the fluid pressure would exceed lithostatic for the largest ~ value, which slightly exceeds the "critical" value for this geometry and permeability (from Walder and Nur, 1984~.

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TIME-DEPENDENT HYDRAULICS OF THE EARTH'S CRUST corresponding rates increase to a few hundred years. Sprunt and Nur (1977) found that porosity can be reduced signifi- cantly (by 30 to 40 percent) in laboratory experiments in sandstones subject to moderate shear stress at 250C over a period of 2 weeks. The corresponding period of porosity reduction at 150C would be, using the Smith and Evans activation energy, 102 to 103 longer, yielding at least sev- eral tens of years. Walder (1984) and Walder and Nur (1984) used a dif- ferent approach to estimate the minimum time for pore pressure to reach lithostatic pressure by considering the extreme case of a totally sealed rock mass. In this case the rate of pore pressure increase with time, AP//\t, is simply proportional to the rate of porosity change with time AP 1 . Sanyo, (7.3) T no pow where the proportionality constant By is given by p(~)(1 v) where ~ is the compressibility of the rock, ps is grain compressibility, and v is the rock's Poisson's ratio, which, by using the parameters listed earlier, reduces to AP ~ (2 x 10~ Pa) x 0 x At . `7.5' Thus, for a given porosity reduction rate , it is possible to estimate from Eq. (7.1) the critical permeability re- quired to cause pore pressure to build up and from Eq. (7.5) to estimate the time for this buildup to take place. As mentioned above, it is the decrease of pore volume or porosity with time that drives the pore pressure up, when permeability is sufficiently small. It is reasonable, for example, on the basis of the results of Sprunt and Nur (1977), to expect that porosity reduction would be espe- cially likely in porous rocks undergoing tectonic deforma- tion (and hence subject to shear stresses). Strain rates associated with active crustal deformation such as in oro- genesis or accretionary wedges are generally estimated at 10-~4/s to 10-~/s (Price, 1970; Heard and Raleigh, 1972; Rutter, 1974), whereas strain rates at or near faults are much higher (Pfiffner and Ramsay, 1982; Wojtal and Mitra, 1986~. If we assume that the pore volume strain rate o is only a small fraction of the total strain rate (e.g., 0/ = 0.01), we obtain 0 in the range of 10-~6 to 10-~3 so, and for / = 0.10, 0 is in the range of foes to 10-~2 so. Clearly, even these conservative estimates of porosity reduction rates as fractions of total strain rates are more sufficient to drive the pore pressure toward lithostatic while porosity lasts. Boat :E / OCR for page 113
122 GEOLOGICAL DURATION AMOS NUR AND JOSEPH WALDER taking pf = 3 x 10-5 per bar for water, Eq. (7.9) indi- cates that pressure rises to lithostatic of ~ = 100, 300, and 1000 bars required 1/3, 1, and 3 percent reduction of the Next we need to determine how many cycles of P release can take place at a given location. For this purpose initial porosity, respectively. Accordingly, if these lip we need to estimate the duration I2 of the crustal drying values represent realistic P fluctuation, somewhere be process and the porosity elimination. One estimate can be tween 30 and 300 episodes are possible. This value is in made by assuming that the cyclic buildup and release of P reasonable agreement with the estimate of fez based on the will proceed as long as porosity remains or 12 = A. Thus, duration ratio of Eq. (7.6) and is consistent with crack seal for 0 = 10-~6 s~', 12 ~ 300 x 106 yr, and for ~ = 10-15 so, T2 layers documented by Ramsay (1980). ~ 30 x 106 yr. These values are probably high estimates, first because porosity may begin to lose its connectivity at some finite value, thus reducing the amount available for the reduction process considered here. Furthermore, the rate of porosity reduction may be slower with lowered porosity. But even if we allow only one-tenth of the total porosity reduction to influence pore pressure increase, we still obtain periods of 30 x 106 yr (for o = 10-~6 so) and 3 x 106 yr (for o = 10-~5 so). These shorter values for T2 over yield the number of natural hydraulic fracturing epi sodes n ~2 A:. n ~ (7.6) ~1 with ~ = 104 to 106 yr, and I2 = 107 to 108 yr, we obtain n = 10 to 104 events. A different estimate of the number of P cycles n can be p made by considering the amount of porosity reduction needed to raise Pp to lithostatic pressure per Pa cycle. Assuming that the mass of fluid in the decreasing pore space is conserved during the Pp buildup phase of each cycle and is being reduced only during the expulsion phase, we can write AVf Mop (7.7) where Vf is the pore fluid volume, AVf is the change of pore fluid volume due to pore pressure AP, and Of is the fluid's compressibility. The quantity Ap represents the magnitude of the induced Pp. fluctuation during a cycle. If we ignore, as first approximation, the change of fluid density during the porosity reduction cycle, we can write AVf ~ , (7.8) Vf where Ao is the porosity change during a cycle. Combin- ing Eqs. (7.7) and (7.8) we obtain A0 ~ Hip (7-9) To WATER REPLENISHED BY SUBDUCTION The duration T2 of the time over which the crust dewa- ters could be significantly prolonged if additional waters are supplied to the crust from the lower crust or mantle below (Figure 7.12~. The most obvious possible source of such waters is associated with subducted oceanic slabs. It is generally thought that the oceanic slab is rich in water and hydrous minerals and that this water plays major roles in controlling the onset, amount, and rate of melting in and above the downgoing slab. A recent study by McGeary et al. (1985) showed, for example, that most of the promi- nent gaps in the circum Pacific active volcanic chains are associated with the subduction of anomalous oceanic crust, usually in the form of thick-rooted oceanic rises. One explanation for these gaps is that the rises somehow re- duce the supply of water to the melt zones, thus raising the 1. ~ ~'~ oceanic ~ L, Condren~l cow Oceanic crust ~ FIGURE 7.12 Cartoon illustrating the supply of subducted water into the crust overlying a subduction zone and some of the parameters that determine the magnitude of this supply and hence its effects on prolonging the episodic hydraulic behavior of the crust.

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TIME-DEPENDENT HYDRAULICS OF THE EARTH'S CRUST TABLE 7.2 The Main Time Constants for Time Dependent Hydraulic Behavior of the Crust Duration of a Pp cycle Time for crust to dry up Duration of subduction 103 to 105 yr 106 to 107 yr 107 to 108 yr melting temperature and causing a temporal cessation or reduction of volcanism. This model suggests that the subduction of normal oceanic crust does provide for a continuous supply of water into crustal regions below which subduction is taking place. Most probably this water is initially stored in the heavily fractured oceanic lithosphere, some of which migrates upon subduction into the overly- ing lithosphere and crust. Constraints on the amount of water that might be added this way to the crust overlying a slab may be obtained from a comparison between the pore fluid volume in the crust and the pore fluid volume that passes underneath while subduction lasts. The volume of fluid in the conti- nental crust Vc per unit length of subduction zone (Figure 7.12) is roughly Vc = TIDE, where To is thickness, D is the width of the crustal region overlying the subducted slab and tectonically affected by the subduction process, and is the average porosity over the thickness T. In the continental crust we consider the pore fluid to be present in the top T. = 12 km, with the average porosity ~ = 1 percent. With D = 300 km as a representative length of the crust overlying the subducting slab and which is tectonically affected by the subduction process, the vol- ume of water present per unit length of the crust is on the order of 30 km2. The total volume of fluid that is sub- ducted with the oceanic crust per unit subduction zone over the duration of subduction is V0 = v x ~ x T2 x 40, where v is subduction rate, 13 iS the subduction duration (and v x I3 = L2 iS the total length of slab subducted), T2 is the thickness of the porous oceanic crust, and 0 is its average porosity. For the subducted oceanic crust we take crustal thickness To = 6 km, average porosity also 1 per- cent, duration of subduction of 100 Ma, and subduction rate of 5 cm/yr, which yields a volume of subducted free water per unit width of slab on the order of 300 km2. This value of V0 is about 10 times Vc, which suggests that the waters released from the slab at depth can replenish dissi- pated crustal water, adding as much as several times the volume of initial fluid to the continental crust. As a result, the duration of the cycles of pore pressure buildup, natural hydrofracturing, and sealing may continue for longer peri- ods of time up to the duration of the subduction process, on the order of 103 yr (see Table 7.2~. 123 DISCUSSION AND CONCLUSIONS The original question posed in this chapter was whether free water is generally deep in the crust. As it turns out this question is inseparable from the question of the nature of porosity, permeability, and pore pressure in the crust and, most significantly, their dependence on time, as illus- trated in Figure 7.9. If we assume that porosity and, consequently, permeability and pore pressure are time invariant, and consider the hydrological evidence for easy fluid flow in the crust, it follows that crustal pore pressure must be generally hydrostatic to a depth of 10, 15, or even 20 km. This conclusion is in conflict with geological and laboratory evidence that implies that permeable paths in rock tend to clog very rapidly by healing, sealing, and inelastic deformation, all of which become very effective in crustal rocks even at moderately elevated temperatures. One way to reconcile the conflict between rapid flow on the one hand and rapid clogging on the other is to consider crustal hydrological behavior as varying with time. Although direct data are very sparse, the analysis in this chapter suggests that the most likely state of crustal porosity and water content is transient, with both porosity and water content as well as permeability decreasing with time. It is quite unlikely that these quantities are constant over geological time because inelastic deformation below a depth of a few kilometers in the crust must tend to cause pore closure. Such a tendency will be accompanied by squeezing of water out of the crust due to induced pore pressure. If crustal permeabilities are high enough and the rate of permeability decreases with time or porosity is sufficiently small, the dewatering of the crust will be a gradual, monotonic process. However, if permeability is low and its rate of reduction with porosity is relatively fast, the pore pressure of the trapped fluid will rapidly rise to overcome the least principal stress, leading to natural spontaneous hydrofracturing accompanied by the pulsed release of water and the loss of a little porosity (Figure 7.13~. This is followed by a drop in pore pressure, a prolonged buildup period, another hydrofracturing epi- sode, etc. It is especially intriguing that the episodic release process is most probable when tectonic deforma- tion, even at fairly low strain rates, is taking place. Estimates of the time required for P to reach lithostatic p and the amount of porosity reduction, especially in tec- tonically active areas, suggest that this kind of episodic hydrological and mechanical behavior of the crust is quite probable. The number of cycles expected at a given site depends on strain rate, permeability, depth, and other rock parameters, but simple analysis suggests that tens to hun- dreds of cycles may be expected. The duration of each cycle is estimated at 103 to 105 yr, whereas the duration of

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124 the crustal dewatering process is estimated at 106 to 107 yr if no additional waters are supplied to the crust. Such supply may be common where the ocean lithosphere was or is being subducted underneath the system. In such situations the geologic duration of the cyclic pore pressure behavior may last as long as subduction does, on the order of 108 yr. The likelihood that the Earth's crust experiences cycli- cal pore pressure buildup as suggested by Norton and Knight (1977) in conjunction with igneous intrusions, with P magnitude oscillating somewhere above hydrostatic to l~thostatic, has profound implications for crustal processes and our understanding of these processes. One such pro- cess is the formation of hydrothermal ore deposits and had (a) <~3, (b) FIGURE 7.13 Cartoon illustrating the pore pressure buildup and release envisioned in this chapter. (a) Pore pressure in the region of porosity reduction reached the minimum compressive stress and caused natural fractures to occur in the sealed rock surround- ing this region. Some fluid escapes through these fractures into the overlying lower pore pressure (Ph) region, causing a drop AP in pore pressure (dotted region) before (b) the induced fractures close again. AMOS NUR AND JOSEPH WALDER mineralized veins (Cathles and Smith, 1983; Vrolijk,1987~. Extensive geological evidence indicates that several types of ore deposits are formed by periodic precipitation from brines. Similarly many types of veins in rocks have been shown to have formed from repeated episodic precipita- tion from fluids in fractures (Ramsey, 1980~. The cyclic pore pressure behavior described in this chapter provides a very simple and compelling mechanism for the formation of these bodies. The cyclic fluctuation in crustal pore pressure may also play an intriguing role in the control and initiation of large earthquakes, which tend to be cyclic in time. In the past it has often been assumed that the repeat time of large earthquakes is basically controlled by the rate at which tectonic strain is accumulating, with fault strength essentially constant. More recently it has become apparent that some sort of time-dependent fault strength is required, if only to reconcile laboratory rock failure results with in situ fault rupture. The increase of P toward lithostatic during a pore pressure cycle as described above provides a simple mechanism for cyclic fault weakening, which in turn leads to cyclic failure. Unlike pore pressure changes associated with elastic and elastic dilatant defor- mation (e.g., Nur and Booker, 1971; Nur, 1972; Rice, 1975, 1979; Rudnicki, 1977) in which Pp buildup is very sensitive to geometrical details, pore pressure buildup due to the inelastic process considered here is fairly insensitive to the details of the stress field buildup around the impend- ing failure zone. Rather it is a robust process of sealing and trapping of the pore fluid in and around the fault zone and the gradual buildup of Pp due to porosity decrease until fault rupture begins. A related effect of this process has been suggested by Sibson et al. (1975) in which ine- lastic deformation and dilatancy work together to induce seismic pumping, which enhances the instability during failure. A third manifestation of the presence of high Pp may be deep crustal reflectors. As discussed by Eaton (1980), laboratory results (Nur and Simmons, 1969; Todd and Simmons, 1972) and field observations (Berry and Mair, 1977) together have suggested that high pore pressure zones in the crust would show up as seismic low-velocity zones. Eaton further suggested that such zones may come about when crustal waters are trapped under a permeabil- ity barrier or seal. Jones and Nur (1984; Figure 7.14) and Walder and Nur (1984) showed that such a seal can be effective but only when its permeability is maintained at very low values. Because such a seal is most likely to be broken repeatedly in areas subject to earthquakes, it can be effective only if healing and sealing processes are continu- ously active. It is quite possible that the process we out- lined in this chapter is therefore responsible for dynami- cally trapping high pore pressure zones in mid-crustal depth. These zones will last as pronounced seismic reflec

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TIME-DEPENDENT HYDRAULICS OF THE EARTH'S CRUST FIGURE 7.14 The possible role of high pore pressure zones on crustal reflections (from Jones and Nur, 1984~. Portion of the Wind River line 1 on the left, showing reflections from the Pacific Creek thrust at 6 s. Synthetics computed for a series of zones 110 m in thickness, alternating ones that have an initial lithostatic pore pressure. Several cases show the change in reflectivity as the pore pressure diffuses out as the product tk increases. tore as long as enough water remains in the pore space. The possibility that crustal seismic reflectors may be high pore pressure zones and hence mechanically weak is espe- cially intriguing in view of the growing evidence that these reflectors may represent subhor~zontal crustal de- tachment zones. Such detachments are mechanically very difficult to explain unless high pore pressure is actually involved. Finally, Oliver (1986; Chapter 8, this volume) suggested that deep crustal fluids can migrate horizontally over very large distances away from consumption or colli- sion zones. Our proposed processes of pore pressure development, and its consequent episodic behavior, espe- cially in continental crust overlying subducted slabs, pro- vide a mechanism that can drive fluids honzontally, the pore pressure needed to sustain such flow, and the low- permeability barrier needed to prevent the escape of pres- sur~zed brines upward. 125 ACKNOWLEDGMENTS The ideas and speculations presented in this chapter are the result of collaboration and discussions with students and colleagues for over a decade. Many of the ideas here can be traced back to work and papers by Eve Sprunt, Terry Jones, Lee Bell, Ken Winkler, Sue McGeary, Mark Zoback, Bill Brace, Gene Simmons, Brian Evans, Jim Byerlee, Mike Ether~dge, Denis Norton, and Rick Sibson. The work by these investigators and others has made it possible to understand as much as we do at present, but they should not be held responsible for any errors or mis- takes that we may have made in this chapter. We also wish to thank Steve Kirby and Bill Brace for their insight- ful comments, which helped clarify several important points. Much of the funding for the research reported here was provided by the Division of Mathematical and Physi- cal Sciences of the U.S. Department of Energy. REFERENCES Bell, M. L., and A. Nur (1978~. Changes due to reservoir- induced pore pressure and stresses and application to Lake Oroville, Journal of Geophysical Research 83(B9), 4469-4483. Bernabe, Y., B. Evans, and W. F. Brace (1982~. Permeability, porosity and pore geometry of hot-pressed calcite, Mechanics of Materials 1, 173-183. Berry, M. J., and J. A. Mair (1977~. The nature of the Earth's crust in Canada, in The Earth's Crust: Its Nature and Physical Properties, J. G. Heacock, ea., Geophysical Monograph Se- nes, American Geophysical Union, Washington, D.C., pp.319- 348. Brace, W. F. (1980~. Permeability of crystalline and argillaceous rocks: Status and problems, International Journal of Rock Mechanics in Mineral Science and Geomechanical Abstracts 17, 876-893. Brace, W. F., and D. L. Kohlstedt (1980~. Limits on lithospheric stress imposed by laboratory experiments, Journal of Geo- physical Research 85, 6248-6252. Brace, W. F., J. B. Walsh, and W. T. Frangos (19681. Permeabil- ity of granite under high pressure, Journal of Geophysical Research 73, 2225-2236. Bredehoeft, J. D., and B. B. Hanshaw (1968~. On the mainte- nance of anomalous fluid pressures. I. Thick sedimentary sequences, Geological Society of America Bulletin 79, 1097- 1106. Byerlee, J. D. (1967~. Frictional characteristics of granite under high confining pressure, Journal of Geophysical Research 72, 3639. Carter, N. J. (1976~. Steady state flow of rocks, Reviews of Geophysics and Space Physics 14, 301-360. Cathles, L. M., and A. T. Smith (1983~. Thermal constraints on the formation of Mississippi Valley-type lead-zinc deposits and their implications for episodic dewatering and deposit genesis, Economic Geology 78, 983-1002.

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