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9 INTRODUCTION Smoluchowski's Dilemma Revisited. A Note on the Fluid Pressure History of the Central Appalachian Fold-Th~ust Belt . TERRY ENGELDER The Pennsylvania State University ABSTRACT Cross-fold joints in the Central Appalachian fold-thrust belt propagated during periods of abnormally high fluid pressure prior to tectonic compaction and the development of first-order Alleghanian structures in the valley and ridge. These early joints, found in both the valley and ridge province and the plateau province, are organized in sets forming patterns that correlate across the Allegheny Front. Examples of early joints are found in the Devonian Brallier and Trimmers Rock Formations of the Pennsylvania Valley and Ridge and in the Genesee Group of the Appalachian Plateau. One interpretation is that high fluid pressures were generated by topographically driven flow across the Appalachian Basin as a con- sequence of uplift of the core of the Appalachians early in the Alleghanian Orogeny. The high fluid pressures accompanying this topographically-dnven flow system later facilitated the development of first-order structures in the valley and edge. Later joint sets that do not correlate across the Allegheny Front are more likely to be a consequence of fluid pressure pulses developed during local tectonic compaction and the development of first-order Alleghanian structures. These later joint sets vary in number and orientation from location to location. Smoluchowski's (1909) famous dilemma is that thrust sheets are too wide for emplacement by "dry" frictional sliding. Theoretically, the back end of wide thrust sheets should collapse under the large tectonic stress necessary to push the entire thrust sheet against frictional resistance. 140 The most popular solution to Smoluchowski's dilemma was presented by Hubbert and Rubey (1959) and Rubey and Hubbert (1959), who pointed out that the theoretical width of thrust sheets is greatly increased by an increase in fluid pressure and concomitant reduction in effective nor- mal stress across the basal decollement. Because fric- tional resistance is directly proportional to effective nor
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FLUID PRESSURE HISTORY OF THE CENTRAL APPALACHIAN FOLD-THRUST BELT mat stress, a reduction in effective normal stress has the net effect of reducing the push (i.e., tectonic stress) neces- sary for emplacement of wide thrust sheets. Lower tec- tonic stress reduces the tendency for fracture and thicken- ing at the back end of the thrust sheet (Davis et al., 19831. A reduction in effective normal stress occurs if the base of the thrust sheet cuts through a stratigraphic section containing abnormally high fluid pressures. How this high fluid pressure evolves is still subject to debate. Two mechanisms for generating high fluid pressures as men- tioned by Hubbert and Rubey (1959) are artesian flow and mechanical compaction of water-filled pores. In their companion paper Rubey and Hubbert (1959) focus on the generation of abnormally high fluid pressures by three mechanisms: (1) the uplift of sealed sand lenses, (2) tec- tonic compaction, and (3) compaction by overburden weight. They gave no further consideration to artesian flow. There are, of course, other mechanisms such as aquathermal pressuring (Barker, 1972), diagenetic dewa- tering of clays (Schmidt, 1973), and generation of CO2 and CH4 during the breakdown of hydrocarbons (Spencer, 1987~. Rubey and Hubbert (1959) do not examine artesian flow as a mechanism for generation of abnormal fluid pressures in foreland fold-thrust belts. By implication they consider it less important than tectonic compaction as a source for abnormal fluid pressures in overthrust terrain. The problem is that tectonic compaction occurs well after the initiation of thrusting. The development of overthrust terrain would be greatly facilitated if high fluid pressures developed before the onset of thrusting. Artesian flow may permit such a buildup in fluid pressure. Furthermore, experience in the Alberta Basin suggests that it should be taken seriously as a model for generating high fluid pres- sures in foreland basins (Toth, 1980~. Artesian flow is commonly understood to be groundwa- ter flow from a topographically high recharge area to a topographically low discharge area. This type of flow, also called topographically driven flow, is modeled by Toth (1962, 1980) using a flow net first illustrated by Hubbert (1940~. One consequence of topographically driven flow is that the discharge area is subject to pore water pressures in excess of hydrostatic developed be- cause the mechanical energy per unit volume of pore fluid is highest in the recharge area and lowest in the discharge area. A fortuitous combination of aquitards and topogra- phy can lead to near-lithostatic fluid pressures in the dis- charge area (Engelder and Bethke, 1985~. A topographi- cally driven flow system is steady state; leakage is bal- anced by recharge. This is in direct contrast to compac- tion-driven flow, where fluid pressure gradually returns to hydrostatic once compaction stops. Are there geological structures that enable the geologist 141 to distinguish topographically driven flow from other mechanisms including tectonic compaction that might have been the source of high fluid pressures in a foreland fold- thrust belt? In principle, regional joint sets could serve as such structures. This paper presents further evidence supporting the regional correlation of cross-fold joint sets (Joints with normals subparallel to regional fold axes) in the Appalachian foreland fold-thrust belt and then deals with the geological consequences of regionally developed cross-fold joint sets in terms of a mechanism for generat- ing the necessary pore-fluid pressure. CORRELATION OF CROSS-FOLD JOINTING ACROSS THE CENTRAL APPALACHIAN FORELAND FOLD-THRUST BELT Cross-fold joints are very prominent in Upper Devonian outcrops along the edges of the Finger Lakes of New York State (Figure 9.1~. By the first decade of the twentieth century geologists recognized that these cross-fold joints were organized into more than one set (Sheldon, 1912~. While tracing these cross-fold joints along strike of the New York Plateau for more than 200 km, Parker (1942) recognized that they maintained an orientation normal to fold axes despite a 30° change in strike of the fold axes. Parker made no judgment about whether cross-fold joints on either end of the map area are part of the same joint set. Nickelsen and Hough (1967) were the first to map joints as systematic sets in the Central Appalachians. They identi- fied five cross-fold joint sets in sandstones of the Appala- chian Plateau in Pennsylvania. By extrapolating to New York State, they identified three joint sets in Parker's map area. On mapping in the Appalachian Valley and Ridge, Nickelsen (1979) and Orkan and Voight (1985) attempted to correlate joint sets between the valley and ridge and plateau of Pennsylvania. Orkan and Voight (1985) identi- fied six cross-fold joint sets in the valley and ridge (Figure 9.2~. Nickelsen and Hough's (1967) and Orkan and Voight's (1985) technique for correlation of joints along strike depends largely on the orientation of joints. Their as- sumption is that joints of one set have similar orientations over large regions. If a suite of joints at an outcrop is misoriented by, say, 15° from an established joint set, this suite belongs to another joint set regardless of its orienta- tion with respect to local structures. As is illustrated in Figure 9.2, the consequence of this assumption is that members of a joint set do not change orientation even as fold axes swing through the Central Appalachians. On a regional basis the change in strike of fold axes is accom- modated by the overlap of joint sets of different orienta- tions. The notion for overlapping joint sets is supported by outcrops containing more than one joint set. Nickelsen
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FLUID PRESSURE HISTORY OF THE CENTRAL APPALACHIAN FOLD-THRUST BELT has many of the same difficulties as correlation along strike of the Appalachians, both Nickelsen and Hough (1967) and Orkan and Voight (1985) feel that joints corre- late across the Allegheny Front. [The Allegheny Front, which is the boundary between the Appalachian Valley and Ridge and Plateau, is largely controlled by the south- eastern edge of the Silurian salt basin where decollement faulting climbed up from the Cambrian shales into the salt beds. Low strength of the salt changed the character of the Appalachian foreland tectonics from duplex structures of the valley and ridge to layer parallel shortening of the Appalachian Plateau (Davis and Engelder, 1987~.] A correlation may be based on the common occurrence of a clockwise rotation of joint propagation in both the valley and ridge and the Appalachian Plateau. [Although the clockwise rotation of joint propagation is common through- out the region, Helgeson and Aydin (1989) report that a counter-clockwise rotation is well developed in some outcrops.] At Bear Valley Strip Mine Nickelsen (1979) identified eight stages of deformation with the first three being two phases of jointing followed by layer parallel shortening. These prefolding events witness a prefolding compression that rotates clockwise (Geiser and Engelder, 1983; Engelder, 1985~. All along the Allegheny Front from Williamsport to State College, Pennsylvania, early I,, A A A ~ D ~ N e w ... . .. .. .. '; ... . .'. . .. 143 cross-fold jointing shows a sequence indicating a clock- wise rotation of compression (Lacazette, The Pennsylva- nia State University, personal communication). This same sequence is well displayed in the Devonian Brallier For- mation at Huntingdon, Pennsylvania. The Devonian Brallier Formation of the central Appa- lachian Valley and Ridge is equivalent in age and litho- logic composition to the Genesee Group of the Appala- chian Plateau. Of all the lithologies in the valley and ridge from Cambrian carbonates up through Carboniferous flu- vial deposits, none carry joints that more closely resemble those seen on the Devonian section of the Appalachian Plateau. At an outcrop just south of Huntingdon, Pennsyl- vania, the Brallier dips to the southeast at about 15°. Like joints in the sandstone-shale beds of the Genesee Group on the Appalachian Plateau, two sets of cross-fold joints cut the Brallier, with the finer-grained beds carrying joints striking about 140° and the coarser beds carrying joints striking about 158°. The relative time of propagation of the joint sets may be determined using a joint spacing criterion developed by DeGraff et al. (1987) in the Genesee Group at Taughannock Falls, New York. Toward the north end of the Brallier outcrop joints in siltstone beds can be seen propagating upward from joints in shale beds. Based on the spacing criterion, joints in the silty shale FIGURE 9.2 Orkan and Voight's (1985) map of regional joint sets within the Central Appa- lachian fold-thrust belt. Sets A through E are those of Nickelsen and Hough (1967~. Set F was identified by Orkan and Voight (1985~. Regional joint sets are based on the data of Nickelsen and Hough (1967) and Engelder and Geiser (1980~.
144 (140°) propagated prior to those in the sandstone (158°) and, hence, show the same clockwise rotation as seen throughout the Appalachian foreland. Aside from the fact that these joints look like those found in the flat-lying Devonian rocks of the Appalachian Plateau, two pieces of evidence suggest that the cross-fold joints in the Brallier preceded folding. First, the joints have been rotated to dip between 84° and 87° to the south- west. If the present dip of the Brallier is removed, these joints are vertical, presumably the orientation at which they propagated. Second, some joints in the silty shale beds are decorated with slickensides and fibrous calcite, indicating a left-lateral shear. This is the type of slip expected for the compression responsible for later folding. Furthermore, the orientation of the calcite fibers indicates that slip direction has a shallower plunge than bedding dip. These are some of the same arguments used by Nickelsen (1979) to demonstrate early jointing at Bear Valley. It is likely that early joint sets propagated prior to the formation of the Allegheny Front. The Allegheny Front became significant only with the development of first- order structures of the valley and ridge, an event that took place long after early joint propagation, as shown by Nick- elsen (1979) at Bear Valley. Joints correlate across the Allegheny Front largely because that structural front did not exist at the time the joints formed. The mechanism for early joint propagation must precede and be independent of the development of first-order structures of the Appala- chian Valley and Ridge. In summary, the Upper Devonian shales and siltstones of the entire Central Appalachian foreland contain Alleghanian cross-fold joints that predate both major tectonic compaction and the development of first-order folds. FLUID PRESSURE AND JOINTING The regionally developed cross-fold joints of the Appa- lachian foreland formed at depth in the crust of the Earth, where the propagation of such joints requires the develop- ment of effective tensile stresses within the rock (e.g., Nickelsen, 1979; Narr and Currie, 1982~. Effective tensile stresses are possible under conditions of cooling (Voight and St. Pierre, 1974), curvature above the neutral fiber of a fold (Price, 1974), or significantly high fluid pressures (Secor, 1965~. In the foreland portion of mountain belts where folding would favor the propagation of strike joints (joints striking parallel to fold axes), curvature can be ruled out as a likely driving mechanism for cross-fold joints. At full depth of burial rocks have not cooled appreciably, so thermal cracking can also be ruled out as a driving mechanism. In contrast, a growing body of evi- dence suggests that high fluid pressure serves as the driv TERRY ENGELDER ing mechanism for joints at depth. Joints filled with such minerals as quartz, calcite, and chlorite are often cited as a manifestation of fluid pressure-driven joint propagation (i.e., hydraulic fracturing; e.g., Beach, 1977~. The mul- tiple fracture of crack-seal veins (e.g., Ramsay, 1980) and the repeated arrest of joints during propagation (e.g., Engelder, 1985) are fracture-related structures associated with the cracking of rock under the influence of high fluid pressure. An understanding of the extent to which joints correlate in both time and space is critical to identifying the mecha- nisms for generation of high fluid pressures in a mountain belt. Although rapid joint propagation occurs on the scale of outcrops, the timing of joint propagation at different locations across a foreland is less certain. Presently it is not clear whether fluid pressure increases simultaneously everywhere across a foreland or whether high fluid pres- sure occurs as local pulses affecting only small parts of the mountain range at one time. This, of course, leads to uncertainty about whether joint sets of the same orienta- tion should correlate across distances of tens to hundreds of kilometers. Certainly, based on data discussed above, current dogma for the Appalachians is that early joint sets do correlate over large distances (e.g., Nickelsen and Hough, 1967; Engelder and Geiser, 1980; and Orkan and Voight, 1985). Figure 9.2 suggests that joint sets, such as "set A," extend from the Great Valley of Pennsylvania to the far reaches of the Appalachian Plateau near Buffalo, New York. This is the Orkan and Voight (1985) interpretation of regional joint sets where joint development cuts across tectonic boundaries such as the Allegheny Front. If a correlation across the Allegheny Front is valid, the evolu- tion of a high pore pressure must have been a foreland- wide event. Not all mechanisms for generation of high pore pressure are regional in extent. Although deposi- tional and diagenetic mechanisms for the generation of high fluid pressure may be regional, they are considered unlikely mechanisms for a regional pore pressure event in the Appalachian fold-thrust belt because the earliest cross- fold joint sets are Alleghanian and, hence, developed long after deposition and diagenesis of the foreland sediments containing the joints. Although tectonic compaction af- fects an entire foreland, it was not uniform, as indicated by a variation is strain. The upper crust does not have the strength to simultaneously compact across the foreland until the core of the mountain belt has built into a sizable wedge (Davis et al., 1983~. Furthermore, strain in fore- lands is much too low to have been continuously active at plate tectonic rates for the duration of an erogenic event such as the Alleghanian orogeny in the Appalachians. For these reasons tectonic compaction seems unlikely to have contributed to a foreland-wide pore pressure event of the
FLUID PRESSURE HISTORY OF THE CENTRAL APPALACHIAN FOLD-THRUST BELT type required for early jointing. The only mechanism for generating a regional pore pressure event that cannot be rejected out of hand is the topographically driven flow system. Therefore, it is assumed to be the most likely source for high fluid pressures causing the simultaneous development of a joint set across the foreland, particularly during early stages of foreland development. DISCUSSION: OROGENIC PULSES AND THE GENERATION OF ABNORMALLY HIGH FLUID PRESSURE Early foreland-wide joint sets may be reconciled with topographically driven flow systems. In this case a re- gional flow system may have formed in response to uplift of mountains to the southeast of the Great Valley. To generate the high pressures for joint propagation, such a topographically driven flow system is, of course, going to require regional aquitards and a significant topographic gradient across the foreland. Because the upper Paleozoic section of the Central Appalachians developed very few through-going thrust faults, it may have served as a re- gional aquitard. Furthermore, evidence is accumulating that suggests that during the Alleghanian orogeny the Central Appalachians southeast of the Allegheny Front was quite thick (Levine, 1983; Paxton, 1983; Orkan and Voight, 1985~. Vitrinite reflectance and fission track data suggest that the Devonian and Carboniferous of New York and Pennsylvania may have been buried to a depth of 6 km (Friedman and Sanders, 1982~. Current studies of crustal flexure suggest that external forces were necessary for the magnitude of crustal depression necessary for the depth of burial found in Pennsylvania (Beaumont, 1981~. Such crustal loading can be accomplished during continent- continent collisions. The Alleghanian Orogeny was a period during which the continent of Africa collided with North America, producing continental edges having a topogra- phy similar to the India-Asia collision. This interpretation of regional joint sets requires that uplift at the core of the mountain belt preceded the development of first-order structures in the foreland. The early development of a regional flow system with elevated pore pressures facili- tates later thrusting and the development of first-order structures, particularly in the discharge area of the fore- land. Regardless of their correlation, everyone agrees that some cross-fold joints in the central Appalachian foreland fold-thrust belt propagated early and are organized into discrete sets rather than being distributed randomly or uniformly. The existence of multiple joint sets indicates that the syntectonic stress field changed in orientation during the evolution of the foreland fold-thrust belt. This regional organization of joints leads to the inference that 145 joint propagation took place during punctuated events. Not only did the orientation of the stress field change with time but the magnitude of the effective stress varied. Fluid pressures were not continuously at a level necessary for joint propagation, but rather some poorly understood events caused fluid pressure to fluctuate up and down throughout a region. Such events took place a finite number of times during the development of the foreland portion of the Central Appalachians. Mountain belts include a complex combination of dia- chronous structures superimposed over periods as long as 1 billion years ago. During the evolution of foreland fold- thrust belts, deformation is punctuated rather than continu- ous. Punctuated events called orogenic pulses are identi- fied on the basis of the appearance of an arbitrarily chosen set of structures within the mountain belt. For example, a regionally developed disjunctive cleavage may be attrib- uted to one orogenic pulse, whereas a second cross-cutting cleavage may be attributed to a later orogenic pulse. With few exceptions the duration of an orogenic pulse is ex- tremely difficult to measure. The intensity of an orogenic pulse is often correlated with the finite strain within rocks or the regional shorten- ing associated with folding and faulting. Orogenic pulses become increasingly hard to discriminate as the finite strain or regional shortening decreases. Although the case may be argued that major structures such as folds are the signa- ture of a single orogenic pulse, multiple joint sets within folds are themselves witness for multiple orogenic pulses prior to the folding event. Regional joints, particularly sensitive indicators of individual orogenic pulses, are commonly found in the unmetamorphosed foreland where more than one set may cross-cut. Cross-fold joints may propagate even during very mild orogenic pulses and in many instances before significant bed rotation. These mild orogenic pulses in the foreland may reflect uplift events in the core of the mountain belt or periods of rapid tectonic compaction. Unlike faults, folds, or finite strain markers of any sort, the propagation of joints is so close to instantaneous that one moment in the history of mountain building is recorded. The convenience of joint sets is that stress trajectories associated with an orogenic pulse can be mapped with reasonable confidence (Ode, 1957~. The development of several joint sets suggests that fluid pressures were not continuously lithostatic through- out the Alleghanian orogeny. If fluid pressures were continuously at lithostatic during realignment of the stress field, then joints should have a uniform distribution of orientations rather than appear as isolated joint sets. Multiple joint sets suggest that fluid pressures rise to lithostatic levels during short-lived events before pore fluids leak off to drop the pressure well below that needed for joint propagation. Fluid pressures rise again once the
10 Fluid Pressure History in Subduction Zones: Evidence from Fluid Inclusions in the Kodiak Accretionary Complex, Alaska PETER VROLIJK~ GEORGIANNA MYERS2 University of California, Santa Cruz ABSTRACT Fluid inclusions offer a simple and elegant means to examine the history of fluid pressure, temperature, and composition at intermediate levels in subduction zones. At deeper levels ductile deformation mechanisms tend to disrupt fluid inclusion relationships in veins. Fluid inclusions provide a direct record of the fluid phase and apparently preserve relatively short-term changes in fluid pressure. More- over, fluid inclusions are found in veins that can be directly tied to the develop- ment of structural fabrics in the rock. In syntectonic veins of the Kodiak accre- tionary complex, Alaska, fluid inclusions record fluctuating fluid pressures. These fluctuations reflect a history of fracture opening, continued fracture growth, and creation of an interconnected fracture network, with inferred fluid flow toward shallower levels within the subduction zone. Fluid inclusions also record fluid temperature at the time of inclusion entrap- ment and thereby indicate the temperature of fluids involved in the deformation of rocks in the decollement zone during active subduction. Data from the Kodiak accretionary complex indicate that fluid temperatures at 10 to 15 km in the ancient Kodiak subduction zone were two to three times higher than predicted by conduc- tive heat flow models. The cause of this temperature anomaly appears to be the migration of warm fluids along the decollement zone from deeper structural levels. These data, in conjunction with emerging data from both modern and ancient subduction complexes, suggest that high fluid pressures are common in subduc iCurrent Address: Exxon Production Research Company, Houston, Texas 2Current Address: Minnesota Pollution Control Agency 148
FLUID PRESSURE HISTORY IN SUBDUCTION ZONES 149 lion zones and that the presence of high fluid pressures has a profound influence on the geology at convergent margins. The manifestations of high fluid pressures include the style of structural deformation, heat flow, modifications of diagenesis and metamorphism by tectonically driven fluid flow, and effects on the global water and geochemical budgets. INTRODUCTION High fluid pressures are probably more common in subduction zones than in any other tectonic environment. In subduction zones water-rich sediments are rapidly dragged with the subducting oceanic crust to great depth. The sediments directly overlying the oceanic crust, which have the greatest potential for being subducted, are typi- cally fine "rained and pelagic with low intergranular per- meability (Moore, 1975; Shepherd and Bryant, 1983~. The rapid sediment burial afforded by plate convergence and subduction, in combination with the common occurrence of fine-grained sediments, should theoretically lead to the pervasive development of high fluid pressures (Walder and Nur,1984~. Understanding the fluid pressure history in subduction zones has regional and global significance. Many aspects of the geology, including the shape of accretionary wedges (Davis et al., 1983), the development of thrust faulting (Hubbert and Rubey, 1959), fold vergence (Seely, 1977), heat transport (Reck, 1987; Vrolijk et al., 1988), the di- agenetic and metamorphic history (Etheridge et al., 1983; Ritger et al., 1987), and the support of benthic organisms (Suess et al., 1985), are affected by high fluid pressures and resulting fluid flow. The global water and geochemi- cal budgets also depend on the fluid pressure distribution in subduction zones because mass balance calculations suggest that water must return to the ocean through sub- duction complexes to prevent the world's oceans from being subducted into the mantle (e.g., Fyfe et al., 1978; Ito et al., 1983~. Fluid pressures appear to play a direct role in mineral diagenesis (e.g., Bird, 1984; Koster van Groos and Gug- genheim, 1984, 1986, 1987) and therefore may in part determine the depth at which water is expelled from hy- drous minerals. In the presence of high fluid pressure, montmorillonite retains interlayer water to much higher confining pressures than under hydrostatic conditions (Hall et al., 1986; Colten-Bradley, 1987; Koster van Groos and Guggenheim, 1987~. Smectites in ocean crust and sedi- ments subducted beneath accretionary prisms may lose water according to the fluid pressure distribution. Deter- mining where water-rich minerals dehydrate in a subduc- tion zone also has important implications for the genesis of arc magmatism (e.g., Gill, 1981~. EVIDENCE FOR HIGH FLUID PRESSURES Investigations in modern subduction zone environments have led to the discovery of several tantalizing results. On DSDP Leg 78A in the Barbados Ridge Complex, Moore and Biju-Duval (1984) inferred high, near-lithostatic fluid pressures along the decollement zone, or detachment hori- zon, between the subducting Atlantic and overnding Car- ibbean plates. In the Japan trench, von Huene et al. (1980) attributed lower sediment density in highly fractured cores to fracture porosity and overpressuring. Similarly, wells in subduction zone forearc settings record fluid pressures far above hydrostatic (Shouldice, 1971; Hottman et al., 1979~. The common occurrence of mud volcanoes and mud diapirs in accretionary complexes also suggests the presence of high fluid pressures (Shouldice, 1971; von Huene, 1972; Brown and Westbrook, 1987; Langseth et al., 1988~. Whereas none of these studies have determined the distribution of fluid pressures in subduction zones, they strongly suggest that high fluid pressures may be common. Indirect evidence for high fluid pressures in modern environments comes from pore water chemical and ther- mal data (e.g., Yamano et al., 1982; Davis and Hussong, 1984; Kulm et al., 1986; Moore et al., 1987; Ritger et al., 1987; Gieskes et al., 1989~. Both types of data indicate anomalies along subduction zones, and further considera- tion of these data suggest that anomalies can be sustained only by relatively rapid fluid flow; which is likely aided by high fluid pressures. Mechanical models of subduction zones also suggest that high fluid pressures are present (e.g., Davis et al., 1983; Shi and Wang, 1988~. In addition, a conceptual model of subducting sediments suggests that fluids cannot easily escape along sedimentary layers toward the seafloor (Figure 10.1~. In the model presented in Figure 10.1 a tectonically undisturbed sedimentary layer extends from in front of the deformation front far beneath the accretion- ary prism; this bed remains within the subducting plate throughout the model. The geometry of the subduction zone is modeled after the Eastern Aleutian trench (von Huene et al., 1985~. During subduction a fluid pressure gradient will develop along the sedimentary bed because of the increased load of the accretionary prism, which will encourage fluid flow from beneath it. However, in a fixed
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