A simplified analysis of parameters controlling dewatering in accretionary prisms

Transcription

1 Earth and Planetary Science Letters, 109 (1992) Elsevier Science Publishers B.V., Amsterdam [MKI A simplified analysis of parameters controlling dewatering in accretionary prisms Barbara A. Bekins and Shirley J. Dreiss Earth Sciences Board, University of California, Santa Cruz, CA 95064, USA Received March 19, 1991; revision accepted November 15, 1991 ABSTRACT One of the many dynamic geologic processes taking place at subduction zones is the compaction-driven dewatering of seafloor sediments as they are accreted to the overriding plate. The rate of dewatering is equal to the divergence of the sediment matrix velocity field. This rate can be estimated analytically if simplifying assumptions are made about the geometry of the prism and motion of the sediments. The analytical expression depends only on the sediment accretion velocity, thickness of the accreted section, prism taper angle, and sediment porosity distribution. A sensitivity analysis of the solution shows that the fluid production distribution is relatively insensitive to the sediment porosity distribution. However, the solution is very sensitive to the taper angle of the wedge. High-angle wedges expel almost all of the incoming water within 20 km, while low-angle wedges may retain a significant fraction of the incoming water for 50 or more kilometers. Thickness of the incoming section is also important. Dewatering of thin accreted sections is more concentrated near the toe of the wedge. Analyses of transects through the Northern Barbados, Makran, Vancouver, and Nankai accretionary prisms illustrate a range of dewatering rates and spatial distributions of dewatering. 1. Introduction The fate of pore fluids entering subduction zones is a topic that recently has attracted much interest because of the possible effects of fluid flow and elevated pore pressures on sediment properties, heat and solute transport, and diagenetic reactions. An initial step toward understanding these processes is the computation of a fluid mass balance, including sediment dewatering rates in the accreted sediments. A number of studies have estimated fluid balances for accretionary prisms (e.g., Nankai [1], Barbados [2,3], Makran [4], and Cascadia [5]). These estimates, which demonstrate that rates of fluid generation vary greatly among different prisms, necessarily contain large uncertainties. Such uncertainties arise because of the sparseness of available data, required simplifying assumptions for complex mechanical processes, and spatial and temporal vari- Correspondence to: Barbara A. Bekins, Earth Sciences Board, University of California, Santa Cruz, CA 95064, USA. ability in both the processes and material properties. In this paper, we revisit mass balance calculations for estimating fluid losses from porosity differences in accreted sediments. Our goal is to determine the sensitivity of these calculations to uncertainty in the data by developing a solution in which the parameters describing the data can be easily varied. Conceptually, it is easiest to envisage sediment compaction relative to the moving solids (Fig. la). If we consider the fate of a particular packet of sediments as it enters the prism and migrates arcward relative to the deformation front, we see that its burial depth increases so that it undergoes further consolidation and porosity decreases. The volume of water lost from the sediment packet is equal to the change in pore space as the packet is incorporated at greater distances and depths into the prism. The rate of fluid production then depends on the velocity at which the sediments migrate relative to the deformation front and the porosity change along the sediments' travel path. Thus, when computing dewatering rates, it is usually most convenient to use a X/92/$ Elsevier Science Publishers B.V. All rights reserved

2 276 B.A. BEKINS AND S.J. DREISS a. bo W 1 z Coordinate Mapping... Sediment Paths Fig. 1. Schematic of a prism profile and the idealized uniformly divergent path of an accreted sediment packet as it enters the prism and moves arcward. The variables used in the dewatering solution are: the accreted sediment thickness, h0; the accretion velocity, v0; the seafloor slope angle, a; the subduction angle, /3; the depth of an incoming sediment packet, z0; the depth of the same packet in the wedge at some later time under our assumption of uniformly diverging trajectories, z; the distance arcward, x; and the vertical coordinate, y. The dewatering solution is found by mapping the wedgeshaped domain at the top to the rectangular domain shown below it. (See Appendix A.) The variables in the mapped domain are: distance arcward, u, and vertical distance, w. flame of reference pinned to the deformation front and to assume that the wedge propagates as a self-similar prism. In this flame of reference, we can look at a particular elemental volume in the wedge that is stationary relative to the deformation front, and has both solid matrix and saturated pore space moving through it. This is the flame of reference that is most commonly used to calculate fluid production and the calculation is based simply on the conservation of mass of the solid matrix. Sediments are assumed to enter the upstream side of the elemental volume with some mean porosity and velocity and may leave the element with a different mean porosity and velocity. If we assume that no net change in the solid mass occurs, then any change in sediment velocity within this volume is equivalent to the fluid loss. r U X If simplifying assumptions are made about the geometry of the prism and motion of the sediments, an analytical expression can be derived for the dewatering rate throughout the prism. Here, we derive an expression for dewatering in a cross-section with a self-similar geometry, in which the dewatering rate depends on only the accretion velocity, thickness of the accreted section, prism taper angle, and sediment porosity distribution. We then examine the effects of each of these parameters on computed dewatering rates to describe how the distribution of dewatering might be expected to differ between prisms with different geometries and sediment properties. These generic simulations demonstrate which of the parameters most affect the computations and therefore need to be well defined. Finally, w e compare the amount and distribution of dewatering rates along profiles in four accretionary prisms: Makran, Vancouver, Nankai, and Northern Barbados. 2. Estimation of the dewatering rate The fluid production from loss of storage in compacting sediments appears as a term in the equation for fluid flow in deforming saturated sediments [6]. When applied to an accretionary complex, the rate of fluid production is equivalent to the sediment velocity change in a control volume with fixed coordinates with respect to the deformation front [2]. This term represents the volume of water freed per unit time by a unit volume of the compacting sediments. To compute the dewatering rate which is given by the divergence of the sediment velocity field, V.V, we first develop an analytical method to compute the sediment velocities in the prism. We start with the steady-state equation for conservation of sediment mass: V. [ps(1-n)v] =0 (1) where ps is the density of the individual sediment grains, n is porosity, and V is the sediment velocity. If we assume that the sediment grains are incompressible, then this equation can be rearranged by expanding the product derivative: b~.~n V.V (1 -n) (2)

3 A SIMPLIFIED ANALYSIS OF PARAMETERS CONTROLLING DEWATERING IN ACCRETIONARY PRISMS 277 For a two-dimensional cross-section of a wedge, with the coordinate system shown in Fig. la, eqn. (2) becomes: vx~ x +vy (3) ~x ay 1 - n where v x and vy are the unknown horizontal and vertical components of the sediment velocity. The relationship between the vertical coordinate, y, in the Fig. la coordinate system and depth below the seafloor, z, is: h0 z = -~- +x tan a-y (4) where h 0 is the thickness of the incoming accreted section, and a is the slope angle. We seek a solution which gives v x and vy in terms of the porosity, position in the prism, and the relative plate convergence velocity. The first step is a simplifying assumption about the sediment trajectories through the prism. We assume that the flow lines diverge uniformly from the deformation front (Fig. la). For this type of flow field, Karig [7] traced the path of a sediment packet which enters the prism at a depth z o. When this packet has progressed to a distance x arcward from the deformation front, its depth in the Fig. la coordinate system is given by: z --z 0 [x 1 + ~--~0 (tan a + tan/3) l (5) where /3 is the subduction angle. We find the sediment velocities by mapping the wedge-shaped problem domain to a rectangle (Fig. lb). In the new domain, the sediment velocity for our simplified flow field has no vertical component. Thus in this domain, there is only one unknown, the horizontal sediment velocity. We transformed eqn. (3) to the new domain with linear mapping and found the solution for this velocity. Appendix A gives a detailed description of the solution method. Once the horizontal velocity is found, the vertical velocity component immediately follows from the assumption of uniform divergence. The two velocity components are: vx( x' z ) = v ~(( x, ~ (6) [ v (o, Zo)] v,(x, z) = Vx [ v0 (7) where v 0 is the incoming x-component of the sediment velocity at the deformation front and is constant for the whole accreted section. Inspection of this solution shows that the horizontal velocity is controlled by two effects: thickening and porosity loss. In this model, the factor (Zo/Z) is always less than or equal to one since the depth of sediments proceeding through the idealized wedge always increases. This factor thus quantifies the decrease of sediment velocity caused by the thickening of the wedge arcward. It does not depend on depth but is constant along any vertical profile. In other words, if the sediment porosity was a constant value for the whole wedge such that the velocity was only affected by thickening, then the horizontal sediment velocity would be the same along each vertical profile. The second factor is the ratio of the fraction of solids in a sediment packet as it enters the prism to the fraction in the same packet at a distance x from the deformation front. Generally porosity decreases in a packet as it proceeds through the prism, so that n(x, z) < n(0, z0). Thus this factor is also less than one and quantifies the rate of sediment slowing caused by porosity loss. The vertical velocity in eqn. (7) is given by the horizontal velocity, Vx, times the ratio of the vertical sediment velocity of a sediment packet when it is accreted, vy(0, z0), to the horizontal accretion velocity, v 0. In other words, a packet accreted at an initial depth z 0 follows a path with a fixed ratio of vertical to horizontal velocity. This result is consistent with our assumption that the sediment lines follow uniformly diverging trajectories. We may now compute the sediment dewatering rate. Expanding the right hand side of eqn. (3) using eqns. (5), (6), and (7) gives: voh o [1 - n(0, Zo) ] [ho+x(tan a+tan/3)] [1-n(x, z)] 2 Vz(0, z0) n] x Ox v o Oz (8) This expression depends on the incoming sediment velocity, Vo, and thickness, h0, the prism taper angle, a +/3, and the porosity distribution, n(x, z). Note that the rate of fluid production, V-~', is a function of both the arcward distance

4 278 B.A. BEKINS AND S.J. DREISS from the deformation front, x, and the depth below the seafloor, z. For any accretionary complex, estimates for the prism taper angle, entering sediment velocity, and porosity distribution, combined with eqn. (8) yield estimates of the rate of pore fluid storage loss at any location in a cross-section of the accreted sediments. These estimates may be used to predict pore fluid pressures and fluid flow velocities in the prism following, for example, [6]. Since the parameters used to describe a specific prism complex may be poorly constrained, we conducted a series of computations to determine which parameters have the greatest effect on the distribution of fluid production. 3. Sensitivity analysis To investigate the importance of the various parameters controlling dewatering, we computed a non-dimensional quantity which allows consistent comparison between different cases. This quantity is the ratio of the volume rate of fluid expulsion to the rate that pore fluid enters the 1.0 [ a) Variation with prism.+ taper... angle..+_:_:.~::_:::1 1.0 b) Vari~ n with incoming r~limont thiekne~" I ,"'"'""... o " o.8.=~ ,," 0.2 r/ ~-._..!Od~g. i 0.2 ' ' ~ 1.Okra kin ,, Distance 0an) Distance 0an) 1.0 c) Variation with seafloor porosity 1.0 d) Variation with porosity-depth panmeter.,% i ' n o = / b = 0.6/kin... n o = o.so... b = 0.4/kin , l. t.,. l... l,... i.. i., i.,. i Distance 0=n) Distance (kin) Fig. 2. The ratio of the cumulative rate of dewatering to the rate that pore water enters the prism in the accreted sediment column. This ratio is always less than one since the cumulative expulsion rate cannot exceed the rate at which fluid enters the complex. The plots were made with the following base parameter values: h 0 = 1.0 km, a = 1.0, /3 = 2.0, n o = 0.60, b = km -1. In (a) the taper angle is varied while the other parameters are held at the base values. In (b) the incoming sediment thickness is varied. In (c) the seafloor porosity is varied and in (d) the porosity-depth parameter is varied.

5 A SIMPLIFIED ANALYSIS OF PARAMETERS CONTROLLING DEWATERING IN ACCRETIONARY PRISMS 279 complex with the accreted sediments. Sediments entering the accretionary complex tectonically transport the fluid volume contained in their pore space into the complex. The rate that this volume of fluid enters the complex may be estimated by: h0 Oo = vohofo n(o, z) dz (9) Much of this incoming pore fluid is eventually driven from the prism by compaction. The volumetric rate of total fluid loss at a distance x from the deformation front is the integral of the sediment dewatering rate over the prism: fx fz~(x)-~ Q(x) =~0-0 V-~'dz dx (10) where Zd(X) is the depth of the decollement at a distance x arcward from the deformation front. Now consider the ratio Q(x)/Q o. This ratio ranges from zero to one and represents the fraction of the incoming pore fluid that is expelled from the prism within x of the deformation front. We computed this ratio for a number of cases with different geometries and porosity distributions and plotted the results against distance arcward from the deformation front (Fig. 2). In all of these cases the prism porosity was described by Athy's equation [8]: n(z) =n o e -bz (11) where n o is the value of the sediment porosity at the seafloor and b describes the porosity loss with depth. We assume for this first analysis that n o and b are uniform over a given prism so that the porosity-depth profile does not change with distance arcward from the deformation front. Figure 2 shows the fraction of incoming water which is expelled for cases with different parameters. The parameters varied in each plot were respectively: the prism angle, a +/3, the accreted thickness, h 0, the seafloor porosity, n 0, and the porosity loss with depth, b. In the following paragraphs we discuss methods for estimating these parameters and describe the results of our sensitivity analysis. 3.1 Prism geometry Typically, the geometry of an accretionary complex can be obtained from high-quality depth-corrected seismic sections. Published values for the thickness of the incoming sediment section, the slope angle and the subduction angle are available for a number of prism complexes. The validity of these estimates varies since the thickness of the incoming section may change with time and the total prism angle may vary with distance from the deformation front. Nevertheless these parameters are better constrained than those which describe the porosity distribution of the prism sediments. From Fig. 2, we can see that the prism angle has the strongest effect on the distribution of dewatering of any of the factors we considered. High-angle prisms lose most of their incoming pore water by about 20 km from the deformation front, while low-angle prism sediments may retain this water for more than 60 km. Clearly, in the higher-angle prisms a large fraction of the accreted sediments is deeply buried within a short distance of the deformation front. This burial results in compaction which significantly affects the pore fluids in the first 20 km of the toe. If the sediments are sufficiently permeable there may be substantial fluid flow and associated transport over this region. Alternatively, in low permeability sediments, we might expect high pore fluid pressures to persist in this zone. The important result here is the distance over which these effects may be significant and the fact that the angle of the wedge is the primary controlling factor. In prisms with lower angles, the effects of compaction-generated pore fluids are spread out over a larger distance from the deformation front and may appear less significant in field observations. The second most important parameter controlling the distribution of dewatering is the thickness of the accreted section. Although the volume of water expelled from a thin incoming section is small compared to a thicker one, compaction is more concentrated near the toe in thinner sections. Thin sections have a higher average porosity than thick ones, so the initial effect of stacking and burying is more significant. From Fig. 2b we see that for a thin sediment section the dewatering is concentrated within about 20 km of the deformation front, while thicker sections may continue to exhibit dewatering effects for 60 km or more.

6 280 B.A. BEKINS AND S.J. DREISS 3.2 Prism porosity The uncertainty associated with sediment porosity estimates is much greater than for geometry estimates. Porosity data may be obtained directly from measurements of core or dredged samples. We used porosity data from the Ocean Drilling Program (ODP) Leg 110 reference site, 672, to estimate the porosity parameters for Northern Barbados by performing a least-squares fit using eqn. (11) (Table 1 and Appendix B). However, the data from this site show considerable variability, primarily from differences in lithology [9]. Alternatively, porosities may be estimated from seismic compressional velocities together with empirical relations appropriate for the sediment lithology. This method was used by Davis et al. [5] for Vancouver and by Minshull and White [4] for Makran to obtain values for n o and b that best fit the porosity profiles of the incoming seafloor sediments and the prism sediment sections (Table 1). Porosity parameters estimated in this manner are dependent on the model that is used to interpret the seismic velocities and do not necessarily represent local variations in porosities. Fortunately, computed dewatering rates are less dependent on the values used for n o and b in eqn. (11) than on the geometry of the prism and the thickness of the incoming sediments. Figures 2c and 2d show the distribution of dewatering for values of n o between 50 and 80% and b between 0.4 and 1.0 km -1. Sediments with higher surface porosities lose a slightly greater fraction of their pore water. This is because the derivative of porosity with respect to depth is greater when the surface porosity is higher. Since the derivative describes the decrease in porosity with depth, the higher surface porosities lead to stronger burial induced dewatering. However there is very little difference between the curves for the various values. The depth factor, b, has a somewhat greater influence on the dewatering process. Recall that a low depth factor indicates that the porosity in the section decreases slowly with depth. Thus in this type of section, deeper burial results in a relatively small porosity loss. By the same reasoning, a higher depth factor leads to greater burial-induced porosity loss and dewatering. 4. Site analyses Examples of accretionary prisms at four specific sites serve to illustrate the results of our sensitivity analysis. These sites are: Northern Barbados, along the ODP Leg 110 transect, Vancouver, along the seismic line [5], Makran, TABLE 1 Parameters used for site-specific dewatering calculations Site and Reference Total Angle ct+~ (deg.) Accretion Velocity Vo (cm/yr) Accreted Thickness ho (kin) Seafloor Porosity no Porosity Depth-loss b (/o~-i) Entering Volume x I0 6 Qo (m2/s) Vancouver Line [5] Makran [4] Northean Barbados ODP Leg 110 Transect [11] and Table 3 Nankai DSDP Leg 87 Transect [10], [12] I.I ().675

7 A SIMPLIFIED ANALYSIS OF PARAMETERS CONTROLLING DEWATERING 1N ACCRET1ONARY PRISMS la) ~ ~ / ~ --- Northern Barbados " --_ I o.2?/~..... M~ran J ~Vancouver 0.0 ' ' ' ~ ', J ' ' ' ~ ', ~ J, 1.6.(~- ~ Distance (km) o.8. \... ~. 0.4 ~ : ~ ~ 0.2 ~:~ o Vancouver ~ ~-... ~ - ~ ~ Distance (kin) Fig. 3. (a) Relative dewatering rates and (b) absolute fluid production rates for transects at Vancouver, Northern Barbados, Makran, and Nankai. The parameters and location for each site are given in Table 1. along the section described by Minshull and White [4], and Nankai along the DSDP Leg 87a transect [10]. Table 1 gives the model parameters used in the calculations for each site. Although the table lists single values with no error bars, this is not meant to imply that these values are known exactly. They are representative values chosen from the sources listed and used to produce the plots in Fig. 3. For porosity, we used the parameters n o and b, to describe the porosity profile in the seafloor sediments before they are accreted. These values are appropriate for calculating the volume of pore water entering the prism complex. In the initial calculation of water expelled, we use these same parameter values for sediments in the prism so that the porosity profile does not change with distance from the deformation front. Thus these calculations represent minimum or conservative estimates of expulsion rates. Later we examine the effect of varying the porosity-depth relationship in the prisms at Makran and Vancouver. Figure 3a shows relative dewatering rates for the four sites. This plot represents the fraction of the incoming pore fluid which must be expelled to maintain the porosity profile of the incoming sediment section. This computation is appropriate if we assume that the abyssal plain sediments were normally consolidated and that prism sediments conform to this same consolidation profile. Figure 3b shows the calculated rate of dewatering per unit surface area for each site. This is computed using: r(x) = fzgx)v'fdz (12 / ~0 where za(x) is the depth of the decollement at x km arcward from the deformation front. The value r(x) represents the total compaction-generated fluid volume summed over a vertical column at a distance x from the deformation front. Thus Fig. 3b compares the total magnitudes of dewatering rates expected at the four locations as a function of distance from the deformation front. The Barbados transect has an extremely thin accreted section of 0.26 kin. This, coupled with a relatively high incoming surface porosity of 71%, gives a dewatering distribution in which most of the compaction occurs within 20 to 40 kin of the deformation front (Fig. 3a). However, from Fig. 3b it is clear that the actual rate that fluid is produced in this manner is relatively small compared to sites with thicker incoming sections and higher accretion rates. Analyses of physical properties data from ODP Leg 110 are consistent with these results. Taylor and Leonard [13] showed that sediments are underconsolidated near the toe of the prism. In addition, the porosity analysis presented in Appendix B, indicates that sediments are underconsolidated for at least 20 km arcward from the deformation front. In the lowpermeability environment of the Leg 110 transect, the high pore pressures necessary to drive the compaction-generated fluid through the sediments may contribute to underconsolidation of the wedge sediments. Our analysis indicates that the high pore pressures and related underconsoli-

8 282 B.A. BEKINS AND S.J. DREISS dation should be concentrated within about 20 km of the deformation front. The Vancouver transect, in contrast to Barbados, has an extremely thick incoming section with a very large wedge taper angle. Recall that the sensitivity analysis showed that a large taper angle causes most compaction to occur within 20 km of the deformation front. Since the incoming section at Vancouver is thick, this partly offsets the effect of the taper angle. Thus, as Fig. 3a indicates, the zone within 20 to 40 km arcward of the deformation front has the most compaction. The effects of this compaction should be significant, since the rate that pore fluids enter the wedge is an order of magnitude greater than at the Leg 110 site. This higher flow rate is due to the higher accretion rate and the thicker incoming section. Davis et al. [5] suggest that significant advective heat transport by pore fluids is present to a decreasing extent for 40 km arcward of the deformation front. At this time, however, the seafloor heat flow data are not adequate to show whether these effects die out after 40 km (Davis, pers. commun., 1991). Our model results suggest that this should occur. Like Vancouver, the Makran transect has a very thick incoming section. However, unlike Vancouver it has a low wedge taper angle. The sensitivity analysis indicates that both of these properties lead to compactive fluid losses distributed for 60 km or more arcward into the wedge. Like Vancouver, the volume of fluid entering this complex per unit time is quite high. Thus we expect to see significant compactive flow effects which persist relatively far arcward. Minshull and White [4] have analyzed surface heat flow for this site and compared this to heat flow predicted from the depth to the base of the gas hydrate layer. They suggest that advective heat transport is important for more than 60 km arcward of the deformation front. This result would be consistent with our model predictions. The Nankai profile has about the same taper angle as Vancouver but half the accreted thickness. We performed a least-squares fit to the porosity data from DSDP Leg 87a site 582 to obtain the porosity parameters listed in Table 1. The value of b obtained, 0.2 km-1, indicates an unusually low porosity loss with depth. This gives a dewatering distribution which is almost evenly distributed for more than 80 km arcward (Fig. 3a). The actual volume of expelled fluid is midway between Northern Barbados and Makran (Fig. 3b). However, the distribution of the dewatering over such a large area could prevent dramatic heat or chemical transport effects at the seafloor. 5. Discussion The dewatering calculations we have presented were based on a number of simplifying assumptions. First, the formula for estimating dewatering rates applies only to the prism sediments and not to the underthrust sequence. This is less of a problem at some sites than at others. For example, at Vancouver no underthrust sequence may be present [5], and in Southern Barbados the whole underthrust sequence may be underplated before the difference in burial rates between the underthrust and accreted sediments becomes significant [3]. Certainly, some of our results apply in a qualitative fashion to the prism and the underthrust taken together. For example, a small total prism angle leads to relatively slow burial for both regimes. In this case the compaction dewatering will be distributed for a longer distance from the deformation front. The fact that the underthrust is buried even faster than the base of the prism just accentuates this effect, further extending the distance from the deformation front that significant compaction dewatering sources may be present. Secondly, we have assumed uniformly diverging trajectories for the sediment packets in the prism. The sediments however follow much more complex paths as they are buried beneath imbricate thrust slices. Since dewatering is relatively intense below active faults, the actual spatial distribution of dewatering on a local scale will differ from our computed rates. Another assumption in our calculation is that the total prism ongle is constant over the wedge. However, at Nankai, Makran, and Cascadia, there are low-angle protothrust zones between the deformation front and the frontal thrust. Each wedge taper angle changes dramatically at the frontal thrust. Our calculations for these sites used taper angles which are appropriate for the area arcward of the frontal thrust. However, cal-

9 A SIMPLIFIED ANALYSIS OF PARAMETERS CONTROLLING DEWATERING IN ACCRETIONARY PRISMS 283 s < 1.5 0~ ~ 1.0 "2,~ Makran variable porosity --~- Makran... Vancouver variable porosity ~ V a n c ---~ '~----- o u v Vancouver e " Distance (krn) Fig. 4. Absolute fluid production rates for transects at Vancouver and Makran comparing values computed using the same porosity-depth curve throughout the prism against values computed by varying the porosity parameters linearly with distance arcward from the deformation front. The porosity parameter variations used for each site are listed in Table 2. culations which include the protothrust can be performed with eqn. (8) by using one taper angle, thickness, and velocity for the protothrust and changing to new values for the wedge arcward of the frontal thrust. Finally, in the sensitivity analysis and the site characterizations, we assume that a single porosity-depth profile represents the sediments in the entire prism. In our dewatering solution, it is possible to vary the porosity-depth relation by specifying n o and b as functions of distance arcward into the prism, although the sensitivity analysis showed that the dewatering estimates are relatively insensitive to the porosity distribution used. In fact, the sediment porosity distribution in the wedge may differ from that of the incoming seafloor sediments. In some cases such as Makran and Vancouver, the wedge has a lower average porosity for the same depth of column than that of the incoming seafloor sediments [4,5]. Bray and Karig [1] refer to this change in the porosity distribution as tectonic dewatering. Figure 4 shows the effect of including tectonic dewatering at Vancouver and Makran by varying the porosity distributions using linear interpolations of n o and b. (See Table 2 for the variation rate.) Including the tectonic porosity loss at these sites increases the estimated dewatering rate. Thus our Fig. 3 results can be considered as minimum estimates. Alternatively, at some sites such as Northern Barbados, the wedge has a slightly higher average porosity for the same depth than the incoming sediments (see Appendix B). In this case, our estimates are slightly high for the dewatering rate near the toe of the prism. However, we found that varying the porosity distribution at this site had little effect on the curve shown in Fig. 3b. Although our assumptions are a simplification, they permit calculations which provide insight into the gross dewatering behavior at various sites. In particular, the dewatering expression is a function of both the distance from the deformation front and the depth in the prism. An estimate of the two-dimensional spatial distribution of the dewatering is necessary to solve the full groundwater flow equation and thus obtain pore pressures and pore fluid velocities. For example, we found that when sediment porosities are described by Athy's equation (11), the maximum decrease in sediment velocity and associated rate of fluid production occurs about one kilometer deep in the wedge. This pattern, in turn, will influence the pore pressure distribution with depth in a prism. 6. Summary We have presented an analytical method for calculating the dewatering rate of accreted sediments. A sensitivity analysis performed using this TABLE 2 Values used for variable porosity distributions Site and Reference I Type of Interpolation Initial Sealloor Porosity rio Initial I Initial to Depth-loss J Final Distance b l (k.m l ) x(km) Final Seafloor Final Porosity Depth-loss n% b2(tm -I) Vancouver [5] linear Makran [4] linear

10 284 B.A. BEKINS AND S.J. DREISS method indicates that: (1) the taper angle of the prism is the most important factor influencing the dewatering distribution; (2) second in importance is the thickness of the accreted section; (3) the values used to describe the prism porosity are relatively unimportant although the porosity-depth factor is more important than the value used for seafloor porosity. We examined the total rate of dewatering and the distribution of dewatering for cross-sections of four accretionary prisms: Northern Barbados, Vancouver, Makran, and Nankai. Of these, the Vancouver site is notable for both the highest total rate of dewatering and the most concentrated dewatering distribution. In total rate of flow the ranking of the other sites was: Makran, Nankai and lastly, Barbados. In concentration of distribution of dewatering or focusing near the toe, the ranking was Barbados, Nankai, and Makran. These results give a framework for predicting the relative importance and spatial extent of the dewatering phenomenon for any given transect of an accretionary complex. In interpreting observations, the site analyses show that both the distribution and the total rate of dewatering are important. The total dewatering rate possible is limited by the rate that pore water enters the complex with the accreted sediments. Thus we would expect significant dewatering effects at sites where both the total rate of water entering the complex is high and the distribution of dewatering is concentrated near the deformation front. Acknowledgements This research was sponsored by National Science Foundation grant OCE and an ARCS Fellowship. Casey Moore, Dan Karig, Greg Moore, and one anonymous reviewer contributed many helpful comments. Finally, we wish to especially thank Juli Morgan for working through each step of the derivation in Appendix A. As a result of her efforts, the explanation given is substantially improved. Appendix A: solution for sediment velocities ment velocity: av x avy 1 [ an a~y] (A.I) --+--= - - VX~x +Uy ax ay 1 - n where v x and vy are the horizontal and vertical velocity components in the coordinate system shown in Fig. la. Now assume that the sediment packets moving through the prism follow uniformly diverging streamlines. Along any such path, the ratio of the vertical to horizontal velocity is a constant given by: Uy Z 0 -- = tan u - T-(tan a +tan/3) (A.2) U x no where z 0 is the initial accretion depth of a sediment packet, h 0 is the thickness of the accreted sediment section, and a and/3 are the slope angle and subduction angle, respectively. Next, transform the wedge-shaped solution domain of Fig. la to the rectangular domain of Fig. lb. In this new solution domain, the assumption of uniform sediment divergence from the deformation front corresponds to no vertical flow. This coordinate transformation is given by: X=U 1-wl(h +utan/3 ) 2,,2 (A.3) where u and w are the new coordinates. In this coordinate system, eqn. (A.1) becomes: 0v. [ T 1 ]a-q ~ = 0 (A.4) au h o + T u 1- n Ou vu where T= tan ct +tan/3, v, is the horizontal velocity in the new coordinate system, and ~7(u, w) is the transformed porosity function. This is an ordinary differential equation for v u. It requires one boundary condition which may be given by: L,u(0, ~) = v0 (A.5) where v 0 is the velocity of the subducting plate with respect to the advancing deformation front. The solution to (A.4) is obtained by integration and application of the boundary condition (A.5). It represents the horizontal velocity in the mapped coordinate system: Uu h 0 (1 - -q(0, w)) L' h o + ru (1 -,7(u, w)) (A.6) Now, transforming the result (A.6) back to the original coordinate system using the inverse mapping from (A.3) gives: h 0 (1- n(o, Zo) ) ~x=v ho+rx O-,,(x, z)) (A.7) Combining this result with eqn. (5) yields eqn. (6), as desired. Similarly, eqns. (A.2) and (A.7) yield the expression for the vertical component of the sediment velocity given in (7). Appendix B: analysis of Northern Barbados drill core data Recall that conservation of mass of the solid fraction We used direct porosity measurements from ODP Leg 110 yields a first-order partial differential equation for the sedi- and DSDP Leg 78a to continuously estimate the two porosity

11 A SIMPLIFIED ANALYSIS OF PARAMETERS CONTROLLING DEWATERING IN ACCRETIONARY PRISMS 285 LEG 110 TRANSECT ~4 Deformation ~ D ~ t / Front 672,,l II-,, o..... Site 673: Normally Consolidated Site 541: Under Consolidated F 100 o/: I ooe~o (9o ' oOo... i... i... I... i... 4O Site 672: Normally Consolidated o o d~eioo o 080 ~o ~ o~o o oo io o k... b~,o,9.,., Porosity (%) Fig. 5. The three plots show least-squares fits to porosity data from three drilling sites in Northern Barbados. The cross-section shows the locations of the drill holes. The fit for site 672 shown on the right may represent a normally consolidated porosity profile for the incoming ocean-floor sediments before they are accreted. The fit for site 541 pictured in the center, shows iittle porosity loss with depth. This indicates that sediments in this profile are under-consolidated compared to those at site 672. The fit for site 673 pictured on the left, shows a porosity loss with depth that is closer to that of site 672 indicating that the sediment profile is approaching normal consolidation arcward. parameters, n o and b, along the ODP Leg 110 transect of the Barbados prism. The horizontal variation of these parameters reflects systematic trends in porosity as sediments move arcward through the prism. For this effort, we made three assumptions. First, there exists a steady-state wedge geometry which is fixed relative to the deformation front. Second, within this wedge, the idealized porosity is a function of only the depth and distance from the deformation front, so that at fixed location in the wedge it does not change with time. Finally, since this desired porosity distribution represents a time-average for the prism it should not reflect the contemporary spatial variation in porosity caused solely by sediment composition differences, Porosity variations are a striking feature of all of the Barbados core data. The causes of this variation have been described by Wilkens et al. [9]. They found that a high TABLE 3 Fitted parameters for porosity data from Northern Barbados Drilling Site ] Fitted Surface Porosity [ Porosity Loss with Depth ] RMS for Fit i 0, , ,

12 286 B.A. BEKINS A N D S.J. DREISS percentage of ash-derived smectite and biogenic silica raises the porosity of the early Miocene sediments. Thrusting of these sediments over younger sediments appears in the data as a series of high-porosity intervals at the position of the thrust faults. However, in spite of this variability, they found that the reference sites seaward of the deformation front (Leg 110 site 672 and Leg 78a site 543) have porosity-depth profiles similar to normally compacted clays. In addition, they found that the most arcward sites (Leg 110 sites 673 and 674) have 5-15% lower porosity than the same depth sediments at the reference sites. These observations give a good basis for deriving an idealized porosity distribution. The postulated porosity distribution takes the form: n(x, z) = n0(x) e -b~x~z (B.1) where n is the porosity in the prism, x is horizontal distance arcward from the deformation front, z is the depth below the seafloor, no(x) is the porosity at the seafloor, and b(x) is the porosity loss with depth. Note that the values of no(x) and b(x) may vary with the distance from the deformation front, x. Functions describing the variation of n o and /3 with x were obtained from core sample porosity measurements as follows. First we corrected the Leg 110 data to remove systematic instrument errors described by Wilkens et al. [9]. Next we fit Athy's equation (11) to the data for each site to obtain values for n o and b for that location. Fits for ODP Leg 110 sites 672 and 673 and DSDP Leg 78a site 541 are shown in Fig. 5. The best fit values obtained for all the sites are listed in Table 3. We plotted these values against distance from the deformation front and analyzed the plots for trends. The values for the parameter describing porosity loss with depth, b, showed a strong trend (Fig. 6). As noted earlier, Wilkens et ai. [9] found that the porosity-depth profile for the incoming ocean-floor sediments at the reference site, 672, closely matched that obtained by Hamilton [14] for normally consolidated clays in the Indus Fan. Thus we assumed that 0.8 Value orb for Site 672 ~ 673 'E "'"" e , i,, i,, i,, 5, I Distance Arcward (km) Fig. 6. Plot of the porosity-depth factor, b, versus the distance of the drill hole from the deformation front. The curve shown is a fitted exponential decay, which asymptotically approaches the value of b obtained for the reference site, 672 (dashed line). the value we obtained for b at site 672 represents the correct one for normally consolidated sediments of this type. Within the prism, we found that the values for b at sites adjacent to the deformation front were much lower than that for the reference site. However, for sites farther arcward from the deformation front, the values obtained for b are much higher and approach that obtained for the reference site. We feel this trend is best described by the fitted exponential decay curve shown in Fig. 6. These results show that the rate of porosity loss with depth, b, is lowest immediately adjacent to the deformation front and increases with distance from the deformation front. This indicates that the sediments in the toe of the prism are less consolidated than the incoming seafloor sediments. Furthermore, the prism sediments appear to approach the normal consolidation profile of the seafloor sediments as they move arcward. The values obtained for the fitted surface porosity, no, at each site do not show much of a trend. A line fit through the values for all of the sites, including the reference site, shows a slight downward trend of 0.1%/km. This appears insignificant when compared with the usual errors of 5% obtained in the fits for each site and suggests that compaction by subhorizontal tectonic stress is small in the first 15 km from the toe of the prism. References 1 C.J. Bray and D.E. Karig, Porosity of sediments in accretionary prisms and some implications for dewatering processes, J. Geophys. Res. 90, , E.J. Screaton, D.R. Wuthrich and S.J. Dreiss, Permeabilities, fluid pressures, and flow rates in the Barbados Ridge Coml~lex, J. Geophys. Res. 95, , X. Le Pichon, P. Henry and S. Lallemant, Water flow in the Barbados accretionary complex, J. Geophys. Res. 95, , T. Minshull and R. White, Sediment compaction and fluid migration in the Makran accretionary prism, J. Geophys. Res. 94, , E.E. Davis, R.D. Hyndman and H. Villinger, Rates of fluid expulsion across the northern Cascadia accretionary prism: constraints from new heat flow and multichannel seismic reflection data, J. Geophys. Res. 95, , J. Bear, Dynamics of Fluids in Porous Media, 764 pp., American Elsevier, New York, N.Y., D.E. Karig, Experimental and observational constraints on the mechanical behaviour in the toes of accretionary prisms, in: Deformation Mechanisms, Rheology and Tectonics, E.H. Rutter, ed., pp , Geol. Soc. Spec. Publ., L.F. Athy, Density, porosity, and compaction of sedimentary rocks, Bull. Am. Assoc. Pet. Geol. 14, 1-35, R. Wilkens, P. McClellan, K. Moran, J.S. Tribble, E. Taylor and E. Verduzco, Diagenesis and dewatering of clay-rich sediments, Barbados accretionary prism. Proc. ODP, Sci. Results 110, , Shipboard Scientific Party, Site 582, Init. Rep. DSDP 87, 1986.

13 A SIMPLIFIED ANALYSIS OF PARAMETERS CONTROLLING DEWATERING IN ACCRETIONARY PRISMS G.K. Westbrook, J.W. Ladd, P. Buhl, N. Bangs and G.J. Tiley, Cross section of an accretionary wedge: Barbados Ridge complex, Geology 16, , G.F. Moore, T.H. Shipley, P.L. Stoffa, D.E. Karig, A. Taira, S. Kuramoto, H. Tokuyama and K. Suyehiro, Structure of the Nankai trough accretionary zone from multichannel seismic reflection data, J. Geophys. Res. 95, , E. Taylor and J. Leonard, Sediment consolidation and permeability at the Barbados forearc, Proc. ODP, Sci. Results 110, , E.L. Hamilton, Variations of density and porosity with depth in deep sea sediments, J. Sediment. Petrol. 46, , 1976.