Water budgets in accretionary wedges: a comparison

Direct or indirect measurements of fluid flow out of the toe of accretionary wedges have now been made in the Barbados, Central Oregon, Northern Cascadia and Nankai subduction zones. The steady-state local compaction model predicts velocities of fractions of a millimetre per year and total outflows from the toe of a few cubic metres per year per metre of length along strike of the subduction zone (m2 a-1). Sea bottom measurements reveal channellized flows at velocities of hundreds of metres per year and total outflows from the toes of a few hundreds of square metres per year. Thermal arguments show in the Nankai area that all of this large surface flow cannot come from as deep as the decollement and that consequently a significant dilution by shallow sea water convection must be present. We propose that this convection is driven by the reduced density of less saline fluid of deep origin. Thus the outflow of water of deep origin may be only a few tens of square metres per year. We note, however, that there are indications in the Barbados area of massive flow of low salinity water at depth along the decollement. These flows imply the existence of large scale non-steady-state lateral transport and require the existence of sources of low salinity water. These might include the smectite-illite transformation and the fluid contained in the oceanic crust. However, these sources are limited and the possibility exist that other more important sources may be required such as long distance transport of fresh water from adjacent sedimentary basins and (or) recharge mechanisms such as the seismic pumping one.


Introduction
We compare quantitative estimates of fluid outflow from the toes of accretionary wedges in subduction zones, based on various direct or indirect measurements, with steady-state flow due to compaction of the sediment incorporated within the wedge. We use recent indirect measurements of flow made on the Eastern Nankai wedge (Le Pichon et al. 1990a ;Foucher et al. 1990a;Henry et al. 1990), direct (Carson et al. 1990) and indirect (Davis et al. 1990) measurements made on the Oregon wedge and indirect measurements made on the Barbados wedge (Foucher et al. 1990b;Fisher & Hounslow 1990;Le Pichon et al. 1990b, c;Langseth et al. 1990). We conclude that in all these cases the outflow is significantly larger than the volume of fluid released by compaction processes.

Fluid outflow due to steady-state compaction of sediments
Typically, the sediments entering subduction zones have a high porosity, especially if they consist of recently deposited terrigenous sediments. Tectonic stacking of thrust packages at the toe of an accretionary wedge results in rapid compaction and expulsion of most of the interstitial water. Thus, following Bray & Karig (1985), several authors have computed the expected steady state fluid outflow due to compaction using simplifying assumptions (Langseth et al. 1990; Screaton et al. 1990;Le Pichon et al. 1990c). They have shown that the expected outflow velocities do not exceed a fraction of a millimetre per year and that the total expected flux out of the toe is a few square metres per year (cubic metres per year per metre of length along strike of the wedge). The following discussion amplifies these two conclusions.
Le Pichon et al. (1990c) have shown that a single porosity depth function from the basin to the wedge fits reasonably well existing data. We use this relation for the porosity g as given by them T = T0 exp (-az), (2.1) where 90 = 0.7, a = 0.67 km-l and z is the depth in kilometres.

The average porosity of a vertical column is p = (qo/az)[ -exp (az)] (2.2) and the equivalent height of water contained in a vertical column is Hw = (T/a) [1 -exp (-az)]. (2.3)
The maximum Hw is p0/a which is close to 1 km. For a thickness of sediment of 1 km, the height of water Hw is about 500 m and for 3 km, it is 900 m. Increasing the thickness of the sedimentary column above 3 km would not increase significantly the amount of interstitial water. For typical entering thicknesses of sediment (1-4 km), the equivalent height of water Hw changes by a factor of less than 2 and is about 700 m + 30 %.
The actual volume of water entering the wedge per unit time is  where a is the wedge taper angle. The maximum velocity of escape is obtained at the toe for z' = z and decreases as the wedge thickens. U(z,-5) tan avS. (2.8) The maximum local steady-state outflow velocity does not continuously increase with thickness z of the entering column. It is maximum for a value of about 1.5 km and changes little (+ 10 %), staying close to 0.3, between z = 1 and z = 4 km. This is because Uz/v tan a rapidly increases from 0 for z = 0 to 0.333 for z = 1.66 km but then slowly decreases to 0 at infinity. To summarize, the local outflow velocity should not be affected by the thickness of the entering sediment column and should only depend on the product of the taper by the subduction velocity. Table 1 compares different parameters for the areas we discuss in this paper. For Northern Cascadia and Central Oregon, we have adopted the subduction velocity given by Davis et al. (1990), taking into account the obliquity of subduction to the wedge in Central Oregon. The volume of water lost after 1 km of thickening, AVw, varies between 5 and 10 m2 a-1 and is controlled by the subduction velocity; Uz/vs tan o has the same value of 0.3 for all the margins whereas Uz, the maximum escape velocity at the toe, changes from a minimum of 0.3 mm a-1 in Northern Barbados to 1.6 mm a-1 in Northern Cascadia. The average velocity over the first kilometre of thickening is minimum for Northern Barbados (0.23 mm a-1) and maximum for Northern Cascadia (1.2 mm a-l).
Thus, with local steady-state compaction, expected velocities are indeed very small. As a consequence, the heat flow should not be significantly affected (Langseth et al. 1990;Screaton et al. 1990;Le Pichon et al. 1990c). Note that even if all the water of the latest thrust package is channelized through the decollement or along the main thrust fault, the expected flow is not more than 5 or 10 m2 a-1. Are there other possible sources of fluid within the sediment or below the sedimentary column within the oceanic crust ? As discussed by Von Huene & Lee (1983) and more recently by Moore (1989), fluid structurally bound to clay minerals should be released upon burial and heating. Also, the hydrous oceanic crust liberates fluids upon heating (Peacock 1987, this symposium). Below, we briefly show that the order of magnitude expected is less or equal to the values computed above, that is less than a few square metres per year. More important, most of the release of water from smectite occurs at temperatures larger than 60-100 ?C and from the oceanic crust at temperatures larger than 300 ?C and consequently well to the inward side of the accretionary wedge.
Let us first consider the fluid contained within the oceanic crust. Peacock (1987) proposes a conservative volatile content of 2 % in weight for the 8 km thick oceanic crust. Using a density of 3000 kg m-3, this is equivalent to 480Vs m2 a-1 or 10-20 m2 a-l for the wedges considered in table 1. As the estimate of 2 % in weight appears to be conservative these values could possibly be doubled to 20-40 m2 a-. These values are comparable with the total amount of interstitial water released from the wedge in steady state.
Next, we consider the smectite-illite transformation. To get a rough estimate of the amount of water produced by the smectite-illite transformation at temperatures larger than 60 ?C, we assume that three volumes of smectite give two volumes of illite and one of water. According to Tribble (1990), in the Barbados area, the proportion of smectite in the solid phase is 300%. Then, using table 1, we can obtain the additional volume of water produced by transformation of smectite, which would be 1 m2 a-'. Assuming the same proportion of smectite in Oregon, which is certainly an overestimation, we obtain 6 m2 a-l. This value is significant, but is smaller than the original volume of interstitial water. However, at the depth at which this transformation occurs (T > 60 ?C), the low porosity there ensures that the resulting fluid will be much less saline than sea water.

Water budget of the Eastern Nankai accretionary wedge
The outer Eastern Nankai accretionary wedge has been investigated along a 20 km section with in situ measurements, observations and samplings coupled with deep tow surveys and surface geophysical observations ; Le Pichon et al. 1990a). Fluid outlets have been identified from the presence of clam colonies, vestimentifera, calcareous concretions, chimneys and white patches. Studies of the chemistry of sea water and interstitial water give qualitative indications on the type of fluid venting whereas instantaneous and long term temperature gradient measurements within the sediments give indirect estimates of the velocity of fluid venting (Foucher et al. 1990a;Henry et al. 1990). An important discovery of this study is that, for a given clam colony type, the range of fluid advection velocities below it is relatively small. Thus an estimation of the surface area occupied by the different types of clams colonies can be converted into a water outflow estimate (Foucher et al. 1990a Venting sites were classified on a biological basis ) and one dive was devoted to estimation of the surface area covered by each type of colony. The submersible followed straight parallel lines 100 m apart, exploring a 625 m by 500 m zone along the upper part of the slope and on the plateau. The surfaces occupied by colonies were measured on camera images. The area seen on the video represents 4 % of the area surveyed. We thus obtain estimates of the proportion of the surface covered by each of the different types of colonies in the explored 4 %. We further assume that the same proportions exist in the unexplored 96 % of the area surveyed.
Most of the estimated fluid flux (85%) come from the so-called A-type colonies where the population density is about 1000 clams per m2. During this dive, 122 Acolonies, covering a total surface area of 60 m2, were observed and consequently the statistics made should be significant.
Thirty-six measurements of the temperature gradient over the first 50 cm of sediment were made within this venting zone. The temperature gradients are linear outside the colonies but show a rapid downward decrease below the A-colonies (Foucher et al. 1990a) (figure 2). The temperature gradient below one of these Acolonies was continuously recorded for two months. It is used to obtain a value of sediment thermal diffusivity compatible with a thermal conductivity of about 1 Wm-' K- ). The corresponding thermal diffusivity for fluid advection is 2.5 x 10-7 m2 --1 (7.9 m2 a-l). It is used to model the upward fluid flows below colonies which reproduce the observed thermal gradients.  04 x 625 m)). This flux ignores the limited amount of venting observed 5 km further inward along the outcrop of the second thrust. It is also limited by the fact that this thermal estimate cannot detect flows of less than 10 m a-1. Finally, as stated above, it ignores the important zone of fluid venting discovered 10 km further inward near the summit of the second thrust unit. Consequently, the proposed flux is certainly significantly lower than the actual flux. Yet it is about 40 times larger than the amount obtained assuming local steady-state dewatering.

Central Oregon and Northern Cascadia fluid flux estimates
Direct measurements of fluid venting from clam colonies on the toe of the Central Oregon accretionary wedge are reported by Carson et al. (1990). The fluid appears to come from relatively shallow depth as the methane it contains is biogenic (Kulm & Suess 1990). No decreased salinity has been measured. The obtained Darcy velocities are about 65 m a-l over two vents. Four such vents each having a surface area of about 9 m2 were discovered within an area of the toe that is about 5 by 2 km. The authors have not indicated how much of these 10 km2 were visually explored during their dives but the density of submersible tracks shown suggests that 4% of the 1.5 km wide most densely covered area was explored. If 4 % is a correct proportion, the average flux from this 1.5 km wide portion of the toe is about 40 m2 a-1 whereas the expected local steady-state dewatering would be about 6 m2 a-1 (see table 1 (c) Dilution models For a given fluid dilution factor d = Qc/Qr, both the sloping aquifer model and the unidimensional advection model give ranges of values for the temperature at the depth of the shallow decollement. It is thus possible to determine the probable amount of dilution by looking for the compatibility domain of these two models. Mixing with sea water occurs within the shallow decollement at depth H. Thus, upward flow from decollement to the surface is equal to Qc/S and temperature at depth 0 to H is given by equation (6.2). As explained in Appendix B a relationship between temperature in the decollement below the colonies and the temperature of incoming fluids can be obtained from the heat balance equation at the shallow decollement level.
But the structure of the temperature field in and around clam colonies has been interpreted as an indication that recharge with sea water occurs at a shallow depth (1 or 2 m), implying local convection around the colonies ). We consequently consider another case when dilution occurs by convection near the surface. We assume that a uniform advection model applies in the domain between the shallow decollement and the base of the convection cells (see Appendix B). Then, the temperature predicted in the shallow decollement by this model must be equal to the temperature T of incoming fluids.
Comparing these two models, convection near the surface requires higher dilution than mixing in the decollement, the actual dilution factor being most probably between 6 and 15. Temperature in the decollement should be very low if sea water is flowing into it, but should not be anomalous if dilution occurs near the surface. On the other hand conductive heat flow is expected to be significantly higher than normal north of the active zone if mixing occurs in the decollement as the predicted temperature for incoming fluid is higher.
(d) Numerical estimates of dilution When applying either model, the major source of uncertainty is the value of f, the thermal gradient below the shallow decollement, which is supposedly equal to the 'regional' gradient.
There are few measurements which can be used as references for heat flow. One measurement made in the trench between Tenryu Canyon and Zenisu ridge gives 67 mW m-2 (Nahihara et al. 1989). As conductivity is in the range 0.7-1.3 W m-1 K-1 but more probably around 1 W m-l K1, this value is quite compatible with the measured gradient of 60 mK m-1 in the toe area. Measurements were recently made closer to the Kaiko-Nankai area (Kinoshita & Kazumi 1990) on the lower tectonic unit to the northeast. At the northeastern extremity, the thermal gradient is 60 mK m-1, while closer to the explored area but near the base of the upper tectonic unit, the thermal gradient is low, around 40 mK m-l. In the absence of fluid advection, heat flow tends to decrease landward because of tectonic thickening of sediments in the wedge, and because of the slab burial effect (Toksoz et al. 1975 [ 98 For a value of the background gradient of 40 mK m-l, dilution should be between 6.5 and 9; for 50 mK m-l, between 10 and 15; for 60 mK m-1, between 20 and more than 30, but this last determination is also very dependent on other parameters such as thermal conductivity, aquifer slope and aquifer depth below the active zone. Salinity contrast, rather than temperature gradient, is probably driving convection ). As noted earlier, fluids originated from deep within an accretionary complex tend to have a low salinity, but the actual salinity of incoming fluids is not known in the Kaiko-Nankai area. A salinity difference of a few per mil between sea water and source is enough to start convection if conduit permeability is high, but the major constraint is that flow in the conduit, at a velocity of 100 m a--1, has then to be driven by buoyancy of the diluted fluids. Assuming that fluids have, after dilution, a density a few grams per litre less than sea water, conduit permeabilities of the order of 10-10 m2 are required ). Dilution factors of more than 10 are thus unlikely.
(e) Applicability to other wedges The model proposed for Kaiko-Nankai area might be applied to the 12? N section of the Barbados accretionary wedge, as the context is somewhat similar. There, fluids presumably flow along a major thrust into a shallow decollement, and are expelled through faults in the overlying thrust outcrop wedge of deformed sediment (Foucher et al. 1990b). The corresponding heat flow increase is moderate (40 %), indicative of a deep fluid flux of the order of 20 m2 a-1. However, we do not know if vents are present on these thrust outcrop wedges and consequently whether there is some convection.
In the Oregon diving sites, the venting fluids are probably diluted, as their salinity is normal and as the large amount of fluid flux is not compatible with local shallow sources. Then convection would occur between the surface and permeable sand strata acting as conduits for lateral migration. As in the Kaiko-Nankai area, major vents with associated clam colonies were found at the top of the anticline, but other types of vents were also found in association with permeable sand strata on the eroded slope just below the active zone. However

Conclusion
We have shown that on the Eastern Nankai area very large fluid outflows measured on the toe of the accretionary wedge include a large component of locally derived sea water, probably resulting from haline convection. However, the amount of low salinity water necessary to drive this convection is still of the same order of magnitude as the water produced by compaction of the whole sedimentary column. In the Barbados area previous work has given further evidence for large-scale flow of low salinity water along the decollement, this flow being an order of magnitude larger than possible flow from compaction of the whole sedimentary column.
Where does the large amount of low salinity water come from ? The smectite-illite transformation and the hydrate layer are obvious sources but cannot provide amounts larger than a few square metres per year to at most 10 m2 a-. Another possible source is the oceanic crust if it includes a sizeable thickness of serpentinized peridotite. For example 2 km of 50 % serpentinized peridotite would contain more water than the sedimentary column. This source would not be sufficient if the amount of low salinity water required is indeed larger than a few tens of square metres per year in steady state. Then, one would have to invoke long distance transport of fresh water from the adjacent subaerially exposed basins and (or) exotic recharge mechanisms such as the seismic pumping mechanism (Sibson et al. 1975).

Appendix A. Model of fluid flow along an aquifer
Steady state is assumed and diffusion along the horizontal (x) axis is neglected. The geometry is as shown on figure 3. The aquifer is thin, so that the fluid temperature T(x) is uniform across it. The depth of the aquifer below the surface is H(x). The fluid flux in the aquifer is Q. In steady state, heat flow below the aquifer is unaffected by the fluid flow because all the additional heat must be conducted upward to the surface. Thus we assume that the heat flow below the aquifer is uniform and constant, equal to the heat flow at the surface in the absence of fluid flow. As we also assume a uniform thermal conductivity (A), the temperature gradient below the aquifer (f) is a constant. Because horizontal heat diffusion is neglected, the temperature profile between the aquifer and the surface is linear and the gradient above the aquifer is Tf/H. The heat lost by water flowing along the aquifer is then related to the discontinuity of gradient across the aquifer by the following equation ( For v < 1, which corresponds to high fluid flux, the gradient tends to infinity where the aquifer reaches the surface. This artefact is a consequence of the assumption of no horizontal heat conduction, which is no longer valid. When v < 1, fluid temperature in the aquifer stays constant, equal to the source temperature until it comes very close to the outlet. For v > 1, which corresponds to low fluid flux, the gradient tends to a finite limit fi at the outlet. This value is independent of the temperature of the fluid source fi = /(vp-1)f.

(A 5)
In the cases considered in the text, v > 1.5. Then, the limit f, is a good approximation of the temperature gradient in a wide zone beginning at the outlet. We finally obtain for each case a set of equations which determines the dilution factor d from known parameters. Note that, rigorously, the heat balance at the decollement should also be applied to the model with dilution near the surface. In this case, it implies continuity of the Phil. Trans. R. Soc. Lond. A (1991) temperature gradient across the aquifer. This additional condition theoretically determines the value of F. However, this condition is not satisfied exactly, as the actual fluid flow pattern is not strictly one dimensional. In particular, part of the fluids continue to flow along the aquifer and release some heat. Thus we tolerate gradient discontinuities of the order of 10 mK m-1.