Earth and Planetary Science Letters 501 (2018) 138–151

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Earth and Planetary Science Letters

www.elsevier.com/locate/epsl

Three-dimensional models of hydrothermal circulation through

a seamount network on fast-spreading crust

Rachel M. Lauer a,b,c,∗, Andrew T. Fisher b,c, Dustin M. Winslow b,c,d

a Department of Geoscience, University of Calgary, Calgary, Alberta, Canadab Earth and Planetary Sciences Department, University of California, Santa Cruz, 95064, USAc Center for Dark Energy Biosphere Investigations, University of California, Santa Cruz, 95064, USAd GrowthIntel, 25-27 Horsell Road, London N5 1XL, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 25 February 2018Received in revised form 17 July 2018Accepted 14 August 2018Available online xxxxEditor: M. Bickle

Keywords:hydrothermal circulationridge flanklow-temperaturecoupled modeling

We present results from three-dimensional, transient, fully coupled simulations of fluid and heat transport on a ridge flank in fast-spread ocean crust. The simulations quantify relationships between rates of fluid flow, the extent of advective heat extraction, the geometry of crustal aquifers and outcrops, and crustal hydrologic parameters, with the goal of simulating conditions similar to those seen on 18–24 M.y. old seafloor of the Cocos plate, offshore Costa Rica. Extensive surveys of this region documented a ∼14,500 km2 area of the seafloor with heat flux values that are 10–35% of those predicted from conductive cooling models, and identified basement outcrops that serve as pathways for hydrothermal circulation via recharge of bottom water and discharge of cool hydrothermal fluid. Simulations suggest that in order for rapid hydrothermal circulation to achieve observed seafloor heat flux values, upper crustal permeability is likely to be ∼10−10 to 10−9 m2, with more simulations matching observations at the upper end of this range. These permeabilities are at the upper end of values measured in boreholes elsewhere in the volcanic ocean crust, and higher than inferred from three-dimensional modeling of another ridge-flank field site where there is less fluid flow and lower advective power output. The simulations also show that, in a region with high crustal permeability and variable sized outcrops, hydrothermal outcrop-to-outcrop circulation is likely to constitute a small fraction of total fluid circulation, with most of fluid flow occurring locally through individual outcrops that both recharge and discharge hydrothermal fluid.

© 2018 Elsevier B.V. All rights reserved.

1. Introduction: ridge-flank hydrothermal circulation through outcrops

Seamounts and basement outcrops are common features of the global ocean floor (Hillier and Watts, 2007; Wessel et al., 2010)and can influence hydrothermal circulation in the volcanic ocean crust (Anderson et al., 2012; Davis et al., 1992; Fisher et al., 2003a;Fisher and Wheat, 2010; Hutnak et al., 2006; Villinger et al., 2002; Winslow and Fisher, 2015). The volcanic ocean crust on the flanks of mid ocean ridges is commonly blanketed by low-permeability sediment that limits direct fluid exchange between the ocean and underlying crustal aquifer (Fisher and Wheat, 2010;Spinelli et al., 2004). Seamounts form pathways for fluids to enter

* Corresponding author at: Department of Geoscience, University of Calgary, Cal-gary, Alberta, Canada.

E-mail address: rachel.lauer@ucalgary.ca (R.M. Lauer).

https://doi.org/10.1016/j.epsl.2018.08.0250012-821X/© 2018 Elsevier B.V. All rights reserved.

and exit the seafloor, bypassing the sedimentary boundary layer, (e.g., Davis et al., 1992; Fisher et al., 2003b; Stein and Fisher, 2003;Wheat and Fisher, 2008; Wheat et al., 2013). Subseafloor hy-drothermal circulation is responsible for ∼15–25% of global heat loss (Hasterock et al., 2013; Mottl, 2003; Stein and Stein, 1994), and influences the thermal and geochemical state of subducting plates, the formation and sustainability of the deep biosphere, and the geochemical evolution of the oceans (e.g., Edwards et al., 2012;Spinelli and Wang, 2008; Wheat and Mottl, 2004).

Based on analyses of satellite gravimetric data, bathymetric (swath) maps and ship-based profile data, the global seamount population is 104–105 (Kim and Wessel, 2011; Wessel et al., 2010). Most seamount locations are poorly known because they are too small (height <1 km and/or diameter <3.5 km) for identifica-tion by satellite. Some field studies have explored the roles of seamounts in facilitating heat loss on ridge flanks (e.g., Fisher et al., 2003a, 2003b; Hutnak et al., 2006; Villinger et al., 2002), and mod-eling studies have examined the influence of single- and multiple-

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Fig. 1. Maps and cartoons illustrating field site and simulation approach. (A) Regional map showing the general location of study area (inset), and cool part of the Cocos Plate, shaded gray area (modified from Hutnak et al., 2008). This 14,500-km2 region of ∼18–24 Ma seafloor formed at the fast-spreading East Pacific Rise, and containing 11 mapped outcrops (black circles), has seafloor heat flux that is just 10–35% of lithospheric values. (B) Modeling conceptualization of an outcrop network, with highlighted area representing a single simulation domain having one small and one large outcrop located at the corners. (C) Summary of potential grid configurations based on having two, three, and four outcrops at the corner of the rectangular domains, with two outcrop sizes (small, large). The simulated outcrops comprise 1/4 of actual outcrop size, based on symmetry of the domain with respect to an outcrop network. The six outcrop configurations included in the current study are highlighted in thick, blue lines.

outcrop geometries (e.g., Anderson et al., 2012; Harris et al., 2004;Hutnak et al., 2006; Kawada et al., 2011; Winslow and Fisher, 2015).

Ridge-flank hydrothermal circulation between recharging and discharging seamounts is driven by the pressure difference be-tween cool (descending) and warm (ascending) columns of crustal fluids, forming a “hydrothermal siphon” (Fisher et al., 2003a;Fisher and Wheat, 2010). There are two regions where hydrother-mal circulation influenced by seamounts has been studied espe-cially intensively: the eastern flank of the Juan de Fuca Ridge (JFR, central Juan de Fuca Plate, summarized briefly in this section), and the eastern flank the East Pacific Rise (EPR, eastern Cocos Plate, the focus of this paper, described in the next section). Thick sediments cover young basement rocks across much of the first region be-cause of rapid Pleistocene sedimentation and trapping of sediment by abyssal hill topography (Davis et al., 1992; Underwood et al., 2005). Detailed studies have focused on ∼3–4 Ma seafloor located 90–110 km east of the JFR, where isolated volcanic outcrops pene-trate the sediment, several of which are known sites of hydrother-mal discharge and recharge (Davis et al., 1992; Fisher et al., 2003a;Hutnak et al., 2006; Wheat et al., 2000).

The best-studied discharge site in this area is Baby Bare out-crop, the tip of a volcanic edifice from which ∼5–20 L/s of low-temperature (∼25 ◦C) hydrothermal fluids flow (Mottl et al., 1998; Thomson et al., 1995; Wheat et al., 2004). Baby Bare flu-ids are highly altered following reaction with basement rocks at ∼60–65 ◦C. These fluids recharge through Grizzly Bare out-crop, a much larger edifice located 52 km south-southwest (e.g., Fisher et al., 2003a; Hutnak et al., 2006; Wheat et al., 2013;Wheat and Mottl, 2000). Numerical simulations of outcrop-to-outcrop hydrothermal circulation in this setting suggested that the volcanic crustal aquifer is relatively thin (≤300 m) and has perme-ability on the order of 10−13 to 10−12 m2 (Winslow et al., 2016). These models also showed that recharge is favored through larger

outcrops and discharge is favored through smaller outcrops. There is presently no regional, seafloor heat-flux deficit caused by the circulation of hydrothermal fluids from Grizzly Bare to Baby Bare, because the fluid flow rate is low and little heat is extracted ad-vectively (Fisher et al., 2003a; Hutnak et al., 2006). There were more basement outcrops in this region, and likely more vigorous hydrothermal circulation, when sediment cover was thinner and less complete (Hutnak and Fisher, 2007).

In this study, we focus on a contrasting hydrothermal system, located on ∼18–24 Ma seafloor of the Cocos Plate (Fig. 1). The physical geometry of outcrop-to-outcrop hydrothermal circulation in this area is similar to that around Grizzly Bare and Baby Bare, but the systems are different in terms of fluid flow rates, the ef-ficiency of lithospheric heat extraction, and the properties of the volcanic crust.

2. Advective heat loss from the western Cocos Plate

This study was motivated by extensive seismic reflection pro-files, swath mapping, coring, and heat flux surveys made on 18–24 Ma seafloor offshore of Costa Rica, eastern Equatorial Pa-cific Ocean (Fig. 1) (Fisher et al., 2003b; Hutnak et al., 2007). This part of the Cocos Plate comprises lithosphere generated by the fast spreading East Pacific Rise (EPR) and the intermediate spreading Cocos Nazca Spreading Center (CNS) (Barckhausen et al., 2001). CNS-generated seafloor has heat flow that is consistent (on av-erage) with conductive lithospheric cooling models. In contrast, part of the EPR-generated seafloor, having an area of 14,500 km2, has heat flux that is 10–35% of predictions from conductive litho-spheric cooling models, a regional deficit of 1.0–1.5 GW (Hutnak et al., 2008). Both of these areas (warmer and cooler) exhibit anoma-lous heat flux values compared to global means for 18–24 Ma seafloor, which tends to have a heat flux that is 40–90% of con-ductive predictions (e.g., Hasterock, 2013; Stein and Stein, 1994).

140 R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151

The boundary between warmer and cooler parts of the Co-cos Plate does not correspond consistently to tectonic bound-aries: the cool part of the plate is located entirely on EPR-generated seafloor, whereas the warm part of the plate includes CNS-generated seafloor and a part of EPR-generated seafloor on which there are no mapped seamounts (Fig. 1A). The cool part of the Cocos Plate has eleven mapped outcrops (Hutnak et al., 2007, 2008; Fisher and Wheat, 2010). One small seamount, Dorado outcrop, was identified as a possible site of focused hydrother-mal discharge on the basis of elevated heat flux (>1 W/m2) near the outcrop edge, and rapid discharge of low-temperature pore fluid through thin sediments (Fisher and Harris, 2010; Wheat and Fisher, 2008; Wheat et al., 2017). The closest area of basement ex-posure where nearby heat flux measurements indicate hydrother-mal recharge is Tengosed outcrop, ∼20 km to the east (Hutnak et al., 2007). Recharge through Tengosed and discharge through Dorado is consistent with smaller outcrops being favored as ridge-flank discharge sites (e.g., Winslow and Fisher, 2015).

Dorado and Baby Bare outcrops have similar surface areas and are both surrounded by thick sediments, but the hydrothermal system that cools a large part of the Cocos Plate is very differ-ent from that around Baby Bare. Lithospheric heat flux around Baby Bare is significantly greater than that surrounding Dorado, given the large difference in crustal ages (∼3–4 versus ∼20–24 M.y.). Upper basement temperatures between Tengosed and Do-rado (calculated from seismic reflection and heat flux data) are 10–20 ◦C, rather than 60–65 ◦C around Baby Bare and Grizzly Bare (Hutnak et al., 2007, 2006). Cooler crustal fluids around Dorado outcrop are inferred to move more quickly, having less time for heating while in transit, and have low 14C ages com-pared to those discharging from Baby Bare (Walker et al., 2008;Wheat and Fisher, 2008). Fluid samples collected from springs on Dorado outcrop have major ion chemistry that is little different from that of bottom seawater, but spring fluids have less dissolved oxygen and measurably higher concentrations of elements such as Mo, Rb and V (Wheat et al., 2017). In contrast, Baby Bare fluids are highly altered relative to bottom seawater (e.g., Mottl et al., 1998;Wheat et al., 2004). Based on the regional power deficit, discharge from Dorado outcrop may be 1000 to 20,000 L/s (Hutnak et al., 2008), 50 to 4000 times more than flows from Baby Bare.

3. Simulations of ridge-flank hydrothermal circulation

3.1. Conceptual approach and simulation domains

We explored several geometric arrangements for volcanic edi-fices that can help explain efficient advective heat extraction on the cool part of the Cocos Plate, focusing on outcrops having sizes and shapes similar to Dorado and Tengosed (Hutnak et al., 2008, 2007; Table 1). We ran a suite of >350 simulations in which we varied: domain geometry, number(s) and size(s) of outcrops, crustal aquifer thickness and permeability, and the permeability of outcrops. Each simulation was run to dynamic steady-state, and fluid and heat fluxes were assessed and compared to each other and regional field observations.

We don’t know the extent to which multiple outcrops could contribute to recharge and discharge of hydrothermal in this re-gion, but given a regular distribution of outcrops arranged in a two-dimensional field (Fig. 1B), there are 18 unique combinations of two, three, or four outcrops (comprising sets of one or two sizes) that could occur (Fig. 1C). Based on the symmetry inherent in this representation of outcrop distribution (Fig. 1B), simulations represent a continuous field of outcrops, extending well beyond the scope of the numerical domains. In our simulations, outcrops were placed at domain corners, with each edifice representing 1/4 of an outcrop volume and area of exposure (Fig. 2). For an initial

Table 1Outcrop geometries as represented in simulations in this study.

Domain sizea

(length/side)Outcrop exposure areab

(km2)Outcrop heightc

(m)

Two small outcrops 20 km 0.141 65Large/small outcrop 20 km 0.141–14.1 65–500Large/small outcrop 40 km 0.141–14.1 65–500Two large outcrops 20 km 14.1 500

a Each domain consists of a square prism, with outcrops located at opposite grid corners.

b Cross sectional area of full outcrop exposed at seafloor (quarter outcrop ×4).c Height of outcrop above seafloor.

Table 2Formation properties assigned to different regions in the simulation domain.

Porosity φ(–)

Permeability k(m2)

Thermal conductivity λ(W/m-K)

Sedimenta 0.62–0.80 5.8 × 10−17 to 3.0 × 10−15 0.805–0.927Crustal aquiferb 0.1 10−15 to 10−9 1.82Outcrop 0.1 10−12 to 10−8 1.82Conductive crust 0.05 10−19 1.93

a Sediment properties vary with depth below seafloor. Thermal conductivities ad-justed as needed to give correct values for cumulative thermal resistance at a given depth, as discussed in Winslow et al. (2016).

b Crustal aquifer permeabilities of ≤10−12 m2 are not shown in this study, as these simulations failed to sustain a hydrothermal siphon and/or generate flow rates high enough to mine lithospheric heat as seen in the cool part of the Cocos Plate.

set of simulations, we modeled six arrangements having outcrop spacing of 20 to 56 km. Geometric assumptions and hydrogeologic limitations of this approach are discussed later. Simulations with two outcrops are presented in the main text, and examples with three and four outcrops are shown in the Supplementary Materi-als, along with an overview of numerical methods.

Simulations were run using two main sets of model grids, both based on a rectangular (tabular) domain, with dimensions of 20 or 40 km on a side (Figs. 1C and 2). Given this geometry, a pair of outcrops placed at two corners were spaced ∼20 to 28 km or ∼40 to 56 km apart (for outcrops on a common side or arranged diago-nally, and for grids 20 or 40 km on a side, respectively). This range of outcrop spacing is consistent with that seen on the cool part of the Cocos Plate. Domains were divided vertically into three tabu-lar layers, with outcrops at the corners, comprising ≤450-m layer of low permeability sediments, a crustal “aquifer,” and a thick con-ductive boundary layer representing the deeper crust, which allows space for warping of conductive isotherms in response to vigorous convection and lateral flow in the overlying crust.

Outcrops were placed at domain corners, extending above sur-rounding seafloor sediments and connecting the volcanic crust to the ocean (Table 1, Fig. 2). Outcrops are idealized as ziggurats with sloped sides, based on geometries determined from seismic reflec-tion profiles on the cool part of the Cocos Plate (Hutnak et al., 2007). Sediment properties (porosity, permeability, thermal con-ductivity) were assigned as a function of depth below the seafloor, based on measurements made at nearby drilling sites and calcu-lations of equivalent thermal resistance (e.g., Hutnak et al., 2007) (Table 2). The top of the model domain was prescribed a depth-dependent hydrostatic pressure and constant temperature bound-ary (2 ◦C), consistent with measured bottom water temperatures in this region (Fisher et al., 2003b; Hutnak et al., 2007). The base and sides of the domain are no-flow boundaries, and heat input at the base of the domain is 110 mW/m2, based on a lithospheric cooling curve and crustal age of ∼20 My (Stein and Stein, 1994).

There are no permeability tests in the volcanic ocean crust of the Cocos Plate, but core and borehole observations from IODP Hole 1256D, located on 15 Ma, EPR-generated seafloor along a

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Fig. 2. Example model domain showing system layering and node (element) spacing. Example shows a 20 × 20-km grid with one large and one small outcrop located at the diagonal domain corners, with insets showing a magnified view of each outcrop. All domains in this study include horizontal tabular regions representing a conductive lower layer (red in image), a crustal aquifer layer (orange), and a sediment layer (dark blue) penetrated by ≥2 basaltic outcrops (light blue).

crustal flow line to the west, provide clues as to the possible depth of circulation (Expedition 335 Scientists, 2012). The extrusive sec-tion in this hole extends to ∼750 meters sub-basement (msb), and includes massive lava flows, pillow lavas, and thin layers of hyaloclatites (Expedition 335 Scientists, 2012). Core alteration (Alt et al., 2010) and borehole geophysical logs (Tominga et al., 2009)indicate multiple zones of hydrothermal alteration in the upper 600–700 msb. Based on these observations, we simulated crustal aquifers having a thickness of 100 to 1000 m, and present re-sults from simulations with an aquifer thickness of 300 and 600 m, which were the most consistent with field observations. Coupled, transient simulations of the eastern flank of the JFR explored a similar range of crustal aquifer thickness (Spinelli and Fisher, 2004;Stein and Fisher, 2001; Winslow et al., 2016), and borehole logs and permeability tests in that region indicate high permeabil-ity down to at least ∼300 msb (e.g., Becker and Fisher, 2000;Becker et al., 2013).

3.2. Geothermal constraints and simulation metrics

The distribution of conductive seafloor heat flux between out-crops was used as the primary constraint on the success of a sim-ulation in replicating field conditions. Hundreds of measurements from the cool part of the Cocos Plate show that median heat flux in areas >1–2-km away from outcrops edges is 29 ± 13 mW/m2

(Hutnak et al., 2008), ∼10 to 35% of the age-based prediction. Con-ductive heat flux can be influenced near where sediment pinches out against volcanic outcrops by conductive refraction, secondary convection, and local fluid advection. To avoid these effects in comparing model results to regional observations, we defined a common domain region to be used for assessing seafloor heat flux from all simulations, excluding seafloor nodes within 1 km of the edges of the largest outcrops simulated (Fig. 3A). This approach omits all four corners of the grids when calculating heat flux val-ues from simulation output, equivalent to ∼8% of the 20-km-side domains, and ∼2% of the 40-km-side domains. To simplify com-parison of simulation results to field data, we calculate the heat flow fraction (qf , unitless) as qf = qOBS/qL, where qOBS is observed

heat flux, and qL = lithospheric heat flux input at the base of the simulation domains (110 mW/m2).

As in earlier studies of outcrop-to-outcrop hydrothermal circu-lation (Winslow and Fisher, 2015), and seen in the field (Hutnak et al., 2006; Wheat et al., 2013), even when there is a flowing hy-drothermal siphon (fluid flow into one outcrop exiting the seafloor at another outcrop) there can also be local discharge from an out-crop through which recharge occurs. Siphon flow (Q S, kg/s) is cal-culated by subtracting total simulated recharge from discharge at a discharging outcrop. This corrects for recharge into an outcrop that flows back out from the same edifice. Low permeability sediment effectively prohibits downward seepage at the seafloor, so all sig-nificant recharge supporting a siphon occurs through an outcrop.

The siphon fraction (FS) is defined as FS = Q S/Q TOT, where Q TOT is total outcrop discharge. In simulations with F S < 1, there is local circulation through one or more outcrops (water flows in through an outcrop and discharges through the same outcrop). In simulations for which F S < 0.01, we consider the siphon to be un-sustained (“broken”). In this case, advective heat extraction from the domain (if any) can be attributed to vigorous local circulation through, within, and around individual outcrops, but not from flow through an outcrop network.

4. Simulation results

4.1. Two outcrops (small/small), 20 km domain

The first set of simulations are based on a 20 × 20 km do-main, aquifer thickness of baq = 300 or 600 m, and two small (Dorado-sized) outcrops exposed at the northwest and southeast corners (upper left and lower right in map view). Aquifer per-meability was kaq = 10−11 to 10−9 m2, and outcrop permeability was koc = 10× and 0.1× the value of kaq [as in JFR flank simula-tions that sustained a hydrothermal siphon, Winslow et al., 2016;Winslow and Fisher, 2015]. When kaq = 10−11 m2, heat flow was suppressed close to the recharging outcrop, and little lithospheric heat was advected from the crust (Fig. 3C, F). Additional simu-lations with lower crustal aquifer permeability, kaq ≤ 10−12 m2,

142 R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151

Fig. 3. Distribution of seafloor heat flux as determined with one set of hydrothermal circulation simulations with side dimensions of 20 km, displayed in map view. There are two small outcrops that penetrate regional sediments at the upper left (“northwest”) and lower right (“southeast”) corners of the domains (small squares in black or white lines). Seafloor heat flux was evaluated at locations that are distant from outcrops (or potential outcrops) at corners of the domain (outside the larger squares defined with thick dashed lines in panel A). Seafloor heat flux is contoured and shown on a color scale, varying from very low values at sites of hydrothermal recharge and approaching or exceeding lithospheric values at discharge sites. Inset diagrams show histograms of simulated seafloor heat flux values (blue bars), the median of simulated values (vertical dashed line), and the range of values measured on the cool part of the Cocos Plate, around Dorado and Tengosed outcrops (stippled band; Hutnak et al., 2008). Simulations have aquifer thickness of 300 m (panels A–C) and 600 m (panels D–F). In each case shown, kaq is one order of magnitude higher and lower than the discharging (koc-d) and recharging outcrop (koc-r), as illustrated in panel D.

sustained a siphon but mined even less lithospheric heat, incon-sistent with observations. This suggests that aquifer permeability in the crust around Dorado outcrop is likely to be kaq > 10−12 m2; simulations with kaq ≤ 10−12 m2 are not discussed in the rest of this paper.

Increasing crustal aquifer permeability to kaq = 10−10 m2 re-sulted in faster siphon flow, and suppressed seafloor heat flux across a wider region, but median heat flux values were lowered by only 40–50% relative to lithospheric input (Fig. 3B, E). Seafloor heat flux in these simulations was consistent with global data for 20 Ma seafloor, but higher than observed around Dorado outcrop.

Raising aquifer permeability to kaq = 10−9 m2, with recharging and discharging outcrop permeabilities of 10−10 m2 and 10−8 m2, respectively, allowed a better match to conditions around Dorado outcrop (Fig. 3A, D).

The seafloor heat flux fraction, qf , scales monotonically with aquifer permeability in this initial set of simulations (Fig. 4A), and qf is well within the band of observed values in the field region when kaq = 10−9 m2. The rate of siphon flow, Q S, increases with aquifer permeability, Q S ∼ 100 kg/s to ∼1300 kg/s for kaq = 10−11

to 10−9 m2, and there is slightly more siphon flow for the thinner aquifer when kaq = 10−9 m2 (Fig. 4B). Essentially all of the flow

R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151 143

Fig. 4. Cross-plots of model output vs. permeability (aquifer or outcrop), for simulations with a 20 × 20-km domain with two small outcrops. Panels A, B, and C show results for simulations conducted with aquifer permeability (kaq) that is an order of magnitude greater than and less than that the discharging outcrop (koc-d) and recharging (koc-r) outcrop, respectively. Metrics shown are the heat flow fraction (qf), rate of flow as part of a hydrothermal siphon (Q S), and the fraction of hydrothermal circulation that contributes to siphon (outcrop-to-outcrop) transport (FS). Panels D, E, and F show results for simulations with koc-r = 10−8 m2, and koc-d ranging from 10−12 to 10−9 m2, for two aquifer thicknesses (baq = 300 m and 600 m) and two values of kaq = 10−9 and 10−10 m2. In panels A and D, band marked with diagonal lines indicates typical global values for 18–24 M.y. old seafloor, and gray band indicates range found above cool crust near Dorado outcrop. Symbols have been shifted slightly left or right along X-axis to avoid overlap. Arrows in panels B and E point to results from the same simulation.

through basement is associated with the hydrothermal siphon for kaq = 10−11 to 10−10 m2, but at higher permeabilities, secondary convection becomes increasingly important for simulations with a thicker aquifer (Fig. 4C). The siphon flow fraction drops to ∼0.65 when kaq = 10−9 m2 and baq = 600 m, consistent with lower Q Scompared to that with a thinner aquifer (Fig. 4B).

In simulations with a 600-m aquifer, the computed temperature and pressure differences in the aquifer between the recharging and discharging outcrops are on the order of tens of kPa (Table 3). The sign of the pressure difference depends on position within the aquifer, with the most rapid flow from recharging to discharging sites occurring near the base of the aquifer, and less intense re-turn flow occurring near the top of the aquifer. These pressure patterns illustrate complexities associated with transient, three-dimensional simulations that do not appear in two-dimensional simulations of outcrop-to-outcrop hydrothermal circulation (e.g., Hutnak et al., 2006; Winslow et al., 2016). These pressure dif-ferences are driven by the integrated contrast of fluid density at hydrothermal recharge and discharge sites; even in the case with the highest aquifer permeabilities modeled (10−9 m2), the pres-

sure difference across opposite corners of a 20 km domain is ∼17 kPa.

However, although the calculated flow rates in these simula-tions scale with differences in aquifer permeability, and thus tem-perature and pressure differences, that relation is not linear. A difference of permeability of two orders of magnitude (10−11 ver-sus 10−9 m2) results in �T values that vary by a factor of 6–8×, and �P values and flow rates that vary by a factor of 9–12×. This non-linearity is a fundamental consequence of the transient, three-dimensional coupling of temperature, pressure, and fluid flow rate. One cannot consider that one consequently leads to the other: the thermal, pressure, and flow fields develop simultaneously so as to settle in to a dynamic equilibrium that extracts heat efficiently, given heat input, system geometry, and crustal properties.

We ran additional simulations to test the sensitivity to dif-ferences in the permeability of discharging outcrops, while hold-ing aquifer permeability at kaq = 10−10 to 10−9 m2, and koc-r =10 × kaq (Fig. 4D–E). Setting permeability of the discharging out-crop at koc-d ≤ 10−11.5 m2 failed to remove 65–90% of lithospheric heat by hydrothermal advection (Fig. 4D), a key observation around

144 R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151

Table 3Summary of temperature and pressure differences and mean flow rates between two outcrops arranged on a diagonal for a 20 ×20 km grid domain with 600 m-thick aquifer.

kaqa

(m2)�Taq

b

(◦C)�Paq

b

(kPa)qmean

c

(m/s) (m/yr)

Small outcrop ↔ Large outcropd

Aquifer tope 10−9 −5.9 16.8 −1.4 × 10−7 −4.5Aquifer basee 9.6 16.7 2.3 × 10−7 7.3Aquifer top 10−9.5 −11.5 25.5 −9.3 × 10−8 −2.9Aquifer base 16.9 24.5 1.4 × 10−7 4.4Aquifer top 10−10 −26.3 43.3 −7.7 × 10−8 −2.4Aquifer base 39.2 42.1 1.2 × 10−7 3.7Aquifer top 10−10.5 −34.1 47.8 −3.3 × 10−8 −1.0Aquifer base 43.6 46.0 4.3 × 10−8 1.3Aquifer top 10−11 −46.3 56.9 −1.5 × 10−8 −0.5Aquifer base 57.8 53.7 2.0 × 10−8 0.6

Small outcrop ↔ Small outcropd

Aquifer top 10−9 −7.1 18.8 −1.8 × 10−7 −5.6Aquifer base 11 19.3 3.2 × 10−7 10.1Aquifer top 10−9.5 −12.7 28.2 −1.1 × 10−7 −3.4Aquifer base 19.5 28.4 1.7 × 10−7 5.2Aquifer top 10−10 −21.9 39.2 −6.1 × 10−8 −1.9Aquifer base 31 39.3 8.7 × 10−8 2.7Aquifer top 10−10.5 −31.2 50.9 −3.0 × 10−8 −0.9Aquifer base 47.8 50.8 4.6 × 10−8 1.4Aquifer top 10−11 −36.2 59.8 −1.2 × 10−8 −0.4Aquifer base 63.5 59.2 2.1 × 10−8 0.6

a Permeability in the basement aquifer, with outcrop permeabilities being ±one order of magnitude, as with models shown in Figs. 3D–F, 4A–C, and 5A–C.b �T aq and �P aq indicate the difference in temperature and pressure, respectively, calculated for outcrops on opposite sides of the simulation domain. Values are given

for T and P at the top and bottom of the aquifer layer.c Calculated mean fluid flow rates (specific discharge = volume flow rate/cross-sectional area perpendicular to flow). Positive flow rates occur at base of aquifer in all

cases, at higher rates, indicating the dominant flow direction. Negative flow rates occur at the top of the aquifer in these simulations, indicating flow towards the outcrop that is the primary source of hydrothermal recharge (return flow).

d Two sets of results are shown, for simulations with two small outcrops and simulations with one small and one large outcrop.e Calculations are shown for each value of aquifer permeability (kaq) for difference in T and P and flow rate at the top of the aquifer (base of the outcrop) and at the base

of the aquifer.

Dorado and Tengosed outcrops. When the permeability of the dis-charging outcrop was increased to koc-d ≥ 10−10 m2, simulated seafloor heat flux was consistent with observations for both thicker and thinner aquifers. For permeability of kaq = 10−10 m2, heat flux stabilized at the upper end of the observed range (qf ∼ 0.30 to 0.35), even with higher koc-r. In contrast, for aquifer permeability of kaq = 10−9 m2, higher values of koc-d resulted in commensu-rately greater advective removal of lithospheric heat (Fig. 4D), and higher rates of siphon flow (Fig. 4E). The siphon fraction also in-creased with increasing values of koc-d, reaching FS ∼ 1 for the 300 m-thick aquifer when kaq ≥ 10−11 m2, and FS ∼ 1 for the 600 m aquifer when kaq ≥ 10−10.5 m2.

In summary, initial simulations with two small basement out-crops on opposite corners of a 20 km domain require basement aquifer permeability of kaq ≥ 10−10 m2 to extract lithospheric heat as seen around Dorado and Tengosed outcrops, with the most con-sistent results being closer to 10−9 m2. The efficiency of heat ex-traction is greater when discharging outcrop permeability is higher, provided that recharging outcrop permeability is sufficiently large, with the highest siphon flow rates of Q S ≥ 2000–3000 kg/s when kaq ≥ 10−9 m2. Advective heat extraction is dominated by siphon flow when discharging outcrop permeability is sufficiently high, and aquifer thickness of baq = 600 m is most consistent with seafloor heat flux observations.

4.2. Two outcrops (large/small), 20 km domain

We repeated the initial simulations, but with two outcrops of different size arranged diagonally across the domain (Fig. 2), a geometry that is more consistent with the field area. These sim-ulations were started with the larger outcrop recharging and the smaller discharging, as part of a hydrothermal siphon, which is known to be a favored geometry for an outcrop-to-outcrop sys-

tem (Winslow and Fisher, 2015). As with the previously described set of simulations, permeability in the recharging outcrop was set initially to be 10× that in the crustal aquifer (koc-r = 10 ×kaq), and permeability in the discharging outcrop was set to be 0.1× that in the crustal aquifer (koc-d = 0.1 × kaq).

The efficiency of heat extraction was similar in these simula-tions to those having outcrops of equal sizes, with the results most consistent with observations when aquifer permeability was kaq ≥10−9.5 m2 (Fig. 5A). Siphon flow was similar to that in simulations having two small outcrops, rising monotonically with aquifer per-meability, and was somewhat lower for a thicker aquifer (Fig. 5B). However, the simulations with two outcrop sizes were very dif-ferent in terms of siphon fraction (compare Figs. 4C and 5C). In simulations with two different size outcrops, the siphon fraction was greatest when aquifer permeability was lowest (FS = 0.18 to 0.25 when kaq = 10−11 m2). The siphon fraction decreased mono-tonically to FS < 0.05 as kaq increased to 10−9 m2, yet the rate of siphon flow increased. There was no local recharge at the discharg-ing (smaller) outcrop; all hydrothermal discharge from this edifice originated at the recharging (larger) outcrop. The total magnitude of hydrothermal recharge increased considerably with basement aquifer permeability, but a greater fraction of recharge into the large outcrop circulated locally and discharged from the same out-crop.

These trends were a consequence of the development of vigor-ous secondary circulation at the recharging end of the hydrother-mal siphon, which was responsible for much of the simulated advective heat loss. For simulations with a large outcrop and kaq =10−9 m2, this secondary flow system moved ∼100× as much wa-ter as was moved through the hydrothermal siphon (Figs. 5B and 5C). The calculated pressure and temperature differences beneath recharging and discharging outcrops in 600-m aquifer simulations with a large and a small outcrop, and associated contrasts in

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Fig. 5. Cross-plots of model output vs. permeability (aquifer or outcrop), for simulations with a 20-km domain with one large and one small outcrop. The panels depict the same set of parameters described in Fig. 4. Symbols have been shifted slightly left or right along X-axis to avoid overlap.

fluid flow rates, show similarities and differences in comparison to simulations with two small outcrops (Table 3). Temperature differences tend to be larger when outcrops have different sizes, resulting in larger pressure differences. The largest differences in both �T and �P , and thus the largest increases in fluid flow rates, occur at the upper end of the permeability range tested. Overall, the differences between the two sets of simulations are modest, on the order of 10–20% (Table 3). The flow patterns indicated by these values are similar, with the most rapid fluid flow deeper in the aquifer, and weaker return flow near the top of the aquifer.

We ran additional simulations with two outcrop sizes and dif-ferent permeabilities in the discharging outcrop (Fig. 5D–F). The efficiency of heat extraction was such that, for baq = 600 m and kaq = 10−9 m2, all discharging outcrop permeabilities of koc-d =10−12 to 10−9 m2 matched field observations with qf = 0.10to 0.35 (Fig. 5D). Similar simulations with two small outcrops matched field observations only with koc-r ≥ 10−10 m2 (Fig. 4D). Siphon flow increased monotonically as the permeability of the discharging outcrop was increased (Fig. 5E), but in contrast to sim-ulations with two small outcrops, the siphon fraction was never >0.10 (Fig. 5F). This provides a stark contrast to simulations with two small outcrops (Fig. 4F), in which there was a critical thresh-old for koc-r, above which the siphon fraction went to 1.0.

In summary, for simulations with a 20 km domain and two out-crops, there were large differences in fluid flow patterns and the

efficiency of advective heat extraction as a function of relative out-crop sizes and properties. With one large and one small outcrop, there was much more flow into and out of the crust, but much less of this flow contributed to the hydrothermal siphon compared to simulations with two smaller outcrops.

4.3. Two outcrops (large/small), 40 km domain

The third set of simulations included two outcrops placed diag-onally across from each other, one large and one small, but with each side of the domain measuring 40 km, separating the outcrops by ∼56 km. This spacing is greater than the distance between Ten-gosed and Dorado outcrops, but is consistent with spacing between outcrops elsewhere on the cool part of the Cocos Plate (Fig. 1). The larger domain had a map-view area that was four times the size of that used in the last set of simulations, and we thought this might require higher aquifer permeability to achieve the same fluid-flow rate as with smaller domains.

Large domain simulations with basement permeability of kaq ≥10−11 m2, and outcrop permeabilities that were 10× and 0.1×as great as kaq (recharging and discharging, respectively), all sus-tained a hydrothermal siphon. But in comparison to smaller do-mains, there was less advective heat extraction for given values of aquifer and outcrop permeability (Figs. 5A and 6A). In fact, even with basement aquifer permeability and discharging outcrop per-

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Fig. 6. Cross-plots of model output vs. permeability (aquifer or outcrop), for simulations with a 40-km domain with one large and one small outcrop. The panels depict the same set of parameters described in Fig. 4. Symbols have been shifted slightly left or right along X-axis to avoid overlap.

meability of kaq = 10−9 and 10−8 m2, respectively, seafloor heat flux was greater than observed around Dorado outcrop (Fig. 6A). However, siphon flow rates were 2× to 3× higher in simulations with a larger domain, and the difference was greatest for simula-tions with a thicker aquifer (Figs. 5B and 6B). The larger domain also had higher siphon fractions, especially for simulations with a thicker aquifer (Figs. 5C and 6C).

We extended the large-domain simulations to include varia-tions in permeability in the discharging outcrop, koc-d (Fig. 6D–F). When koc-d ≥ 10−10 m2, simulated seafloor heat flux was consis-tent with field observations around Tengosed and Dorado outcrops (Fig. 6D), and siphon flow was Q S > 7000 kg/s for the thicker aquifer (Fig. 6E). Yet the siphon fraction remained low, never ex-ceeding FS = 0.15 (Fig. 6F). Thus even as the siphon flow doubled or tripled relative to that in smaller domains, so did the amount of fluid that entered the larger outcrop, circulated in the aquifer, then exited through the same outcrop.

4.4. Two large outcrops, 20-km square grid

A fourth set of simulations included two large outcrops on a small domain, 20 km on a side. These simulations sustained a hydrothermal siphon across the range of permeabilities tested, provided there was a contrast in the permeability of recharging

and discharging outcrops, and simulations with both 300 m and 600 m-thick crustal aquifers matched the distribution of field ob-servations of heat flux when kaq ≥ 10−10 m2 (Fig. 7A). In con-trast to earlier simulations, there were large differences in siphon flow rates between simulations with thicker and thinner basement aquifers (Fig. 7B), and siphon flow fractions were considerably greater (Fig. 7C).

Having two large outcrops made it challenging to quantify the influence of convection that recharged and discharged sin-gle outcrops, so we ran a sensitivity study to assess advective heat extraction with a poorly functioning or broken hydrother-mal siphon. This was achieved by making outcrop permeability the same as basement permeability. In contrast to earlier studies that focused on the JFR flank, in which a weak hydrothermal siphon failed completely without a large contrast in permeability be-tween recharging and discharging outcrops (Winslow et al., 2016;Winslow and Fisher, 2015), these large outcrop simulations were able to sustain a hydrothermal siphon under some circumstances with homogeneous permeability (Fig. 7E). Advective heat extrac-tion was consistent with field observations around Tengosed and Dorado outcrops for the 600 m-thick aquifer when kaq ≥ 10−10 m2, but other simulations failed to match observations. In addition, the variability of seafloor heat flux in individual simulations was sig-nificantly reduced in comparison to simulations in which koc �= kaq

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Fig. 7. Cross-plots of model output vs. permeability (aquifer or outcrop), for simulations with a 20-km domain with two large outcrops. Panels A, B and C depict the same set of parameters shown in Fig. 4. Panels D, E, and F show results for simulations in which the permeability of the crustal aquifer and both large outcrops have been set to the same values. Symbols have been shifted slightly left or right along X-axis to avoid overlap.

(Fig. 7D). There were large differences in siphon flow and the siphon flow fraction in simulations with homogeneous basement and outcrop permeability (Figs. 7E–7F). For a 300 m-thick aquifer, siphon flow was Q S ≤ 600 kg/s at an intermediate permeabil-ity, but the siphon was unsustainable when kaq = koc = 10−11 m2

or 10−9 m2. For a 600-m thick aquifer, the highest siphon flow was Q S ≤ 200 kg/s, when permeability was kaq = koc = 10−11 m2, and the siphon was unsustainable at higher permeabilities. The siphon fraction reached a peak for the 300 m-thick aquifer at kaq = koc = 10−10.5 m2, and for the 600 m-thick aquifer at kaq =koc = 10−11 m2. Value of FS ≤ 0.01 were simulated at higher per-meability values, indicating that all advective heat extraction due to hydrothermal circulation was local, with flow into and out of individual outcrops.

4.5. Patterns of fluid flow within the crustal aquifer and outcrops

Additional insight is provided by visualization of flow patterns across the simulation domain within and near basement outcrops (Fig. 8). We focus in this example on a 20 km domain and one large and one small outcrop, most consistent with the geometry of the Tengosed–Dorado outcrop pair, kaq = 10−9 m2 and outcrop permeabilities are 10× (koc-r) and 0.1× (koc-d) this value.

We employed particle tracing to assess the trajectories of fluid parcels associated with both a hydrothermal siphon and local convection, using flow rates and directions after the simulation achieved dynamic steady state. Several hundred virtual particles were “dropped” into the simulation domain within a circular area inside the larger (recharging) outcrop, and the paths of these par-ticles were projected forward in time until they exited the simu-lation domain (Fig. 8A). The vast majority of particles placed cir-culated locally, gathered some heat, then flowed rapidly out of the large outcrop (consistent with FS ∼ 0.05; Fig. 5C). A small fraction of particles flowed towards the smaller outcrop or encountered one of the side boundaries and flowed back towards the center of the domain. Some of these eventually discharged through the large outcrop, but a small fraction continued to the small outcrop, where they exited the seafloor (Fig. 8A). Color coding of particle tracks illustrates mixture of older and younger water discharg-ing through both outcrops, helping to explain why it is difficult to assign a single “age” to fluids that exit the seafloor from a ridge-flank hydrothermal system. In general, the fraction of older water flowing through the smaller outcrop is greater, consistent with apparent fluid ages near Dorado outcrop that are slightly greater than that of bottom water, and fluid chemistry that is lit-

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Fig. 8. Visualization of flow geometry for a simulation with a 20 × 20 km domain, one large outcrop and one small outcrop, with aquifer thickness, baq = 600 m, aquifer permeability kaq = 10−9 m2, and outcrop permeability being higher (large) and lower (small) by factor of 10× (simulation shown in Figs. 3D and 5). A. Sediment and aquifer elements have been removed for visualization, and particle paths are shown above conductive basement. Particles were “dropped” into the simulation within the large outcrop, and go from black to magenta to white as they age. Please see discussion in text, and calculated temperature and pressure differences below the outcrops, tabulated in Table 3. B. Fluid vectors at the large outcrop, viewed from the northeast. Darker vectors are flowing towards large outcrop, and lighter vectors are flowing away from the outcrop. Vectors are plotted with tails at grid node locations, using a natural-log scale. C. Fluid vectors at the small outcrop, viewed from the southwest. Lighter vectors are flowing towards the smaller outcrop, mostly deep in the aquifer.

tle different in terms of major elements (Wheat and Fisher, 2008;Wheat et al., 2017).

Diagrams of fluid vectors at the larger and smaller outcrops il-lustrate complex flow patterns in the adjacent crust (Fig. 8B–C). At the larger outcrop, water enters through both the top and the sloped sides, then flows deeper into the crustal aquifer before flowing laterally. Return flow to the recharging outcrop tends to occur in the shallowest part of the aquifer, consistent with tabu-lated pressure values from this simulation (Table 3), and part of the outcrop surface allows discharge of this fluid to the ocean. Fluid circulation in the aquifer around the outcrop is dominated by lateral flow, but there is mixed convection within the outcrop. There is strongly mixed convection in the basement aquifer near the smaller outcrop, yet the outcrop surface is dedicated entirely to discharge (Fig. 8C).

5. Discussion

5.1. Simulation constraints on upper crustal permeability

Simulations suggest that permeability within the crustal aquifer in the cool part of the Cocos Plate is ∼10−10 to 10−9 m2, with the most consistent results for the upper end of this range (Figs. 5–7).

These crustal permeability values are 10× to 1000× higher than measured in boreholes and inferred from three-dimensional sim-ulations of ∼3.5 Ma seafloor around Baby Bare and Grizzly Bare outcrops (e.g., Becker and Fisher, 2000; Fisher et al., 1997, 2008; Winslow and Fisher, 2015; Winslow et al., 2013). Both sets of sim-ulations show that it is easier to maintain a hydrothermal siphon between recharging and discharging outcrops when there is a sig-nificant contrast in outcrop size and/or permeability. And more simulations are consistent with the magnitude and variability of heat flux around Dorado and Tengosed outcrops when the crustal aquifer is 600 m thick rather than 300 m thick.

Earlier three-dimensional simulations of the eastern flank of the JFR showed the importance of the product of outcrop size and per-meability, termed “transmittance,” for sustaining a hydrothermal siphon (Winslow and Fisher, 2015). In the earlier study, a peak in siphon flow was achieved when the transmittance ratio be-tween recharging and discharging outcrops was ∼100×, whereas the peak in siphon fraction coincided with a transmittance ratio of ∼20×. Those relations were specific to a weak hydrothermal siphon that conveyed only ∼5–20 kg/s and extracted little litho-spheric heat. In contrast, for the hydrothermal system operating on the flank of the EPR on the cool part of the Cocos Plate, simula-tions suggest that the siphon flow rate is >1000 kg/s and perhaps

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as great at 7000 kg/s, in the range estimated from consideration of regional heat budgets (Hutnak et al., 2008).

Crustal aquifer permeabilities of 10−10 to 10−9 m2 are at the upper end of values measured in the upper ocean crust on a global basis, with higher values found mainly on much younger seafloor. In addition, the majority of data from borehole packer or thermal (flow) measurements have been made in crust formed at an intermediate or slow spreading rate, and most elevated values have been found in relatively thin zones in much younger crust (e.g., Becker et al., 1994; Becker, 1990; Becker and Fisher, 2000;Winslow et al., 2013). Only one set of data is from the upper crust formed under fast spreading conditions: Hole 801C in Juras-sic crust in the western Pacific Ocean (Larson et al., 1992). Per-meability from Hole 801C is below that inferred in the present study, but this is not surprising given the extent of alteration and infilling of cracks that is likely to have occurred since the Juras-sic. Other studies have suggested that fast spreading, character-ized by voluminous and relatively frequent outpourings of lava, might contribute to lateral continuity in fluid flow channels and thus high permeability (Fisher et al., 2003b; Hutnak et al., 2008;Hutnak et al., 2007), a hypothesis that remains to be tested with direct measurements of the crust around Dorado outcrop.

Studies of other settings have suggested highly elevated perme-abilities in young ocean crust, including one- and two-dimensional coupled-flow simulations, and calculations of response to pressure tidal, magmatic, and tectonic perturbations (e.g., Lowell and Ger-manovich, 1995; Yang et al., 1996; Davis et al., 1997; Davis et al., 2000; Stein and Fisher, 2003). Direct comparison of these results to those in the present study is problematic because permeabilities “calibrated” with models are strongly influenced by the dimension-ality of the representation, and by use of steady-state simulations, topics explored elsewhere (Winslow et al., 2016).

5.2. Regional versus local fluid circulation

Three-dimensional simulations show that the outcrop-to-outcrophydrothermal system on the cool part of the Cocos Plate may com-prise a small fraction of total fluid flow through the volcanic crust. Given the high crustal permeabilities necessary to allow advective extraction of the majority of lithospheric heat, there is potential to develop vigorous local convection, leading to regional heat extrac-tion by fluids that recharge and discharge through a single outcrop (e.g., Harris et al., 2004; Kawada et al., 2011). There is geochemical and thermal evidence for this form of local convection near Grizzly Bare outcrop (Wheat et al., 2013) and there are also locally ele-vated heat flux values adjacent to large outcrops on the cool part of the Cocos Plate (Hutnak et al., 2008, 2007). New simulations also suggest that outcrop-to-outcrop flow through small outcrops tends to favor siphon flow, whereas flow through large/small out-crops or two large outcrops favor development of local (secondary) circulation.

It will be challenging to distinguish between water that ex-tracts lithospheric heat as part of a hydrothermal siphon between outcrops, and water that travels in and out of a single outcrop during local convection, because both processes can extract heat efficiently and they can occur simultaneously (Fig. 8). Proximity to an outcrop that is suspected of recharging or discharging does not necessarily mean that either of these flow patterns dominates; even an outcrop that is mainly a site of hydrothermal discharge can release fluid that has traveled along heterogeneous flow paths, some local and some regional.

5.3. The influence of domain size and outcrop spacing

We anticipated that larger domains and greater outcrop spac-ing would require higher basement aquifer permeability to mine

an equivalent amount of lithospheric heat and generate commen-surate siphon flow rates. Instead, simulations based on a larger domain and greater outcrop spacing resulted in more and a greater fraction of siphon flow for a given crustal permeability (Fig. 6) in comparison to a smaller domain with the same outcrop geometry (Fig. 5). The best explanation for this observation is that a larger domain draws heat from a bigger map area. Temperatures in up-per basement can only be so low (limited by that of bottom water), so extracting an equivalent fraction of heat from a wider area in-creases the fluid mass flow rate and power output of discharging outcrops. The correlation between domain area, siphon flow and siphon fraction is not linear in these simulations: a four-fold in-crease in domain size corresponds to an increase in siphon flow of 2× to 3×, and an increase in siphon fraction of ≤2×.

Simulations with three or four outcrops can also explain the regional suppression of seafloor heat flux around Dorado and Ten-gosed outcrops (Fig. S-1). Additional geometries are possible, and the use of a square domain in map view, with outcrops placed at two or more corners, prevents fluids from bypassing one nearby outcrop and flowing through a more distant outcrop (Fig. 8). Re-sults of simulations completed to date, which are a small subset of possible fluid flow geometries (Fig. 1), present challenges for as-sessing which outcrops are hydrogeologically “connected” as part of a hydrothermal siphon. Outcrops that are more closely spaced might present the path of least resistance based on distance alone, but heterogeneity in the distribution of crustal permeability (which can vary by orders of magnitude) could result in more distant outcrop pairs being better connected. Detailed seafloor heat flow surveys can help to identify recharging and discharging outcrops, and direct testing with tracers (Neira et al., 2016) may be nec-essary to delineate hydrothermal pathways in these systems with confidence.

6. Summary and conclusions

We have presented the first three-dimensional, transient, fully-coupled simulations of fluid and heat transport on a ridge flank in fast spread ocean crust. Simulations were crafted to quantify rela-tions between the vigor of circulation, the extent of advective heat extraction from the crust, crustal aquifer thickness and permeabil-ity, and outcrop spacing size, and permeability. Extracting 65–90% of lithospheric heat from the cool part of the Cocos Plate appears to require permeability ≥10−10 to 10−9 m2, values at the upper end of measurements made in boreholes elsewhere in the volcanic ocean crust. Advective heat extraction in the field region is more efficient than is typical for similarly aged seafloor, and thus crustal permeabilities here may be higher as well. That said, there is lim-ited data from young to moderate aged ridge flanks formed under fast spreading conditions, and it remains to be determined if per-meabilities of this magnitude can be measured independently.

Simulations also suggest that outcrop-to-outcrop hydrothermal siphon flow in this region is likely to be a small fraction of the to-tal rate at which cool fluids circulate within the crust and extract heat. Much more fluid flow is likely to occur through individ-ual outcrops. Given the global population of seamounts scattered across the seafloor (e.g., Hillier and Watts, 2007; Wessel et al., 2010) and other volcanic rock exposures such as fracture zones and large igneous provinces, the vast majority of these circulation systems remain unexplored. Improved mapping and measurement tools will aid in this effort, and three-dimensional and transient computer simulations can help, but mapping fluid flow paths and rates with confidence will be a challenge.

Future simulations should explore topics that were not ad-dressed in the present study, including the importance of: het-erogeneous permeability paths and irregular boundaries between layers in the volcanic crust; basement outcrops that extend to

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different depths, networks of ≥4 basement outcrops, including variable size, distribution and spacing; and the nature of system responses to transient events such as earthquakes and seamount collapse. Additional field measurements and experiments should be directed towards resolving specific fluid flow pathways and rates of transport, so that future models can be tuned for appli-cation to conditions at individual field sites.

Acknowledgements

This research was supported by National Science Foundation grants OCE-0939564, OCE-1031808, OCE-1260408, and OCE-1355870(ATF). P. Stauffer, C. Gable and G. Zyvoloski (LANL) provided impor-tant gridding and modeling advice, and E. Boring and A. Torres provided essential computer and software support. This is C-DEBI contribution #439.

Appendix A. Supplementary material

Supplementary material related to this article can be found on-line at https://doi .org /10 .1016 /j .epsl .2018 .08 .025.

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