Three-Dimensional Models of Hydrothermal Circulation Through a Seamount Network on Fast-Spreading Crust ∗ Rachel M

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

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Earth and Planetary Science Letters

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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, Canada b Earth and Planetary Sciences Department, University of California, Santa Cruz, 95064, USA c Center for Dark Energy Biosphere Investigations, University of California, Santa Cruz, 95064, USA d 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: We present results from three-dimensional, transient, fully coupled simulations of fluid and heat Received 25 February 2018 transport on a ridge flank in fast-spread ocean crust. The simulations quantify relationships between rates Received in revised form 17 July 2018 of fluid flow, the extent of advective heat extraction, the geometry of crustal aquifers and outcrops, and Accepted 14 August 2018 crustal hydrologic parameters, with the goal of simulating conditions similar to those seen on 18–24 M.y. Available online xxxx old seafloor of the Cocos plate, offshore Costa Rica. Extensive surveys of this region documented a Editor: M. Bickle ∼14,500 km2 area of the seafloor with heat flux values that are 10–35% of those predicted from Keywords: conductive cooling models, and identified basement outcrops that serve as pathways for hydrothermal hydrothermal circulation circulation via recharge of bottom water and discharge of cool hydrothermal fluid. Simulations suggest ridge flank that in order for rapid hydrothermal circulation to achieve observed seafloor heat flux values, upper − − low-temperature crustal permeability is likely to be ∼10 10 to 10 9 m2, with more simulations matching observations coupled modeling 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 and exit the seafloor, bypassing the sedimentary boundary layer, outcrops (e.g., Davis et al., 1992;Fisher et al., 2003b;Stein and Fisher, 2003; Wheat and Fisher, 2008; Wheat et al., 2013). Subseafloor hy- ∼ Seamounts and basement outcrops are common features of the drothermal circulation is responsible for 15–25% of global heat global ocean floor (Hillier and Watts, 2007; Wessel et al., 2010) loss (Hasterock et al., 2013; Mottl, 2003;Stein and Stein, 1994), and can influence hydrothermal circulation in the volcanic ocean and influences the thermal and geochemical state of subducting crust (Anderson et al., 2012;Davis et al., 1992;Fisher et al., 2003a; plates, the formation and sustainability of the deep biosphere, and Fisher and Wheat, 2010; Hutnak et al., 2006; Villinger et al., the geochemical evolution of the oceans (e.g., Edwards et al., 2012; 2002;Winslow and Fisher, 2015). The volcanic ocean crust on Spinelli and Wang, 2008; Wheat and Mottl, 2004). the flanks of mid ocean ridges is commonly blanketed by low- Based on analyses of satellite gravimetric data, bathymetric permeability sediment that limits direct fluid exchange between (swath) maps and ship-based profile data, the global seamount 4 5 the ocean and underlying crustal aquifer (Fisher and Wheat, 2010; population is 10 –10 (Kim and Wessel, 2011; Wessel et al., 2010). Spinelli et al., 2004). Seamounts form pathways for fluids to enter 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., * Corresponding author at: Department of Geoscience, University of Calgary, Cal- gary, Alberta, Canada. 2003a, 2003b; Hutnak et al., 2006; Villinger et al., 2002), and mod- E-mail address: [email protected] (R.M. Lauer). eling studies have examined the influence of single- and multiple- https://doi.org/10.1016/j.epsl.2018.08.025 0012-821X/© 2018 Elsevier B.V. All rights reserved. R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151 139

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; outcrops and discharge is favored through smaller outcrops. There Hutnak et al., 2006;Kawada et al., 2011;Winslow and Fisher, is presently no regional, seafloor heat-flux deficit caused by the 2015). circulation of hydrothermal fluids from Grizzly Bare to Baby Bare, Ridge-flank hydrothermal circulation between recharging and because the fluid flow rate is low and little heat is extracted ad- discharging seamounts is driven by the pressure difference be- vectively (Fisher et al., 2003a; Hutnak et al., 2006). There were tween cool (descending) and warm (ascending) columns of crustal more basement outcrops in this region, and likely more vigorous fluids, forming a “hydrothermal siphon” (Fisher et al., 2003a; hydrothermal circulation, when sediment cover was thinner and Fisher and Wheat, 2010). There are two regions where hydrother- less complete (Hutnak and Fisher, 2007). mal circulation influenced by seamounts has been studied espe- In this study, we focus on a contrasting hydrothermal system, cially intensively: the eastern flank of the Juan de Fuca Ridge (JFR, located on ∼18–24 Ma seafloor of the Cocos Plate (Fig. 1). The central Juan de Fuca Plate, summarized briefly in this section), and physical geometry of outcrop-to-outcrop hydrothermal circulation the eastern flank the East Pacific Rise (EPR, eastern Cocos Plate, the in this area is similar to that around Grizzly Bare and Baby Bare, focus of this paper, described in the next section). Thick sediments but the systems are different in terms of fluid flow rates, the ef- cover young basement rocks across much of the first region be- ficiency of lithospheric heat extraction, and the properties of the cause of rapid Pleistocene sedimentation and trapping of sediment volcanic crust. by abyssal hill topography (Davis et al., 1992; Underwood et al., 2005). Detailed studies have focused on ∼3–4 Ma seafloor located 2. Advective heat loss from the western Cocos Plate 90–110 km east of the JFR, where isolated volcanic outcrops penetrate the sediment, several of which are known sites of hydrother- This study was motivated by extensive seismic reflection pro- mal discharge and recharge (Davis et al., 1992;Fisher et al., 2003a; files, swath mapping, coring, and heat flux surveys made on Hutnak et al., 2006; Wheat et al., 2000). 18–24 Ma seafloor offshore of Costa Rica, eastern Equatorial Pa- The best-studied discharge site in this area is Baby Bare out- cific Ocean (Fig. 1) (Fisher et al., 2003b;Hutnak et al., 2007). This crop, the tip of a volcanic edifice from which ∼5–20 L/s of part of the Cocos Plate comprises lithosphere generated by the fast ◦ low-temperature (∼25 C) hydrothermal fluids flow (Mottl et al., spreading East Pacific Rise (EPR) and the intermediate spreading 1998; Thomson et al., 1995; Wheat et al., 2004). Baby Bare flu- Cocos Nazca Spreading Center (CNS) (Barckhausen et al., 2001). ids are highly altered following reaction with basement rocks CNS-generated seafloor has heat flow that is consistent (on av- ◦ at ∼60–65 C. These fluids recharge through Grizzly Bare out- erage) with conductive lithospheric cooling models. In contrast, crop, a much larger edifice located 52 km south-southwest (e.g., part of the EPR-generated seafloor, having an area of 14,500 km2, Fisher et al., 2003a; Hutnak et al., 2006; Wheat et al., 2013; has heat flux that is 10–35% of predictions from conductive litho- Wheat and Mottl, 2000). Numerical simulations of outcrop-to- spheric cooling models, a regional deficit of 1.0–1.5 GW (Hutnak et outcrop hydrothermal circulation in this setting suggested that the al., 2008). Both of these areas (warmer and cooler) exhibit anoma- volcanic crustal aquifer is relatively thin (≤300 m) and has perme- lous heat flux values compared to global means for 18–24 Ma − − ability on the order of 10 13 to 10 12 m2 (Winslow et al., 2016). seafloor, which tends to have a heat flux that is 40–90% of con- These models also showed that recharge is favored through larger 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- Table 1 cos Plate does not correspond consistently to tectonic bound- Outcrop geometries as represented in simulations in this study. aries: the cool part of the plate is located entirely on EPR- Domain sizea Outcrop exposure areab Outcrop heightc generated seafloor, whereas the warm part of the plate includes (length/side) (km2) (m) CNS-generated seafloor and a part of EPR-generated seafloor on Two small outcrops 20 km 0.141 65 which there are no mapped seamounts (Fig. 1A). The cool part Large/small outcrop 20 km 0.141–14.1 65–500 of the Cocos Plate has eleven mapped outcrops (Hutnak et al., Large/small outcrop 40 km 0.141–14.1 65–500 Two large outcrops 20 km 14.1 500 2007, 2008; Fisher and Wheat, 2010). One small seamount, Dorado outcrop, was identified as a possible site of focused hydrother- a Each domain consists of a square prism, with outcrops located at opposite grid mal discharge on the basis of elevated heat flux (>1 W/m2) near corners. b Cross sectional area of full outcrop exposed at seafloor (quarter outcrop ×4). the outcrop edge, and rapid discharge of low-temperature pore c Height of outcrop above seafloor. fluid through thin sediments (Fisher and Harris, 2010; Wheat and Fisher, 2008; Wheat et al., 2017). The closest area of basement exposure where nearby heat flux measurements indicate hydrother- Table 2 Formation properties assigned to different regions in the simulation domain. mal recharge is Tengosed outcrop, ∼20 km to the east (Hutnak et al., 2007). Recharge through Tengosed and discharge through Porosity φ Permeability k Thermal (–) (m2) conductivity λ Dorado is consistent with smaller outcrops being favored as ridge- (W/m-K) flank discharge sites (e.g., Winslow and Fisher, 2015). − − Sedimenta 0.62–0.80 5.8 × 10 17 to 3.0 × 10 15 0.805–0.927 Dorado and Baby Bare outcrops have similar surface areas and − − Crustal aquiferb 0.1 10 15 to 10 9 1.82 − − are both surrounded by thick sediments, but the hydrothermal Outcrop 0.1 10 12 to 10 8 1.82 − system that cools a large part of the Cocos Plate is very differ- Conductive crust 0.05 10 19 1.93 ent from that around Baby Bare. Lithospheric heat flux around a Sediment properties vary with depth below seafloor. Thermal conductivities ad- Baby Bare is significantly greater than that surrounding Dorado, justed as needed to give correct values for cumulative thermal resistance at a given given the large difference in crustal ages (∼3–4 versus ∼20–24 depth, as discussed in Winslow et al. (2016). − M.y.). Upper basement temperatures between Tengosed and Do- b Crustal aquifer permeabilities of ≤10 12 m2 are not shown in this study, as rado (calculated from seismic reflection and heat flux data) are 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. 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 set of simulations, we modeled six arrangements having outcrop time for heating while in transit, and have low 14C ages com- spacing of 20 to 56 km. Geometric assumptions and hydrogeologic pared to those discharging from Baby Bare (Walker et al., 2008; limitations of this approach are discussed later. Simulations with Wheat and Fisher, 2008). Fluid samples collected from springs on two outcrops are presented in the main text, and examples with Dorado outcrop have major ion chemistry that is little different three and four outcrops are shown in the Supplementary Materi- from that of bottom seawater, but spring fluids have less dissolved als, along with an overview of numerical methods. oxygen and measurably higher concentrations of elements such as Simulations were run using two main sets of model grids, both Mo, Rb and V (Wheat et al., 2017). In contrast, Baby Bare fluids are based on a rectangular (tabular) domain, with dimensions of 20 or highly altered relative to bottom seawater (e.g., Mottl et al., 1998; 40 km on a side (Figs. 1C and 2). Given this geometry, a pair of Wheat et al., 2004). Based on the regional power deficit, discharge outcrops placed at two corners were spaced ∼20 to 28 km or ∼40 from Dorado outcrop may be 1000 to 20,000 L/s (Hutnak et al., to 56 km apart (for outcrops on a common side or arranged diago- 2008), 50 to 4000 times more than flows from Baby Bare. 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 3. Simulations of ridge-flank hydrothermal circulation the Cocos Plate. Domains were divided vertically into three tabular layers, with outcrops at the corners, comprising ≤450-m layer 3.1. Conceptual approach and simulation domains of low permeability sediments, a crustal “aquifer,” and a thick conductive boundary layer representing the deeper crust, which allows We explored several geometric arrangements for volcanic edi- space for warping of conductive isotherms in response to vigorous fices that can help explain efficient advective heat extraction on convection and lateral flow in the overlying crust. the cool part of the Cocos Plate, focusing on outcrops having sizes Outcrops were placed at domain corners, extending above sur- and shapes similar to Dorado and Tengosed (Hutnak et al., 2008, rounding seafloor sediments and connecting the volcanic crust to 2007; Table 1). We ran a suite of >350 simulations in which the ocean (Table 1, Fig. 2). Outcrops are idealized as ziggurats with we varied: domain geometry, number(s) and size(s) of outcrops, sloped sides, based on geometries determined from seismic reflec- crustal aquifer thickness and permeability, and the permeability of tion profiles on the cool part of the Cocos Plate (Hutnak et al., outcrops. Each simulation was run to dynamic steady-state, and 2007). Sediment properties (porosity, permeability, thermal con- fluid and heat fluxes were assessed and compared to each other ductivity) were assigned as a function of depth below the seafloor, and regional field observations. based on measurements made at nearby drilling sites and calcu- We don’t know the extent to which multiple outcrops could lations of equivalent thermal resistance (e.g., Hutnak et al., 2007) contribute to recharge and discharge of hydrothermal in this re- (Table 2). The top of the model domain was prescribed a depth- gion, but given a regular distribution of outcrops arranged in a dependent hydrostatic pressure and constant temperature bound- ◦ two-dimensional field (Fig. 1B), there are 18 unique combinations ary (2 C), consistent with measured bottom water temperatures in of two, three, or four outcrops (comprising sets of one or two this region (Fisher et al., 2003b; Hutnak et al., 2007). The base and sizes) that could occur (Fig. 1C). Based on the symmetry inherent sides of the domain are no-flow boundaries, and heat input at the in this representation of outcrop distribution (Fig. 1B), simulations base of the domain is 110 mW/m2, based on a lithospheric cooling represent a continuous field of outcrops, extending well beyond curve and crustal age of ∼20 My (Stein and Stein, 1994). the scope of the numerical domains. In our simulations, outcrops There are no permeability tests in the volcanic ocean crust of were placed at domain corners, with each edifice representing 1/4 the Cocos Plate, but core and borehole observations from IODP of an outcrop volume and area of exposure (Fig. 2). For an initial Hole 1256D, located on 15 Ma, EPR-generated seafloor along a R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151 141

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 heat flux, and qL = lithospheric heat flux input at the base of the of circulation (Expedition 335 Scientists, 2012). The extrusive sec- simulation domains (110 mW/m2). tion in this hole extends to ∼750 meters sub-basement (msb), As in earlier studies of outcrop-to-outcrop hydrothermal circu- and includes massive lava flows, pillow lavas, and thin layers of lation (Winslow and Fisher, 2015), and seen in the field (Hutnak hyaloclatites (Expedition 335 Scientists, 2012). Core alteration (Alt et al., 2006; Wheat et al., 2013), even when there is a flowing hy- et al., 2010) and borehole geophysical logs (Tominga et al., 2009) drothermal siphon (fluid flow into one outcrop exiting the seafloor indicate multiple zones of hydrothermal alteration in the upper at another outcrop) there can also be local discharge from an out- 600–700 msb. Based on these observations, we simulated crustal crop through which recharge occurs. Siphon flow (Q S, kg/s) is cal- aquifers having a thickness of 100 to 1000 m, and present re- culated by subtracting total simulated recharge from discharge at a sults from simulations with an aquifer thickness of 300 and 600 m, discharging outcrop. This corrects for recharge into an outcrop that which were the most consistent with field observations. Coupled, flows back out from the same edifice. Low permeability sediment transient simulations of the eastern flank of the JFR explored a effectively prohibits downward seepage at the seafloor, so all sig- similar range of crustal aquifer thickness (Spinelli and Fisher, 2004; nificant recharge supporting a siphon occurs through an outcrop. Stein and Fisher, 2001;Winslow et al., 2016), and borehole logs The siphon fraction (FS) is defined as FS = Q S/Q TOT, where and permeability tests in that region indicate high permeabil- Q TOT is total outcrop discharge. In simulations with F S < 1, there ity down to at least ∼300 msb (e.g., Becker and Fisher, 2000; is local circulation through one or more outcrops (water flows in Becker et al., 2013). through an outcrop and discharges through the same outcrop). In simulations for which F S < 0.01, we consider the siphon to be un- 3.2. Geothermal constraints and simulation metrics sustained (“broken”). In this case, advective heat extraction from the domain (if any) can be attributed to vigorous local circulation The distribution of conductive seafloor heat flux between out- through, within, and around individual outcrops, but not from flow crops was used as the primary constraint on the success of a sim- through an outcrop network. ulation in replicating field conditions. Hundreds of measurements from the cool part of the Cocos Plate show that median heat flux 4. Simulation results 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- 4.1. Two outcrops (small/small), 20 km domain ductive heat flux can be influenced near where sediment pinches out against volcanic outcrops by conductive refraction, secondary The first set of simulations are based on a 20 × 20 km do- convection, and local fluid advection. To avoid these effects in main, aquifer thickness of baq = 300 or 600 m, and two small comparing model results to regional observations, we defined a (Dorado-sized) outcrops exposed at the northwest and southeast common domain region to be used for assessing seafloor heat flux corners (upper left and lower right in map view). Aquifer per- −11 −9 2 from all simulations, excluding seafloor nodes within 1km of the meability was kaq = 10 to 10 m , and outcrop permeability edges of the largest outcrops simulated (Fig. 3A). This approach was koc = 10× and 0.1× the value of kaq [as in JFR flank simula- omits all four corners of the grids when calculating heat flux val- tions that sustained a hydrothermal siphon, Winslow et al., 2016; −11 2 ues from simulation output, equivalent to ∼8% of the 20-km-side Winslow and Fisher, 2015]. When kaq = 10 m , heat flow was domains, and ∼2% of the 40-km-side domains. To simplify com- suppressed close to the recharging outcrop, and little lithospheric parison of simulation results to field data, we calculate the heat heat was advected from the crust (Fig. 3C, F). Additional simu- −12 2 flow fraction (qf, unitless) as qf = qOBS/qL, where qOBS is observed lations with lower crustal aquifer permeability, kaq ≤ 10 m , 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.

−9 2 sustained a siphon but mined even less lithospheric heat, incon- Raising aquifer permeability to kaq = 10 m , with recharging − − sistent with observations. This suggests that aquifer permeability and discharging outcrop permeabilities of 10 10 m2 and 10 8 m2, −12 2 in the crust around Dorado outcrop is likely to be kaq > 10 m ; respectively, allowed a better match to conditions around Dorado −12 2 simulations with kaq ≤ 10 m are not discussed in the rest of outcrop (Fig. 3A, D). this paper. The seafloor heat flux fraction, qf, scales monotonically with −10 2 Increasing crustal aquifer permeability to kaq = 10 m re- aquifer permeability in this initial set of simulations (Fig. 4A), and sulted in faster siphon flow, and suppressed seafloor heat flux qf is well within the band of observed values in the field region −9 2 across a wider region, but median heat flux values were lowered when kaq = 10 m . The rate of siphon flow, Q S, increases with −11 by only 40–50% relative to lithospheric input (Fig. 3B, E). Seafloor aquifer permeability, Q S ∼ 100 kg/sto ∼1300 kg/s for kaq = 10 − heat flux in these simulations was consistent with global data for to 10 9 m2, and there is slightly more siphon flow for the thinner −9 2 20 Ma seafloor, but higher than observed around Dorado outcrop. aquifer when kaq = 10 m (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 −8 2 −12 −9 2 contributes to siphon (outcrop-to-outcrop) transport (FS). Panels D, E, and F show results for simulations with koc-r = 10 m , and koc-d ranging from 10 to 10 m , −9 −10 2 for two aquifer thicknesses (baq = 300 m and 600 m) and two values of kaq = 10 and 10 m . 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 sure difference across opposite corners of a 20 km domain is −11 −10 2 kaq = 10 to 10 m , but at higher permeabilities, secondary ∼17 kPa. convection becomes increasingly important for simulations with a However, although the calculated flow rates in these simula- thicker aquifer (Fig. 4C). The siphon flow fraction drops to ∼0.65 tions scale with differences in aquifer permeability, and thus tem- −9 2 when kaq = 10 m and baq = 600 m, consistent with lower Q S perature and pressure differences, that relation is not linear. A − compared to that with a thinner aquifer (Fig. 4B). difference of permeability of two orders of magnitude (10 11 ver- − In simulations with a 600-m aquifer, the computed temperature sus 10 9 m2) results in T values that vary by a factor of 6–8×, and pressure differences in the aquifer between the recharging and and P values and flow rates that vary by a factor of 9–12×. This discharging outcrops are on the order of tens of kPa (Table 3). non-linearity is a fundamental consequence of the transient, three- The sign of the pressure difference depends on position within the dimensional coupling of temperature, pressure, and fluid flow rate. aquifer, with the most rapid flow from recharging to discharging One cannot consider that one consequently leads to the other: the sites occurring near the base of the aquifer, and less intense re- thermal, pressure, and flow fields develop simultaneously so as to turn flow occurring near the top of the aquifer. These pressure settle in to a dynamic equilibrium that extracts heat efficiently, patterns illustrate complexities associated with transient, three- given heat input, system geometry, and crustal properties. dimensional simulations that do not appear in two-dimensional We ran additional simulations to test the sensitivity to dif- simulations of outcrop-to-outcrop hydrothermal circulation (e.g., ferences in the permeability of discharging outcrops, while hold- −10 −9 2 Hutnak et al., 2006;Winslow et al., 2016). These pressure dif- ing aquifer permeability at kaq = 10 to 10 m , and koc-r = ferences are driven by the integrated contrast of fluid density at 10 × kaq (Fig. 4D–E). Setting permeability of the discharging out- −11.5 2 hydrothermal recharge and discharge sites; even in the case with crop at koc-d ≤ 10 m failed to remove 65–90% of lithospheric − the highest aquifer permeabilities modeled (10 9 m2), the pres- 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 3 Summary 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.

a b b c kaq Taq Paq qmean 2 ◦ (m ) ( C) (kPa) (m/s) (m/yr) Small outcrop ↔ Large outcropd − − Aquifer tope 10 9 −5.9 16.8 −1.4 × 10 7 −4.5 − Aquifer basee 9.6 16.7 2.3 × 10 7 7.3 − − Aquifer top 10 9.5 −11.5 25.5 −9.3 × 10 8 −2.9 − Aquifer base 16.9 24.5 1.4 × 10 7 4.4 − − Aquifer top 10 10 −26.3 43.3 −7.7 × 10 8 −2.4 − Aquifer base 39.2 42.1 1.2 × 10 7 3.7 − − Aquifer top 10 10.5 −34.147.8 −3.3 × 10 8 −1.0 − Aquifer base 43.6 46.0 4.3 × 10 8 1.3 − − Aquifer top 10 11 −46.3 56.9 −1.5 × 10 8 −0.5 − Aquifer 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 −5.6 − Aquifer base 11 19.3 3.2 × 10 7 10.1 − − Aquifer top 10 9.5 −12.7 28.2 −1.1 × 10 7 −3.4 − Aquifer base 19.5 28.4 1.7 × 10 7 5.2 − − Aquifer top 10 10 −21.9 39.2 −6.1 × 10 8 −1.9 − Aquifer base 31 39.3 8.7 × 10 8 2.7 − − Aquifer top 10 10.5 −31.250.9 −3.0 × 10 8 −0.9 − Aquifer base 47.850.8 4.6 × 10 8 1.4 − − Aquifer top 10 11 −36.2 59.8 −1.2 × 10 8 −0.4 − Aquifer 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- tem (Winslow and Fisher, 2015). As with the previously described −10 2 charging outcrop was increased to koc-d ≥ 10 m , simulated set of simulations, permeability in the recharging outcrop was set seafloor heat flux was consistent with observations for both thicker initially to be 10× that in the crustal aquifer (koc-r = 10 ×kaq), and −10 2 and thinner aquifers. For permeability of kaq = 10 m , heat flux permeability in the discharging outcrop was set to be 0.1× that in ∼ stabilized at the upper end of the observed range (qf 0.30 to the crustal aquifer (koc-d = 0.1 × kaq). 0.35), even with higher koc-r. In contrast, for aquifer permeability The efficiency of heat extraction was similar in these simula- −9 2 of kaq = 10 m , higher values of koc-d resulted in commensu- tions to those having outcrops of equal sizes, with the results most rately greater advective removal of lithospheric heat (Fig. 4D), and consistent with observations when aquifer permeability was kaq ≥ − higher rates of siphon flow (Fig. 4E). The siphon fraction also in- 10 9.5 m2 (Fig. 5A). Siphon flow was similar to that in simulations creased with increasing values of koc-d, reaching FS ∼ 1for the 300 having two small outcrops, rising monotonically with aquifer per- −11 2 m-thick aquifer when kaq ≥ 10 m , and FS ∼ 1for the 600 m meability, and was somewhat lower for a thicker aquifer (Fig. 5B). −10.5 2 aquifer when kaq ≥ 10 m . However, the simulations with two outcrop sizes were very dif- In summary, initial simulations with two small basement out- ferent in terms of siphon fraction (compare Figs. 4C and 5C). In crops on opposite corners of a 20 km domain require basement simulations with two different size outcrops, the siphon fraction ≥ −10 2 aquifer permeability of kaq 10 m to extract lithospheric heat was greatest when aquifer permeability was lowest (FS = 0.18 to −11 2 as seen around Dorado and Tengosed outcrops, with the most con- 0.25 when kaq = 10 m ). The siphon fraction decreased mono- −9 2 −9 2 sistent results being closer to 10 m . The efficiency of heat ex- tonically to FS < 0.05 as kaq increased to 10 m , yet the rate of traction is greater when discharging outcrop permeability is higher, siphon flow increased. There was no local recharge at the discharg- provided that recharging outcrop permeability is sufficiently large, ing (smaller) outcrop; all hydrothermal discharge from this edifice ≥ with the highest siphon flow rates of Q S 2000–3000 kg/s when originated at the recharging (larger) outcrop. The total magnitude ≥ −9 2 kaq 10 m . Advective heat extraction is dominated by siphon of hydrothermal recharge increased considerably with basement flow when discharging outcrop permeability is sufficiently high, aquifer permeability, but a greater fraction of recharge into the = and aquifer thickness of baq 600 m is most consistent with large outcrop circulated locally and discharged from the same out- seafloor heat flux observations. crop. These trends were a consequence of the development of vigor- 4.2. Two outcrops (large/small), 20 km domain ous secondary circulation at the recharging end of the hydrothermal siphon, which was responsible for much of the simulated We repeated the initial simulations, but with two outcrops of advective heat loss. For simulations with a large outcrop and kaq = − different size arranged diagonally across the domain (Fig. 2), a 10 9 m2, this secondary flow system moved ∼100× as much wa- geometry that is more consistent with the field area. These sim- ter as was moved through the hydrothermal siphon (Figs. 5B and ulations were started with the larger outcrop recharging and the 5C). The calculated pressure and temperature differences beneath smaller discharging, as part of a hydrothermal siphon, which is recharging and discharging outcrops in 600-m aquifer simulations known to be a favored geometry for an outcrop-to-outcrop sys- with a large and a small outcrop, and associated contrasts in R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151 145

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 efficiency of advective heat extraction as a function of relative out- to simulations with two small outcrops (Table 3). Temperature crop sizes and properties. With one large and one small outcrop, differences tend to be larger when outcrops have different sizes, there was much more flow into and out of the crust, but much less resulting in larger pressure differences. The largest differences in of this flow contributed to the hydrothermal siphon compared to both T and P , and thus the largest increases in fluid flow rates, simulations with two smaller outcrops. occur at the upper end of the permeability range tested. Overall, the differences between the two sets of simulations are modest, 4.3. Two outcrops (large/small), 40 km domain 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 third set of simulations included two outcrops placed diag- the aquifer, and weaker return flow near the top of the aquifer. onally across from each other, one large and one small, but with We ran additional simulations with two outcrop sizes and dif- each side of the domain measuring 40 km, separating the outcrops ferent permeabilities in the discharging outcrop (Fig. 5D–F). The by ∼56 km. This spacing is greater than the distance between Ten- = efficiency of heat extraction was such that, for baq 600 m and gosed and Dorado outcrops, but is consistent with spacing between = −9 2 = kaq 10 m , all discharging outcrop permeabilities of koc-d outcrops elsewhere on the cool part of the Cocos Plate (Fig. 1). The −12 −9 2 = 10 to 10 m matched field observations with qf 0.10 larger domain had a map-view area that was four times the size of to 0.35 (Fig. 5D). Similar simulations with two small outcrops that used in the last set of simulations, and we thought this might −10 2 matched field observations only with koc-r ≥ 10 m (Fig. 4D). require higher aquifer permeability to achieve the same fluid-flow Siphon flow increased monotonically as the permeability of the rate as with smaller domains. discharging outcrop was increased (Fig. 5E), but in contrast to sim- Large domain simulations with basement permeability of kaq ≥ − ulations with two small outcrops, the siphon fraction was never 10 11 m2, and outcrop permeabilities that were 10× and 0.1× >0.10 (Fig. 5F). This provides a stark contrast to simulations with as great as kaq (recharging and discharging, respectively), all sus- two small outcrops (Fig. 4F), in which there was a critical thresh- tained a hydrothermal siphon. But in comparison to smaller do- old for koc-r, above which the siphon fraction went to 1.0. mains, there was less advective heat extraction for given values of In summary, for simulations with a 20 km domain and two out- aquifer and outcrop permeability (Figs. 5A and 6A). In fact, even crops, there were large differences in fluid flow patterns and the with basement aquifer permeability and discharging outcrop per- 146 R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151

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.

−9 −8 2 meability of kaq = 10 and 10 m , respectively, seafloor heat and discharging outcrops, and simulations with both 300 m and flux was greater than observed around Dorado outcrop (Fig. 6A). 600 m-thick crustal aquifers matched the distribution of field ob- −10 2 However, siphon flow rates were 2× to 3× higher in simulations servations of heat flux when kaq ≥ 10 m (Fig. 7A). In con- with a larger domain, and the difference was greatest for simula- trast to earlier simulations, there were large differences in siphon tions with a thicker aquifer (Figs. 5B and 6B). The larger domain flow rates between simulations with thicker and thinner basement also had higher siphon fractions, especially for simulations with a aquifers (Fig. 7B), and siphon flow fractions were considerably thicker aquifer (Figs. 5C and 6C). greater (Fig. 7C). We extended the large-domain simulations to include varia- Having two large outcrops made it challenging to quantify tions in permeability in the discharging outcrop, koc-d (Fig. 6D–F). the influence of convection that recharged and discharged sin- −10 2 When koc-d ≥ 10 m , simulated seafloor heat flux was consis- gle outcrops, so we ran a sensitivity study to assess advective tent with field observations around Tengosed and Dorado outcrops heat extraction with a poorly functioning or broken hydrother- (Fig. 6D), and siphon flow was Q S > 7000 kg/sfor the thicker mal siphon. This was achieved by making outcrop permeability the aquifer (Fig. 6E). Yet the siphon fraction remained low, never ex- same as basement permeability. In contrast to earlier studies that ceeding FS = 0.15 (Fig. 6F). Thus even as the siphon flow doubled focused on the JFR flank, in which a weak hydrothermal siphon or tripled relative to that in smaller domains, so did the amount of failed completely without a large contrast in permeability be- fluid that entered the larger outcrop, circulated in the aquifer, then tween recharging and discharging outcrops (Winslow et al., 2016; exited through the same outcrop. Winslow and Fisher, 2015), these large outcrop simulations were able to sustain a hydrothermal siphon under some circumstances 4.4. Two large outcrops, 20-km square grid with homogeneous permeability (Fig. 7E). Advective heat extraction was consistent with field observations around Tengosed and −10 2 A fourth set of simulations included two large outcrops on Dorado outcrops for the 600 m-thick aquifer when kaq ≥ 10 m , a small domain, 20 km on a side. These simulations sustained but other simulations failed to match observations. In addition, the a hydrothermal siphon across the range of permeabilities tested, variability of seafloor heat flux in individual simulations was sig- provided there was a contrast in the permeability of recharging nificantly reduced in comparison to simulations in which koc = kaq R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151 147

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 We employed particle tracing to assess the trajectories of fluid siphon flow fraction in simulations with homogeneous basement parcels associated with both a hydrothermal siphon and local and outcrop permeability (Figs. 7E–7F). For a 300 m-thick aquifer, convection, using flow rates and directions after the simulation ≤ siphon flow was Q S 600 kg/sat an intermediate permeabil- achieved dynamic steady state. Several hundred virtual particles = = −11 2 ity, but the siphon was unsustainable when kaq koc 10 m were “dropped” into the simulation domain within a circular area −9 2 or 10 m . For a 600-m thick aquifer, the highest siphon flow inside the larger (recharging) outcrop, and the paths of these par- ≤ = = −11 2 was Q S 200 kg/s, when permeability was kaq koc 10 m , ticles were projected forward in time until they exited the simu- and the siphon was unsustainable at higher permeabilities. The lation domain (Fig. 8A). The vast majority of particles placed cir- siphon fraction reached a peak for the 300 m-thick aquifer at −10.5 2 culated locally, gathered some heat, then flowed rapidly out of the kaq = koc = 10 m , and for the 600 m-thick aquifer at kaq = − large outcrop (consistent with F ∼ 0.05; Fig. 5C). A small fraction k = 10 11 m2. Value of F ≤ 0.01 were simulated at higher per- S oc S of particles flowed towards the smaller outcrop or encountered meability values, indicating that all advective heat extraction due one of the side boundaries and flowed back towards the center to hydrothermal circulation was local, with flow into and out of individual outcrops. of the domain. Some of these eventually discharged through the large outcrop, but a small fraction continued to the small outcrop, 4.5. Patterns of fluid flow within the crustal aquifer and outcrops where they exited the seafloor (Fig. 8A). Color coding of particle tracks illustrates mixture of older and younger water discharg- Additional insight is provided by visualization of flow patterns ing through both outcrops, helping to explain why it is difficult across the simulation domain within and near basement outcrops to assign a single “age” to fluids that exit the seafloor from a (Fig. 8). We focus in this example on a 20 km domain and one ridge-flank hydrothermal system. In general, the fraction of older large and one small outcrop, most consistent with the geometry water flowing through the smaller outcrop is greater, consistent −9 2 of the Tengosed–Dorado outcrop pair, kaq = 10 m and outcrop with apparent fluid ages near Dorado outcrop that are slightly permeabilities are 10× (koc-r) and 0.1× (koc-d) this value. greater than that of bottom water, and fluid chemistry that is lit- 148 R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151

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 −9 2 permeability kaq = 10 m , 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; These crustal permeability values are 10× to 1000× higher than Wheat et al., 2017). measured in boreholes and inferred from three-dimensional sim- Diagrams of fluid vectors at the larger and smaller outcrops il- ulations of ∼3.5 Ma seafloor around Baby Bare and Grizzly Bare lustrate complex flow patterns in the adjacent crust (Fig. 8B–C). outcrops (e.g., Becker and Fisher, 2000;Fisher et al., 1997, 2008; At the larger outcrop, water enters through both the top and the Winslow and Fisher, 2015;Winslow et al., 2013). Both sets of sim- sloped sides, then flows deeper into the crustal aquifer before ulations show that it is easier to maintain a hydrothermal siphon flowing laterally. Return flow to the recharging outcrop tends to between recharging and discharging outcrops when there is a sig- occur in the shallowest part of the aquifer, consistent with tabu- nificant contrast in outcrop size and/or permeability. And more lated pressure values from this simulation (Table 3), and part of simulations are consistent with the magnitude and variability of the outcrop surface allows discharge of this fluid to the ocean. heat flux around Dorado and Tengosed outcrops when the crustal Fluid circulation in the aquifer around the outcrop is dominated aquifer is 600 m thick rather than 300 m thick. by lateral flow, but there is mixed convection within the outcrop. Earlier three-dimensional simulations of the eastern flank of the There is strongly mixed convection in the basement aquifer near JFR showed the importance of the product of outcrop size and per- the smaller outcrop, yet the outcrop surface is dedicated entirely meability, termed “transmittance,” for sustaining a hydrothermal to discharge (Fig. 8C). siphon (Winslow and Fisher, 2015). In the earlier study, a peak in siphon flow was achieved when the transmittance ratio be- 5. Discussion tween recharging and discharging outcrops was ∼100×, whereas the peak in siphon fraction coincided with a transmittance ratio 5.1. Simulation constraints on upper crustal permeability of ∼20×. Those relations were specific to a weak hydrothermal siphon that conveyed only ∼5–20 kg/s and extracted little litho- Simulations suggest that permeability within the crustal aquifer spheric heat. In contrast, for the hydrothermal system operating on − − in the cool part of the Cocos Plate is ∼10 10 to 10 9 m2, with the the flank of the EPR on the cool part of the Cocos Plate, simula- most consistent results for the upper end of this range (Figs. 5–7). tions suggest that the siphon flow rate is >1000 kg/s and perhaps R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151 149 as great at 7000 kg/s, in the range estimated from consideration of an equivalent amount of lithospheric heat and generate commen- regional heat budgets (Hutnak et al., 2008). surate siphon flow rates. Instead, simulations based on a larger − − Crustal aquifer permeabilities of 10 10 to 10 9 m2 are at the domain and greater outcrop spacing resulted in more and a greater upper end of values measured in the upper ocean crust on a fraction of siphon flow for a given crustal permeability (Fig. 6) in global basis, with higher values found mainly on much younger comparison to a smaller domain with the same outcrop geometry seafloor. In addition, the majority of data from borehole packer or (Fig. 5). The best explanation for this observation is that a larger thermal (flow) measurements have been made in crust formed at domain draws heat from a bigger map area. Temperatures in up- an intermediate or slow spreading rate, and most elevated values per basement can only be so low (limited by that of bottom water), have been found in relatively thin zones in much younger crust so extracting an equivalent fraction of heat from a wider area in- (e.g., Becker et al., 1994; Becker, 1990;Becker and Fisher, 2000; creases the fluid mass flow rate and power output of discharging Winslow et al., 2013). Only one set of data is from the upper outcrops. The correlation between domain area, siphon flow and crust formed under fast spreading conditions: Hole 801C in Juras- siphon fraction is not linear in these simulations: a four-fold in- sic crust in the western Pacific Ocean (Larson et al., 1992). Per- crease in domain size corresponds to an increase in siphon flow of meability from Hole 801C is below that inferred in the present 2× to 3×, and an increase in siphon fraction of ≤2×. study, but this is not surprising given the extent of alteration and Simulations with three or four outcrops can also explain the infilling of cracks that is likely to have occurred since the Juras- regional suppression of seafloor heat flux around Dorado and Ten- sic. Other studies have suggested that fast spreading, character- gosed outcrops (Fig. S-1). Additional geometries are possible, and ized by voluminous and relatively frequent outpourings of lava, the use of a square domain in map view, with outcrops placed at might contribute to lateral continuity in fluid flow channels and two or more corners, prevents fluids from bypassing one nearby thus high permeability (Fisher et al., 2003b; Hutnak et al., 2008; outcrop and flowing through a more distant outcrop (Fig. 8). Re- Hutnak et al., 2007), a hypothesis that remains to be tested with sults of simulations completed to date, which are a small subset direct measurements of the crust around Dorado outcrop. of possible fluid flow geometries (Fig. 1), present challenges for as- Studies of other settings have suggested highly elevated perme- sessing which outcrops are hydrogeologically “connected” as part abilities in young ocean crust, including one- and two-dimensional of a hydrothermal siphon. Outcrops that are more closely spaced coupled-flow simulations, and calculations of response to pressure might present the path of least resistance based on distance alone, tidal, magmatic, and tectonic perturbations (e.g., Lowell and Ger- but heterogeneity in the distribution of crustal permeability (which manovich, 1995; Yang et al., 1996;Davis et al., 1997;Davis et al., can vary by orders of magnitude) could result in more distant 2000;Stein and Fisher, 2003). Direct comparison of these results outcrop pairs being better connected. Detailed seafloor heat flow to those in the present study is problematic because permeabilities surveys can help to identify recharging and discharging outcrops, “calibrated” with models are strongly influenced by the dimension- and direct testing with tracers (Neira et al., 2016)may be nec- ality of the representation, and by use of steady-state simulations, essary to delineate hydrothermal pathways in these systems with topics explored elsewhere (Winslow et al., 2016). confidence.

5.2. Regional versus local ﬂuid circulation 6. Summary and conclusions

Three-dimensional simulations show that the outcrop-to-outcrop We have presented the first three-dimensional, transient, fully- hydrothermal system on the cool part of the Cocos Plate may com- coupled simulations of fluid and heat transport on a ridge flank in prise a small fraction of total fluid flow through the volcanic crust. fast spread ocean crust. Simulations were crafted to quantify rela- Given the high crustal permeabilities necessary to allow advective tions between the vigor of circulation, the extent of advective heat extraction of the majority of lithospheric heat, there is potential to extraction from the crust, crustal aquifer thickness and permeabil- develop vigorous local convection, leading to regional heat extrac- ity, and outcrop spacing size, and permeability. Extracting 65–90% tion by fluids that recharge and discharge through a single outcrop of lithospheric heat from the cool part of the Cocos Plate appears − − (e.g., Harris et al., 2004;Kawada et al., 2011). There is geochemical to require permeability ≥10 10 to 10 9 m2, values at the upper and thermal evidence for this form of local convection near Grizzly end of measurements made in boreholes elsewhere in the volcanic Bare outcrop (Wheat et al., 2013) and there are also locally ele- ocean crust. Advective heat extraction in the field region is more vated heat flux values adjacent to large outcrops on the cool part efficient than is typical for similarly aged seafloor, and thus crustal of the Cocos Plate (Hutnak et al., 2008, 2007). New simulations permeabilities here may be higher as well. That said, there is lim- also suggest that outcrop-to-outcrop flow through small outcrops ited data from young to moderate aged ridge flanks formed under tends to favor siphon flow, whereas flow through large/small out- fast spreading conditions, and it remains to be determined if per- crops or two large outcrops favor development of local (secondary) meabilities of this magnitude can be measured independently. circulation. Simulations also suggest that outcrop-to-outcrop hydrothermal It will be challenging to distinguish between water that ex- siphon flow in this region is likely to be a small fraction of the to- tracts lithospheric heat as part of a hydrothermal siphon between tal rate at which cool fluids circulate within the crust and extract outcrops, and water that travels in and out of a single outcrop heat. Much more fluid flow is likely to occur through individ- during local convection, because both processes can extract heat ual outcrops. Given the global population of seamounts scattered efficiently and they can occur simultaneously (Fig. 8). Proximity across the seafloor (e.g., Hillier and Watts, 2007; Wessel et al., to an outcrop that is suspected of recharging or discharging does 2010) and other volcanic rock exposures such as fracture zones not necessarily mean that either of these flow patterns dominates; and large igneous provinces, the vast majority of these circulation even an outcrop that is mainly a site of hydrothermal discharge systems remain unexplored. Improved mapping and measurement can release fluid that has traveled along heterogeneous flow paths, tools will aid in this effort, and three-dimensional and transient some local and some regional. computer simulations can help, but mapping fluid flow paths and rates with confidence will be a challenge. 5.3. The influence of domain size and outcrop spacing Future simulations should explore topics that were not ad- dressed in the present study, including the importance of: het- We anticipated that larger domains and greater outcrop spac- erogeneous permeability paths and irregular boundaries between ing would require higher basement aquifer permeability to mine layers in the volcanic crust; basement outcrops that extend to 150 R.M. Lauer et al. / Earth and Planetary Science Letters 501 (2018) 138–151 different depths, networks of ≥4 basement outcrops, including Fisher, A.T., Harris, R., 2010. Using seafloor heat flow as a tracer to map subseafloor variable size, distribution and spacing; and the nature of system fluid flow in the ocean crust. Geofluids 10. https://doi .org /10 .1111 /j .1468 -8123 . responses to transient events such as earthquakes and seamount 2009 .00274 .x. Fisher, A.T., Stein, C.A., Harris, R.N., Wang, K., Silver, E.A., Pfender, M., Hutnak, M., collapse. Additional field measurements and experiments should Cherkaoui, A., Bodzin, R., Villinger, H., 2003b. Abrupt thermal transition reveals be directed towards resolving specific fluid flow pathways and hydrothermal boundary and role of seamounts within the Cocos Plate. Geophys. rates of transport, so that future models can be tuned for appli- Res. Lett. 30, 1550. https://doi .org /10 .1029 /2002GL016766. cation to conditions at individual field sites. Fisher, A.T., Wheat, C.G., 2010. Seamounts as conduits for massive fluid, heat, and solute fluxes on ridge flanks. Oceanography 23, 74–87. Harris, R.N., Fisher, A.T., Chapman, D., 2004. Fluid flow through seamounts and im- Acknowledgements plications for global mass fluxes. Geology 32, 725–728. https://doi .org /10 .1130 / G20387.20381. This research was supported by National Science Foundation Hasterock, D., 2013. Global patterns and vigor of ventilated hydrothermal circulation grants OCE-0939564, OCE-1031808, OCE-1260408, and OCE-1355870 through young seafloor. Earth Planet. Sci. Lett. 380, 12–20. https://doi .org /10 . (ATF). P. Stauffer, C. Gable and G. Zyvoloski (LANL) provided impor- 1016 /j .epsl .2013 .08 .016. Hasterock, D., Chapman, D.S., Davis, E.E., 2013. Oceanic heat flow: implications for tant gridding and modeling advice, and E. Boring and A. Torres global heat loss. Earth Planet. Sci. Lett. 311, 386–395. https://doi .org /10 .1016 /j . provided essential computer and software support. This is C-DEBI epsl .2011.09 .044. contribution #439. Hillier, J.K., Watts, A.B., 2007. Global distribution of seamounts from ship-track bathymetry data. Geophys. Res. Lett. 34. https://doi .org /10 .1029 /2007GL029874. Appendix A. Supplementary material Hutnak, M., Fisher, A.T., 2007. 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