Evolution of heat flow, hydrothermal circulation and permeability on the young southern flank of the Costa Rica Rift


 We analyse 67 new conductive heat-flow measurements on the southern flank of the Costa Rica Rift (CRR). Heat-flow measurements cover five sites ranging in oceanic crustal age between approximately 1.6 and 5.7 Ma, and are co-located with a high-resolution multichannel seismic line that extends from slightly north of the first heat-flow site (1.6 Ma) to beyond ODP Hole 504B in 6.9 Ma crust. For the five heat-flow sites, the mean observed conductive heat flow is ≈85 mW m−2. This value is approximately 30 per cent of the mean lithospheric heat flux expected from a half-space conductive cooling model, indicating that hydrothermal processes account for about 70 per cent of the heat loss. The advective heat loss fraction varies from site to site and is explained by a combination of outcrop to outcrop circulation through exposed basement outcrops and discharge through faults. Supercritical convection in Layer 2A extrusives occurs between 1.6 and 3.5 Ma, and flow through a thinly sedimented basement high occurs at 4.6 Ma. Advective heat loss diminishes rapidly between ≈4.5 and ≈5.7 Ma, which contrasts with plate cooling reference models that predict a significant deficit in conductive heat flow up to ages ≈65 ± 10 Ma. At ≈5.7 Ma the CRR topography is buried under sediment with an average thickness of ≈150 m, and hydrothermal circulation in the basement becomes subcritical or perhaps marginally critical. The absence of significant advective heat loss at ≈5.7 Ma at the CRR is thus a function of both burial of basement exposure under the sediment load and a reduction in basement permeability that possibly occurs as a result of mineral precipitation and original permeability at the time of formation. Permeability is a non-monotonic function of age along the southern flank of the CRR, in general agreement with seismic velocity tomography interpretations that reflect variations in the degree of ridge-axis magma supply and tectonic extension. Hydrothermal circulation in the young oceanic crust at the southern flank of CRR is affected by the interplay and complex interconnectedness of variations in permeability, sediment thickness, topographical structure, and tectonic and magmatic activities with age.


I N T RO D U C T I O N
The temporal and spatial evolution of oceanic crust and lithosphere are largely controlled by thermally mediated processes. Parsons & Sclater (1977), Stein & Stein (1994), Hasterok (2013) and Qiuming (2016) have derived somewhat different plate cooling models based on global heat-flow determinations and using various functions based on oceanic crustal age. The widely used Stein & Stein (1992) where q b is the heat flow in mW m −2 and τ is the lithospheric age in Ma. Measurements of conductive heat flow, particularly in young crust, typically lie well below conductive cooling curves (Baker Heat-flow measurements on the southern flank of CRR 279 et al. 1991;Langseth et al. 1992;Fisher et al. 2003a;Hutnak et al. 2008). This discrepancy has long been attributed to heat loss by hydrothermal circulation (e.g . Elder 1965;Langseth & Von Herzen 1970;Lister 1972) and on a global scale, the difference between observed and predicted conductive heat losses indicates that hydrothermal circulation accounts for about 30 per cent of the global oceanic heat flux (e.g. Williams & Von Herzen 1974;Sclater et al. 1980;Elderfield & Schultz 1996;Davies & Davies 2010;Hasterok 2013). Of this, approximately 20-30 per cent occurs between 0 and 1 Ma, with the remainder occurring off axis (Stein & Stein 1994;Elderfield & Schultz 1996). Fig. 1(a) shows the predicted cooling curve from eqs (1a) and (1b) along with globally observed values with their standard deviation averaged in 2 Ma bins.
The style of hydrothermal circulation and heat transfer changes as the crust and lithosphere age from 'active' high-temperature magma-driven hydrothermal circulation at ages < 0.1 Ma (Macdonald 1982) to 'passive' lower temperature circulation on the ridge flanks (Lister 1982). The style of the ridge flank hydrothermal circulation also evolves with lithospheric age. The passive circulation may initially extend to a depth of 6 km into the young crust (Cherkaoui et al. 2003;Craft & Lowell 2009;Theissen-Krah et al. 2011;Hasenclever et al. 2014), and this deep crustal cooling may affect thermal regime of the ridge flank to an age of ∼5 Ma (Spinelli & Harris 2011). As the lithosphere ages the circulation tends to be restricted to the extrusive layer (Fisher 1998;, which typically consists of a highly permeable layer ≈ 150 m thick overlying a less permeable extrusive layer ≈ 400 m thick Salisbury et al. 1985). The extrusive layer, commonly referred to as crustal Layer 2A, will be designated as 2Au and 2Al to represent the upper and lower extrusive layers, respectively. As sediment thickness increases, recharge and discharge becomes restricted to exposed basement and faults (Wheat et al. 2004;Hutnak et al. 2006Hutnak et al. , 2008Fisher & Harris 2010;Anderson et al. 2012).
As the thickness of low permeability sediments increases and oceanic basement topography becomes fully covered, fluid discharge to the ocean declines. Moreover, mineral precipitation and alteration may reduce crustal permeability, and reduced buoyancy forces may also impact the vigour of hydrothermal circulation (e.g. Jarrard et al. 2003). The conductive heat flow gradually approaches the predicted lithospheric cooling curve due to these processes that decrease the driving forces and increase the impeding forces for hydrothermal circulation.
When the conductive heat flow and the cooling curve coincide, the crust is termed 'sealed' (e.g. Anderson & Hobart 1976;Stein & Stein 1994), implying that hydrothermal circulation no longer affects the surface heat flow significantly. A statistical analysis of the global heat-flow data set indicates that on average the sealing age corresponds to a basement age of 65 ± 10 Ma ( Fig. 1a; Stein & Stein 1994). This condition does not mean that hydrothermal circulation is absent. Rather it indicates that if hydrothermal circulation is present it is simply redistributing heat within the crust and does not transfer heat by advection from the crust to the ocean. Studies show that significant advective fluid flow can occur at basement ages much older than the global average 'sealing age' (e.g. Embley et al. 1983;Von Herzen 2004;Fisher & Von Herzen 2005).
The dominant mechanism leading to the cessation of advective heat loss through the seafloor is debated. Based on their analysis of the global data set, Stein & Stein (1994) argue that hydrothermal flow decreases as a result of decreased layer 2 porosity and permeability rather than from burial by sediment. This argument runs counter to results from heavily sedimented ridges. Detailed heatflow studies on the thickly sedimented eastern flank of the Juan de Fuca Ridge (JDFR; Davis et al. 1997Davis et al. , 1999Fisher et al. 2003b; show that mean observed heat flow reaches the predicted curve at ∼1.5 Ma. In addition, heat-flow studies at the Costa Rica Rift (CRR) flank showed that the mean heat flow was near the predicted cooling curve near ODP Hole 504B for which the crustal age was initially estimated to be 5.9 Ma , 1988Hobart et al. 1985). Revised estimates based on magnetic data suggest that the crustal age at Hole 504B is ≈6.9 Ma (Wilson & Hey 1995;Worm et al. 1996;Wilson et al. 2003) which we adopt in this paper. Although ≈6.9 Ma is older than the previously estimated ≈5.9 Ma for Hole 504B, the conductive cooling curve is relatively flat over this 1 Ma age difference. The studies on heavily sedimented ridges suggest that the accumulation of relatively impermeable and laterally continuous sediment is the likely cause of a sealed system at these locations. Further, global compilations of permeability measurements and seismic velocity indicate that the greatest change in the physical properties of the basement occurs in the first 10 Ma (Fisher & Becker 2000), leaving the role of crustal permeability in the sealing age an open question.
Heat-flow studies on the flanks of young heavily sedimented oceanic crust such as JDFR and CRR provide opportunities to better understand the evolution of hydrothermal circulation and mechanisms of advective heat transport within a limited age and distance from the spreading centre. In addition, such studies provide insight into crustal alteration (e.g. Alt 1995), seismic velocity structure (e.g. Carlson 2011Carlson , 2014 and microbial processes (e.g. Huber et al. 2003) that are linked to the thermal regime of the crust.
In this paper, we analyse 67 new conductive heat-flow measurements from the southern flank of the CRR at sites ranging in age between ∼1.6 and ∼5.7 Ma. In our analysis, we also include previously collected heat-flow data (Anderson & Hobart 1976;Langseth et al. 1983Langseth et al. , 1988Hobart et al. 1985;Davis et al. 2003Davis et al. , 2004. The new sites are labelled PB02 to PB06 (Fig. 2) and are co-located along a seismic reflection and multibeam bathymetry profiles, which enable an integrated analysis that elucidates the influence of basement topography and sediment thickness on fluid flow, advective heat transport and changes in the hydrothermal regime as the crust evolves with age.

G E O L O G I C S E T T I N G
The Panama Basin, located in the equatorial Pacific, is bounded by the Cocos Ridge to the north and west, Carnegie Ridge to the south, and Ecuador Trench and Americas to the east. Three spreading centres are located in the basin: CRR, Ecuador Rift (ER), and the Galapagos Rift (GR; Lonsdale & Kiltgord 1978;Fig. 2). The southern flank of the CRR, the focus of our study, has an average half-spreading rate of approximately 3.3 cm yr −1 based on the distance from the CRR axis to the Hole 504B of age 6.9 Ma (Wilson & Hey 1995;Worm et al. 1996;Wilson et al. 2003). The green box (Fig. 2) shows the region where complementary geophysical measurements were made. The seismic reflection profile, the locations of heat-flow and other geophysical data, including swath bathymetry are shown in Fig. 2.

Seismic reflection measurements
A 270 km high-resolution seismic reflection profile (RS-A), along which heat-flow measurements were co-located, was collected with Figure 1. (a) Conductive heat loss as a function of oceanic crustal age. The blue line shows predicted fit using eq. (1a). The pink dots are observed data averaged in 2 Ma bins; the red dotted lines show standard deviation; the green dotted-dashed lines show fit to the binned data (from Heberling et al. 2010). (b) Heat flow on the south flank of the Costa Rica Rift as a function of oceanic crustal age. The blue line shows predicted fit/conductive cooling curve from eq. (1a). Solid pink symbols are 67 new heat-flow measurements divided into five sites (PB02 at 1.6 Ma; PB03 at 2.6 Ma; PB04 at 3.5 Ma; PB05 at 4.5 Ma and PB06 at 5.7 Ma) in this study along with their mean and standard deviation in black. The red open circles show legacy heat-flow data (Anderson & Hobart 1976;Langseth et al. 1983Langseth et al. , 1988Hobart et al. 1985;Davis et al. 2003Davis et al. , 2004. Note that the legacy heat-flow values are projected laterally up to 10 km onto the profile in Fig. 1 a GI airgun array with a source frequency ranging between 20 and 200 Hz recorded on a 4500 m multichannel hydrophone streamer with a 12.5 m group length. The resulting imaging of the sediment and the upper oceanic crust provides a geologic framework for interpreting the heat-flow data. The complete seismic section (Fig. 3) shows that sediment thickness varies considerably with thin sediment accumulations at basement highs and with thicker sediment accumulations at basement lows; the mean sediment thickness increasing from approximately 40 m at 1.6 Ma crust to 275 m at Hole 504B. The seismic profile also shows exposed basement, through going faults, and rough basement topography; however, for crust older than 5.7 Ma (≈ 190 km in Fig. 3), the basement topography is more subdued and becomes completely covered with sediment.

Heat-flow data
Conductive heat-flow measurements were acquired in sediments between 50 and 250 m thick by means of a 'violin-bow' type multipenetration heat-flow probe (Hyndman et al. 1979). It consists of a 3.5 m sensor tube that houses 11 thermistors and a heater wire that is offset from a lance. The configuration allows the probe to be gravity-driven into the sediments and provides the sensitivity to make precise and accurate heat-flow measurements while also being robust so that many measurements can be made by 'pogo-ing' the probe along the bottom. A weight stand containing the data logger and telemetry system sits above the thermistor tube. In addition to logging the temperature time-series, the data logger also records tilt, pressure, time and the bottom water temperature. An ultrashort baseline sensor attached 50 m above the probe provides precise navigation. The probe allows in situ measurements of the shallow thermal gradients and thermal conductivity in sediments on the seafloor. The analysis of heat-flow measurements is based on the scheme presented by Villinger & Davis (1987) as implemented using SlugHeat (Stein & Fisher 2001). The in situ thermal gradient is based on a temperature time-series collected for 7 min, which is long enough to achieve partial equilibrium with the sediments. Equilibrium temperatures are then estimated through an extrapolation based on a line source model of radial heat conduction (Villinger & Davis 1987). A calibrated heat pulse is then applied through the heater wire for 10 s and a 7 min temperature decay provides data for determining thermal conductivity. The heat flow, thermal conductivities, thermal gradient values and sediment thicknesses for all sites are given in Table 1. Heat-flow measurements were closely spaced to avoid aliasing the hydrothermal circulation signal and co-located with the swath bathymetry and seismic reflection data to better understand the measuring environment (e.g. Fisher & Harris 2010). Fig. 1(b) shows the 67 new measured heat-flow values along with the previously published data (Anderson & Hobart 1976;Langseth et al. 1983Langseth et al. , 1988Hobart et al. 1985;Davis et al. 2003Davis et al. , 2004 and predicted heat flow based on half-space cooling curve from eq. (1a). Fig. 1(b) shows heat flow transitioning from values of about 40 mW m −2 at 1.6 Ma to a mean value of 235 mW m −2 at 5.7 Ma, which lies near the predicted cooling curve. Previously published heatflow data indicated by the open circles in Fig. 1(b) also show that heat transfer transitions from advectively to conductively dominated values between ≈ 4.5 and ≈ 6.0 Ma. The average measured heat flow of the 67 new measurements (Table 1) is ∼85 mW m −2 . This value is considerably less than the average expected basal heat flow of ∼280 mW m −2 , obtained by integrating eq. (1a) between 1.6 and 5.7 Ma. The heat-flow fraction (q obs /q b ) is ∼0.3 indicating that ∼70 per cent (∼200 mW m −2 ) of q b is advected. The effect of thermal rebound from deep axial cooling on the south flanks of the CRR between 1.6 and 5.7 Ma crust is small based on observational constraints and modelling studies (Fisher 2003;Spinelli & Harris 2011). Hence these effects on the overall advective heat loss fraction are negligible.

ANALYSIS
In order to quantify the mechanisms responsible for this advective heat loss, we construct a 1-D thermal conduction model of the sediment and basement as a function of age between 1.6 and 6.9 Ma at Hole 504B. This model allows us to compare the expected temperature at the sediment-basement interface (SBI) with the SBI temperature derived from the observed heat-flow measurements. The mathematical formulation is given in Appendix A. The results given by eq. (A2) show that the conduction-derived SBI temperature, expressed as the difference T SBI between seafloor and the base of the sediment, can be written as where 510 τ −1/2 is heat flow in mW m −2 , h s is the sediment thickness, λ s is the thermal conductivity of the sediment and v s is the sedimentation rate. Over much of the heat-flow profile, the sedimentation rate is ≈ 25 m Ma −1 whereas at PB04 and PB06 it is ≈ 40 m Ma −1 , similar to that at Hole 504B (Becker et al. 1983). Definitions and values of symbols are given in Table 2. We use λ s = 0.92 W Kinematic viscosity of the fluid 10 −6 m 2 s −1 ρ f Density of water 1000 kg m −3 τ Age of oceanic crust Ma m −1 K −1 , which is the average thermal conductivity based on Hole 504B's physical property measurements ). Fig. 4 shows the expected SBI temperature versus age for the two sedimentation rates, along with the average SBI temperature for the five heat-flow sites and the data at Hole 504B. The observed SBI temperature at each heat-flow point is determined from the relationship T obs SBI = q obs hs λs . The average SBI temperature at each site, except PB06 and Hole 504B, is much less than predicted by conduction regardless of the sedimentation rate (Fig. 4).
In the extrusive layer of the young oceanic crust south of the CRR, supercritical thermal convection will tend to homogenize the temperature distribution within the basement rocks. The condition . Sediment-basement interface (SBI) temperature as a function of crustal age. The predicted SBI temperatures for sedimentation rates of 40 m Ma −1 (PB04 at 3.5 Ma and PB06 at 5.7 Ma) and 25 m Ma −1 (PB02 at 1.6 Ma, PB03 at 2.6 Ma and PB05 at 4.5 Ma) as obtained from eq. (2) are shown as the solid blue and dotted blue lines, respectively. The black circles show the average SBI temperature (Table 1) based on the observed heat-flow data for all five sites and the bars indicate their maximum and minimum range values. Observed SBI temperature at 6.9 Ma crust in ODP Hole 504B and Hole 896A (Becker et al. 1983;) is shown as the red circle.
for onset of convection is defined by the Rayleigh number Ra. For a layer of thickness h b , with a fixed heat flux q b at the base, and impermeable sediments above , the Rayleigh number and its critical value Ra c are given by (Nield 1968 Assuming that other parameters are constant, eq. (3) shows that Ra decreases as τ 1/2 as the crust ages because of the predicted decline of q b . Using parameter values in Table 2 (Becker et al. 1989). The curves in Fig. 5 show that supercritical convection at 1.6 Ma requires that k must exceed threshold values k th = 3 ×10 −12 and 2 ×10 −13 m 2 , for h b = 150 and 550 m, respectively; whereas k th must exceed 7 ×10 −12 and 5 ×10 −13 m 2 at 6.9 Ma for the same values of h b . The permeability value for h b = 550 m is an 'effective' value for combined Layers 2Au and 2Al , but since the thickness of 2Al is considerably greater than that of 2Au, it is assumed that the effective permeability is nearly the same as that of Layer 2Al.
When Ra Ra c in a permeable layer with a given basal heat flux, vigorous convection tends to homogenize the temperature within the convecting interior, but because the heat flux is fixed, fluid convection will transport the same amount of heat as the conducting layer, hence the Nusselt number is unity. Heat advection within the basement interior will be transported across the SBI by conduction across a thin thermal boundary layer so that both heat flux and temperature at the SBI are continuous. Hence the high Ra supercritical convection regime would not by itself result in a reduction in conductive heat flow across the sediment layer or a decrease in SBI temperature, unless fluid advection can occur through the sediment layer or some other process such as outcrop to outcrop circulation or fluid discharge through faults also takes place. The observation in Fig. 4 that the SBI temperature is much less than predicted by conduction at sites PB02 through PB05 indicates that advective heat transfer is occurring. At PB06, however, the mean SBI temperature is only slightly less than the value predicted by conduction, suggesting that heat is not being advected between the crustal aquifer and the ocean.
In the following subsections, we present a detailed analysis of the heat-flow data as a function of age from the five heat-flow sites labelled PB02 through PB06. This analysis provides estimates of crustal permeability that can be compared with the Rayleigh criterion shown in Fig. 5. The goal is to determine whether there appear to be significant changes in crustal permeability as a function of age that affect the advective heat transfer. The values of calculated permeability are given in Table 3. In performing these analyses, we neglect the effects of heat-flow refraction, fluid flow through the sediments and the effect of sedimentation on reducing the observed heat flow (e.g. Hutchinson 1985; Hutnak & Fisher 2007).
Our estimates of mass flow rate and crustal permeability in the basement are largely based on the well-mixed aquifer model in which we assume that flow is dominantly parallel to the spreading direction. In reality fluid flow is likely 3-D (e.g. Winslow & Fisher 2015;Winslow et al. 2016), but 3-D modelling is beyond the limitations of the data and the scope of this paper. Two recent studies show the impact of flow perpendicular to the spreading direction Niera et al. 2016), and this caveat should be kept in mind when viewing the results. The likely presence of 3-D fluid flow in the natural system does not change the basic conclusion that fluid circulation advects a substantial amount of heat from this system. However, because the dominant fluid flow direction may not align with seismic line RS-A and our heat-flow stations, possible points of fluid recharge and discharge may be located east or west of the seismic line.

Heat-flow site PB02
Site PB02, the closest heat-flow station to the CRR, is located on ∼1.6 Ma old oceanic basement where the mean sediment thickness is about 40 m. These 19 heat-flow measurements (Table 1) have a mean of 41 mW m −2 whereas q b ≈ 400 mW m −2 . These values yield a mean heat-flow deficit (1 − q obs /q b ) of ≈0.9 thereby giving an advective heat flow q adv ≈ 360 mW m −2 . The SBI temperatures have a mean and standard deviation of 1.8 and 0.2 • C, respectively, implying that the upper basement temperatures are homogenized.
Heat-flow values observed at PB02 can be grouped broadly into two sets, A and B (Fig. 6a). Set A shows uniformly low heat flow, whereas set B has a southward increasing trend in heat flow suggesting lateral transport of heat by fluid advection (Fig. 6a). The possible discharge could be at a sparsely sedimented basement exposure to the south. This interpretation is supported by the two heat-flow measurements just south of this basement high that show a northward increasing trend. Recharge could be anywhere in the north as Fig. 6(b) shows continuous thinly sedimented basement; alternatively, recharge could occur to the east or west of the seismic line. Because the SBI temperatures are relatively uniform we apply the well-mixed aquifer model of Langseth & Herman (1981) as outlined in Appendix B to estimate the lateral mass flow through the basement. The data in set B are well fit by an exponential as shown in Fig. 6(a) which could then be applied in eq. (B2) resulting in a volumetric flow rate per unit length ≈415 m 2 yr −1 . Using this flow rate in eq. (B4) enables us to estimate the quantity kh b ; for h b = 150 and 550 m, we obtain permeabilities of ∼6 ×10 −10 and 5 ×10 −11 m 2 , respectively. These values are similar to those in Fig. 5 for Ra ≈ 100Ra c . Hence vigorous supercritical convection would largely homogenize the basement temperature distribution,   Anderson & Zoback (1982); Fisher et al. (1990); Becker (1996); . and outcrop to outcrop circulation would transport low-temperature fluid laterally and advect heat to the seafloor.

Heat-flow site PB03
This site (Fig. 7), at a crustal age of 2.6 Ma, consists of 11 measurements ( Table 1). The mean sediment thickness is ≈ 70 m and mean observed heat flow is 58 mW m −2 . The conductive prediction, from eq. (1a), is 310 mW m −2 yielding a mean heat-flow deficit of about 0.82 and an advected heat flow q adv ≈ 260 mW m −2 .
All measurements at PB03, except one, exhibit a uniformly low heat flow. The highest heat-flow value of 217 mW m −2 appears to occur close to a fault (Fig. 7b) that probably serves as a discharge zone. Assuming isothermal upflow through the fault at a temperature T sp , conductive heat flow is expected to decay as 1/x, where x is the distance from the fault plane. Appendix C outlines the mathematical formulation of this problem. From eq. (C2), with q b = 217 mW m −2 and x = 100 m, we calculate the temperature of the upflow, T sp , in the range of 20-35 • C, depending whether we use the basalt or sediment thermal conductivity, respectively ( Table 2).
The first six uniformly low heat-flow values (from ≈ 83 to 86.5 km in Fig. 7a) with the seventh being the highest at this site suggest lateral advective transport of heat by fluids with the high heat-flow point being adjacent to the discharge fault (Fig. 7b). Possible recharge could be at a sparsely sedimented basement exposure to the north (Fig. 7b). The lateral flow rates through the basement can be estimated by applying the well-mixed aquifer model of Langseth & Herman (1981) as outlined in Appendix B. From eq. (B1), the quantity uh b can be estimated, where dT(x) is the T sp calculated using the fault model. This results in uh b of 1.6 ×10 −5 m 2 s −1 for T sp = 20 • C and 9.2 ×10 −6 m 2 s −1 for T sp = 35 • C. In eq. (B4) using L = 5 km (recharge outcrop to discharge fault) enables us to calculate permeabilities, k, and we obtain k = 10 −10 to 7 ×10 −11 m 2 for h b = 150 m and T sp = 20-35 • C; and k = 10 −11 to 7 ×10 −12 m 2 for h b = 550 m and T sp = 20-35 • C. These values fall in between Ra ≈ 10-100Ra c (Fig. 5).
Given the low estimate of the basement temperature, these results suggest that the discharge fault transports most of the advective heat (from ≈ 83.5 to 87 km in Fig. 5) to the seafloor at this site.

Heat-flow site PB04
Site PB04 consists of 15 measurements (Table 1)  The measurements at PB04 can be broadly grouped into two sets, C and D (Fig. 8a). Set C consists of nine measurements in a sediment pond located between two large topographic highs. Heat-flow values in set C have a mean value of 16 mW m −2 and display a slightly increasing trend to the south. We interpret these data to reflect outcrop to outcrop lateral heat transfer where recharge occurs at poorly sedimented basement high areas to the north of the pond and discharges through a thinly sedimented basement high to the south. The SBI temperatures have a mean and standard deviation of 2.3 and 1.7 • C, respectively, implying that the upper basement temperatures are homogenized. The data are well fit to an exponential as shown in Fig. 8(a). Hence this fit is applied to eq. (B2) in the well-mixed aquifer model (Appendix B) to estimate the volumetric flow rate per unit length ≈115 m 2 yr −1 . Applying this flow rate in eq. (B4), we estimate permeabilities of ∼2 ×10 −10 and 2 ×10 −11 m 2 for h b = 150 and 550 m, respectively. These values are similar to those for Ra ≈ 100Ra c (Fig. 5). Thus, supercritical buoyancy-driven convection significantly homogenizes the temperature distribution within the basement.
In set D, three measurements are of uniformly low heat flow and one exhibits the highest heat flow of 322 mW m −2 at this site. This high heat flow appears to occur close to a fault (Fig. 8b) which could serve as a discharge zone. We can use the fault model methodology outlined in Appendix C and used in the analysis of PB03. From eq. (C2), with q b = 322 mW m −2 , we calculate T sp to be in the range of 25-50 • C accounting for thermal conductivity difference between sediment and basement. The estimated temperature of the fluid discharging through the fault is considerably higher than T obs SBI , suggesting that the fault may be tapping warmer fluids from below the upper basement.
Advective heat transfer at site PB04 stems from different environments, and it is not possible to determine the heat loss and the fluid discharge temperature from each site independently. Given the low value of conductive heat flux in group C, we suggest that most of the advective loss is associated with outcrop to outcrop circulation.

Heat-flow site PB05
The seven heat-flow measurements at this site (Table 1) have a mean of 14 mW m −2 . The crustal age of 4.5 Ma corresponds to a predicted heat flow (eq. 1a) q b = 241 mW m −2 , indicating a deficit of about 0.94. Thus q adv ∼ 230 mW m −2 . The average sediment thickness ≈ 120 m except above the large basement mound (Fig. 9b), where h s varies between 0 and 80 m. From the two-way traveltime data, the basement high is approximately 1 km from the base of the sediment layer to the north where the heat-flow data were obtained. The sediment thickness at the top of the mound and along its southern flank is negligible. Heat flow increases slightly towards the topographic basement high (Fig. 9), suggesting that heat maybe being transferred by advection within it.
If basal heat flow through the basement is 241 mW m -2 , the conductive temperature at the base of the basement high (∼1 km) would be ≈20 • C, whereas the conductive temperature at the base of the nearby sediment would be ≈40 • C. This strong lateral temperature gradient between the sediments and the basement high would drive fluid upwards through the basement. From the scale analysis, the vertical velocity is given by Because we do not know whether the advection is sub-or supercritical, we assume that the permeability corresponds to Ra = Ra c in a 550 m thick aquifer. From Fig. 5, this value is ≈4 ×10 −13 m 2 , yielding u z ≈ 1.6 ×10 −8 m s -1 assuming a mean T = 40 • C driving the flow. If the fluid rising through the basement high exits the sediment-free part of the mound at a typical diffuse flow temperature ≈10 • C (Fisher & Harris 2010), q adv = ρ f c f u z T ≈ 640 mW m -2 , which is approximately three times greater than the mean heatflow deficit of ≈230 mW m -2 . In order for the total advective heat output through the basement high to balance the observed advective heat flux, the area of advective heat loss in the crust surrounding the basement high would thus need to be approximately three times the area through which advective heat is lost through the basement high. Alternatively, heat advection through the basement high resulting from the lateral temperature gradient may be subcritical. The permeability of the basement may thus be an order of magnitude, or more, less than estimated assuming Ra ≈ Ra c .

Heat-flow site PB06
Site PB06 (Fig. 10) consists of 15 measurements in 5.7 Ma crust with a mean observed heat flow of 235 mW m −2 , slightly higher than the predicted heat flow of 214 mW m −2 ( Table 1). The sediment thickness averages 145 m, burying the basement. The relative agreement between the observed and the predicted heat flows is consistent with the thick and continuous sediment cover. The observed heat flow varies from 899 mW m −2 over a basement high to 90 mW m −2 over the basement low (Fig. 10). This variation is greater than can be accounted for with conductive refraction (Von Herzen 2004). The mean observed basement temperature, < T obs SBI > ≈ 26 • C is that expected for this crustal age and sediment thickness, but the variability is larger than can be accounted for with conductive heat flow. Importantly, the SBI temperature is not constant but varies substantially with sediment thickness variations; over the basement high, the sediment thickness is 19 m and T obs SBI is significantly higher (18.8 • C) than predicted (4.4 • C). Over the basement low, the sediment thickness is 226 m and T obs SBI is significantly lower (29 • C) than predicted (52.7 • C). The variability in both heat flow and SBI temperature suggests on going hydrothermal circulation, but because the SBI temperature is not homogenized, convection must be subcritical or only slightly supercritical.
These results suggest upward advective fluid flow in the basement high and downward advective flow in the basement low. These results are similar to those near Hole 504B where heat-flow highs occur over bathymetric ridges, basement highs and regions of thin sediment cover, with lows occur over basement lows and regions of thick sediment cover (Fisher et al. 1990(Fisher et al. , 1994. Because of the complex interplay of these factors it is difficult to quantify fluid flow rates and basement permeability, but the lateral temperature gradients induced by variations in basement topography and sediment thickness may result in circulation at subcritical Rayleigh numbers. Subcritical convection is consistent with the broad spectrum of temperatures at the SBI. Assuming that convection in a 550 m thick layer of basement extrusives is at or near the critical number for Rayleigh convection, gives the mean permeability at PB06 of ∼5 ×10 −13 m 2 .

D I S C U S S I O N A N D C O N C L U S I O N S
The 67 new conductive heat-flow measurements collected on the southern flank of the CRR crust between ≈1.6 and ≈5.7 Ma, together with legacy data, provide important insights into types and patterns of hydrothermal circulation and advective heat loss from young crust. Comparison between the observed heat flow and the predicted half-space lithospheric cooling model yields a mean heatflow deficit of ≈ 70 per cent that is attributed primarily to advective heat transport. Detailed analysis of each site, however, suggests that the magnitude of advective heat transfer (Table 3) is not a simple function of crustal age. These results provide new insights into hydrothermal circulation mechanisms as conductive heat flow approaches the predicted heat-flow curve (Fig. 1).
Our analysis indicates that between sites PB02 and PB04 supercritical Rayleigh convection tends to homogenize the basement temperature distribution. Outcrop-to-outcrop circulation (PB02, PB04) and fluid flow through faults (PB03 and PB04), which are superimposed on the Rayleigh convection regime, act to cool the basement by advecting heat to the ocean (Fig. 3). At PB05, advective heat loss likely occurs as a result of subcritical convective flow driven by a significant lateral mean temperature difference between the basement high and surrounding sediments. The advected heat exits through a sediment-free part of the basement high. At PB06, however, there is little evidence of advective heat exchange between the basement and ocean. Thermal convection in the basement is likely subcritical, driven by differences in basement topography (Figs 3 and 10).
We constructed relatively simple mathematical models and/or used the scale analysis for sites PB02-PB05 to understand advective heat flow and estimate the permeability of the upper crust. At PB06 we estimated permeability assuming Ra ≈ Ra c. Table 3 lists the estimated permeability at each site, along with that for 6.9 Ma crust near Hole 504B. The results of the scale analysis and mathematical modelling points to an order magnitude difference in permeability between the upper 150 m and that of the entire Layer 2A, estimated to be 550 m thick (Table 3). Moreover, the results show that permeability does not decrease monotonically with age, as might be expected from water-rock reactions that tend to fill fracture and pore spaces.
The estimates of basement permeability derived here are not a monotonic function of age. The permeability at site PB03 which has an age of 2.6 Ma appears to be less than at adjacent sites that are both older and younger. Moreover, the estimated crustal permeability drops significantly between ; and it appears to increase again at PB06. At Hole 504B at 6.9 Ma crust, packer measurements yield permeabilities in the range of 10 −13 -10 −14 m 2 (Anderson & Zoback 1982;Fisher et al. 1990) and flowbased determinations produce upper basement permeabilities of 1-5 ×10 −14 m 2 . At Hole 896A, located 1 km from Hole 504B, drill-string packer measurements (Becker 1996) and flow-based determinations  give upper basement permeabilities of 1-4 ×10 −13 m 2 and lower basement permeability of 2 ×10 −14 m 2 . However, the near uniformity of the basement temperature between Hole 504B, Hole 896A and Holes 677, 678, despite large differences in sediment thickness, suggests vigorous convection in the upper crustal layer. Davis et al. (2004) suggest a model-based regional-scale permeability of ∼10 −9 m 2 in the upper 100 m. The substantial transition to decreased permeabilities from 3.5 to 4.5 Ma and a continued decrease in permeability in the shallow crust at 6.9 Ma suggest that the evolution of crustal permeability may not be simply correlated with crustal age.
The variability in estimated crustal permeabilities is similar to the variability seen in tomographic models of seismic P-wave velocity in Layer 2A of the ocean crust (Wilson et al. 2018). The upper oceanic crust older than about 5.7 Ma consistently shows a higher seismic velocity that is interpreted to be a result of porosity reduction (Gregory et al. 2019;Wilson et al. 2019). The crust younger than 5.7 Ma can be segmented into regions characterized by a combination of basement roughness, seismic velocity of Layers 2A and 2B, and ages determined from reinterpretation of magnetic anomaly data . Taken together, these characteristics suggest that the magma supply has waxed and waned with time. Heat-flow measurements at sites PB02 and PB03 lie in a region where the tomography model indicates a lower velocity Layer 2A, which is consistent with the relatively high permeability estimated for this region. Sites PB04 and PB05 are located in a region of variable P-wave velocities in Layer 2A. Wilson et al. (2019) suggest that this region has formed during a period of slower spreading, <35 mm yr −1 halfrate, with enhanced faulting accommodating part of the extension. This may explain the rapid change in estimated permeability. Site PB06 and Hole 504B lie within the transition to significantly faster Layer 2A velocities, which are interpreted to indicate an earlier phase of magma-dominated spreading.
The models used to analyse the heat-flow data along the seismic line from crustal ages of ≈1.6 to ≈5.7 Ma are necessarily simplified. In addition, the models all assume 2-D flow parallel to the spreading direction, whereas enhanced permeability may be aligned parallel to the ridge Neira et al. 2016). Outcrop-to-outcrop flow may also be 3-D (Winslow & Fisher 2015;Winslow et al. 2016), and fault-controlled flow may be both along and perpendicular to the plane of the fault (e.g. Johnson et al. 1993;Lowell 2017). The permeability values estimated for the various sites represent bulk average permeabilities. The estimated values obtained are large, indicating that the permeability is probably fracture controlled, and the actual flow paths may be both anisotropic and defined by a few major fractures rather than by the Darcy flow as used here. Fig. 1(b) shows that heat flow at sites PB02 through PB05 lies well below the predicted cooling curve but begin climbing towards the cooling curve at ≈4.5 Ma, essentially reaching the curve at 5.7 Ma. This result is in contrast with the global data set (Fig. 1a) where heat flow coincides with the predicted heat flow at ≈65 ± 10 Ma. Stein & Stein (1994) argue that the coincidence of conductive heat flow with the predicted cooling curve suggests that hydrothermal circulation is weak as a result of decreasing crustal permeability rather than a result of increasing sediment thickness burying basement rock. This study, where heat flow coincides with the cooling curve at a much younger crustal age of ≈5.7 Ma, however, indicates that the alignment of heat flow with the predicted curve may be a function of original permeability at the time of crustal formation or reduction of permeability, which may result from mineral precipitation as well as mode of crustal generation, as well as sediment accumulation. The data at PB05 and PB06 indicate that a decline in crustal permeability results in subcritical or weakly supercritical convection, driven largely by basement topography. The relatively thick, low permeability sediment cover over crust older than about 5.7 Ma inhibits advective heat transfer to the ocean (Fig. 3). This is similar to the JDFR flank where thick sediment cover also inhibits advective heat loss from young crust (Davis et al. 1997(Davis et al. , 1999Hutnak et al. 2006).
The results of studies at young crust thus suggest that permeability, sediment thickness, topographical structure and variations in tectonic and magmatic activities with age all affect hydrothermal circulation in the oceanic crust in a complex interconnected fashion. This interconnectedness is more site specific than that can be constrained by global data sets and models simply as a function of age. Increased understanding of crustal evolution and hydrothermal circulation will come as individual spreading systems are analysed that include details of crustal creation, tectonic evolution, water rock reactions, sedimentation and age.

A C K N O W L E D G E M E N T S
The authors would like to thank the thorough and constructive reviews from Dr Keir Becker and one other anonymous reviewer that helped improve this manuscript. This research was supported in part by NSF Grants OCE 1353114 and 1558797 to RPL and Grants NSF OCE 1353003 and 1558824 to RNH. The NERC OSCAR project grant NE/I027010/1 (Hobbs & Peirce 2015) underpinned this work. The authors would like to thank the officers, crew, technicians and science party on board the RRS James Cook during cruises JC112, JC113 and JC114. The MCS data were processed using GNS Globe Claritas at Durham University. The swath bathymetry was cleaned and processed using QPS Fledermaus by Gavin Haughton from the National Oceanographic Centre and Emma Gregory from Durham University. Yang Li, Durham University, UK, provided the Monte Carlo Matlab code for calculation of uncertainties. The heat-flow data have been placed on the IEDA data portal, doi: http://dx.doi.org/10.1594/IEDA/324068, seismic data are available on request through the British Oceanographic Data Center or the author RWH.

A P P E N D I X A : 1 -D T H E R M A L C O N D U C T I O N M O D E L
To estimate the expected temperature at the SBI, we construct a 1-D steady-state-layered thermal conduction model consisting of a uniform layer of sediment overlying basaltic basement. We assume that thermal conductivity of each layer is constant, implying that d 2 T dz 2 = 0, where T is temperature and z is depth, subject to the conditions Definitions and values of symbols are given in Table 2. Temperature and heat flux are continuous across the SBI. Consequently, in the sediment layer, ) and the temperature at the SBI, relative to T sw is Applying the half-space cooling model in eq. (1a) and assuming a constant sedimentation rate h s = v s τ , we derive eq. (2).

A P P E N D I X B : T H E W E L L -M I X E D A Q U I F E R M O D E L
To estimate the lateral mass flow through the basement, we apply the well-mixed aquifer model of Langseth & Herman (1981; Fig. B1), where lateral advection dominates heat transport by conduction. The steady-state thermal balance is expressed as The exponential solution to this equation by applying boundary conditions T = T 0 at x = x 0 yields (Kolandaivelu et al. 2017) q (x) For parameters shown in this appendix, refer to Table 2. Here a * = λ s /ρ f c f ; q(x) is heat flow at distance of x from x 0 ; q(x 0 ) is the heat flow at distance x 0 ; x 0 is the distance of the first heat-flow measurement from the recharge outcrop (Table 1). An exponential fit based on the observed data and equating it to exponential in eq. (B2) provides the volumetric flow rate per unit length perpendicular to the flow direction, uh b for a sediment thickness, h s . Extrapolating the exponential fit to the data to the presumed discharge location from first measurement, heat flow at discharge, q d , can be estimated and writing yields T d and therefore the T r as recharge is assumed to occur at 0 • C.
Darcy's law can be modified and expressed as, This expression enables estimating formation permeability, kh b . Substituting the calculated values from eqs (B2) and (B3), we can arrive at permeabilities, k, for h b = 150 m and 550 m.