High Heat Flow Anomaly Within the St Paul Fracture Zone: Heat Advection and/or Inherent Thermal Structure?

Heat flow across oceanic transform faults (TFs) and fracture zones (FZs) has rarely been studied in detail, despite these features representing distinct thermal boundaries within the oceanic lithosphere. Here, we present heat flow measurements across the St Paul fracture zone (SPFZ) in the equatorial Atlantic Ocean, from 48 Ma crust in the south to 71 Ma in the north. To the north of the FZ we find a basal heat flow of 63 mWm−2, and to the south a basal heat flow of 79 mWm−2, both in agreement with plate cooling models. However, within the SPFZ we find a heat flow of 83 mWm−2, greater than the values of the adjacent crust and 10–15 mWm−2 higher than predicted from conductive cooling models, suggesting that the thermal structure of the FZ has been modified. Evidence from seismic and sub‐bottom profiler data indicate recent active deformation within the SPFZ, potentially driven by lithospheric flexure across the FZ or temporal changes in TF configuration. We propose that this deformation may enable fluid circulation and heat advection within the basement, creating the seafloor heat flow anomaly within the FZ. These findings suggest that FZs may remain important zones predisposed to host deformation and fluid flow in the oceanic lithosphere, despite not being active plate boundaries.

ridge-transform configuration over time. The profile is co-located with a deep seismic reflection study, where the base of the lithosphere is imaged at 77 km below the seafloor south of the FZ and deepens linearly to 85 km north of the FZ (Mehouachi & Singh, 2018).
If FZs are truly tectonically inactive features and cool conductively, one would expect the heat flow to vary linearly across the FZ due to lateral conduction. However, active fluid flow, if present, would disturb this pattern (e.g., Stein & Stein, 1994). Furthermore, some recent studies have indicated that the lithospheric structure of TF systems might be more complex (Wang et al., 2022) and crustal thickening by lateral melt sill injection might occur at ridge-transform intersections Growe et al., 2021;Marjanović et al., 2020). This process would lead to rejuvenation of the lithosphere, which is then likely to age and evolve differently to standard oceanic crust. In order to test whether the simple conductive model is valid or not along FZs, we acquired heat flow data across the St Paul FZ (Figure 1).  (Müller et al., 2019). Black box is the area shown in panels (b) and (c). Inset shows the location of the study area (red star) in the wider Atlantic region. (b) Detailed multibeam swath bathymetry of the study area, showing the seismic profile from Mehouachi and Singh (2018) (black line) and heat flow measurement locations (red circles), labeled with the site names. Also shown as black dashed lines are the locations of the northern and southern St Paul Fracture Zones (SPFZ-N and SPFZ-S, respectively), as defined in this study. Plate age in Ma from the global models is shown by white contours (Müller et al., 2019), with the original position of the SPFZ-S indicated by this age model shown by the dark red dotted lines and arrow. Note how the heat flow site HF1768 lies to the south of the new SPFZ-S position, as opposed to the north of the original position. (c) Vertical gravity gradient (Sandwell et al., 2014)

Data and Methods
The heat flow data were acquired in 2017 aboard the German R/V Maria S. Merian, alongside multibeam bathymetry and sub-bottom profiler (sediment echosounder) data (Grevemeyer et al., 2019). Coincident seismic reflection data were also used here to analyze the sedimentary structures, with seismic acquisition details given in Mehouachi and Singh (2018).

Bathymetry and Sediment Echosounding Data
High-resolution multibeam bathymetry data in the study area ( Figure 1b) were acquired using a Kongsberg EM122 system at a resolution of 50 m. Sub-bottom sediment echosounder (Parasound system) data provide a high-resolution single-channel image of the upper ∼100 m (∼0.1 s TWT) of the sedimentary cover, with a lateral resolution of 14 m (average ping spacing).

Heat Flow Survey
Twenty-nine heat flow measurements were made at three sites located on a north-south profile across the St Paul FZ (Figure 1b), with one joint site within the 20 km-wide FZ valley (HF1769 and HF1770) and the other two located ∼50 km to the north (HF1771) and south (HF1768) of the FZ. From the seismic reflection images (Figure 2), we can observe that the whole profile is covered with a thick layer of sediment. Sediment thickness ranges from 320 to 990 m within the FZ valley (average ∼600 m), 110-345 m at the southern site (average ∼240 m) and 590-730 m at the northern site (average ∼620 m). Heat flow measurements were conducted using the 6 m-long Bremen heat flow probe (Villinger et al., 2010), which is constructed in the classical violin bow  (Hasterok, 2013) is shown by the solid gray line. The subsurface model used to calculate the modeled heat flow is shown beneath the graphs: showing water column (blue), sediments (brown), and igneous basement (red), labeled with parameters used during the calculations and the resultant best-fit basal heat flow, with yellow circles representing the measurement locations. The modeled heat flow shows a good fit to the measured values and local variation at each site. (d) Seismic reflection image along the heat flow profile (Mehouachi & Singh, 2018), showing the along-profile locations of the measurements (red inverted triangles). The main, northern St Paul fracture zone (FZ) is labeled as St Paul FZ (N), and the suggested new location for the second, southern FZ is labeled as St Paul FZ (S).
design (Hartmann & Villinger, 2002;Hyndman et al., 1979). The probe contains 21 thermistors distributed over a total length of 6 m in a sensor tube, which also contains a heater wire for in situ thermal conductivity measurements (Lister, 1979). Measurements were made in a pogo-style fashion as described in Hyndman et al. (1979) with a measurement spacing of ∼1 km. In situ thermal conductivity was measured at almost every second penetration and the mean value calculated from the thermal conductivity profile at each site. Interpolated values of the adjacent measurements were used for the intervening stations. All the seafloor heat flow measurements (Table 1,  Figure 2; for a compilation of all temperature profiles see Figure S1) are of high quality with the probe penetrating to full length within the sediment. Basic processing of the data followed the steps outlined in Hyndman et al. (1979), Villinger and Davis (1987), and Villinger et al. (2010). As precise positioning of the probe at the seafloor using an ultra-short baseline system was not possible due to technical problems, the ship's position was instead taken as the location of the probe on the seafloor.

Thermal Modeling
Measured surface heat flow can vary locally as a function of seafloor topography, basement topography, and the thermal conductivity contrast between the sediment and basement. To understand these local effects and calculate true variations in the basal heat flow, taking variations in topography into account, we conducted numerical modeling of the conductive regime at the St Paul FZ. For each site, we created a steady-state 2D purely conductive finite element model with the geometry defined by the seismic profile, using a sediment velocity of 1,700 m/s to calculate sediment thickness (e.g., Christeson et al., 2016;Swift et al., 1998). Constant thermal conductivities of 1.7 and 2.0 Wm −1 K −1 and zero heat production were assigned to the sediments and lithosphere, respectively (e.g., Pribnow et al., 2000). The heat flow into the model at the base of the lithosphere (basal heat flow) was iteratively adjusted for each site until the misfit between the observed and calculated heat flow was minimal, with the final value assumed as a representative heat flow value for each site. The estimated uncertainty in the basal heat flow is ±2 mWm −2 , assuming realistic uncertainties of ±100 ms −1 in sediment velocity and ±10% in thermal conductivity.

Conductive Geotherms
Predicted temperature-depth profiles and surface heat flow were calculated using two different plate cooling models (Table 2) and the plate ages from Müller et al. (2016). The Hasterok (2013) model is constrained by global observations of surface heat flow and seafloor subsidence. The model proposed by Mehouachi and Singh (2018) is based on the plate cooling model of McKenzie et al. (2005) and was used to calculate lithosphere-asthenosphere boundary (LAB) temperatures along the St Paul FZ profile, and uses slightly different thermal and lithospheric parameters. The different models produce similar values for the predicted heat flow for both north of the FZ: 62 versus 59 mWm −2 for the models from Hasterok (2013) and Mehouachi and Singh (2018), respectively; and for the lithosphere south of the FZ: 73 versus 72 mWm −2 . Errors in the predicted heat flow result from errors in crustal age and plate thickness (depth to the LAB). Here, the LAB depth is well constrained within ±2 km (Mehouachi & Singh, 2018). However, the error in plate age from the global models could vary up to ±4-6 Myr (Müller et al., 2008), as crustal age between ∼15°N and ∼5°S in the equatorial Atlantic Ocean cannot be constrained by magnetic lineations due to the north-south strike of the ridge and its equatorial location (Seton et al., 2014). Instead, crustal age is based on reconstruction using finite rotations, resulting in larger errors in age than further north or south of the equator. Across our profile, the global model places the southerly St Paul Fracture Zone (SPFZ-S) at ∼1°20′N, which is south of heat flow site HF1768, resulting in an average age of ∼48 Ma for this site. However, satellite gravity (Sandwell et al., 2014), our multibeam bathymetry and seismic reflection profiles indicate that the FZ is most likely located at 1°34′N, corresponding to ∼20 km along our profile (Figures 1 and 2d). This new location is just north of heat flow site HF1768, suggesting that the age of the lithosphere at this site is likely that of the plate to the south of the FZ system (∼41 Ma), rather than that of the sliver of lithosphere between the two FZs as given by the global plate age model (∼48 Ma). We calculated the predicted heat flow using both ages for this site.

Results
Measured surface heat flow varies between 60 and 90 mWm −2 (Table 1, Figures 2a-2c). All temperature-depth profiles are linear (see Figure S1), indicating steady-state conductive heat transport within the sediments. In general, the observed seafloor heat variations agree well with the modeled heat flow, with an average RMS misfit  Hasterok (2013) and Mehouachi and Singh (2018) Value Parameter Hasterok (2013) Mehouachi and Singh (2018)  of less than 1 mWm −2 . The largest misfit is within the St Paul FZ, which may be due to problems in correctly imaging the complex and steep basement topography used to create the model, and/or non-2D effects.
Compared with the predicted heat flow from conductive plate cooling models (Figure 3), the modeled basal heat flow to the north of St Paul (site HF1771) fits well (63 modeled versus ∼62 mWm −2 predicted), suggesting a purely conductive cooling regime at this site. To the south of St Paul (site HF1768), modeled basal heat flow is ∼6 mWm −2 higher than that predicted from the plate cooling model, using the plate age from the global age model (79 modeled versus ∼73 mWm −2 predicted). The modeled value is only 1 mWm −2 outside the predicted value error bounds of 68-78 mWm −2 , which are dependent on errors in plate age of ±6 Ma (after Müller et al., 2008). If we instead use our suggested age of 41 Ma for the southern site, the predicted heat flow becomes 79 mWm −2 , equal to the modeled value. This supports the relocation of the second FZ to 1°34′N and suggests that the heat flow regime is purely conductive to the south of St Paul. Within the FZ itself (site HF1769/HF1770), the plate age and therefore predicted heat flow is not well constrained but is expected to lie between the values to the north (62 mWm −2 ) and south (73 mWm −2 ) of the SPFZ-N, with an average value of 68 mWm −2 assuming a linear age variation. However, we observe a modeled basal heat flow of 83 mWm −2 , much higher than the predicted and observed values on both sides of the FZ valley. Thus, we have a positive heat flow anomaly of 10-15 mWm −2 compared to the conductive cooling models, suggesting that other processes must be influencing the heat flow and thermal structure within the FZ valley.
The seismic reflection profile and co-located sub-bottom profile provide both large-scale and shallow, high-resolution images, respectively, of the sediments within the FZ valley ( Figure 4). Sediments are expected to comprise typical abyssal plain nannofossil oozes and pelagic clays (Ruddiman et al., 1988). The seismic image (Figure 4a) shows evidence of normal faulting throughout the lifetime of the FZ, which could be related to sediment compaction, as well as some compressional deformation through sediment folding. A ∼170 m-thick, relatively undeformed top package of sub-horizontal sediments suggests the last significant deformation occurred at ∼7-11 Ma, assuming sedimentation rates of 15-22 m/Ma (Ruddiman et al., 1988). However, the sub-bottom profiler image of the upper ∼100 m of sediments shows small-scale deformation occurring until very recently ( Figure 4b). Two acoustically transparent layers which thin to the south are likely recent slump events from the northern valley wall, estimated to be ∼9 and ∼13 m thick and to have occurred 100-200 ka and 1.5-2.0 Ma, respectively. Evidence for compression is also indicated by folding of the sediments and reverse faults offsetting the seabed with a throw up to ∼9 m.

Discussion
The observed heat flow anomaly of 10-15 mWm −2 within the St Paul FZ is a significant deviation from the predicted conductive values, and the basal value (83 mWm −2 ) represents the maximum heat flow measured to date between the bounding MAR ridge segments and the coast of Africa. Nearby measurements within a 400 km radius of our profile have a maximum value of 75 mWm −2 and an average of 65 mWm −2 (Herman et al., 1977;Vacquier & von Herzen, 1964;von Herzen & Simmons, 1972), similar to our observations north and south of the St Paul FZ.
We consider several possible processes which could influence the heat flow within the FZ or explain the observed positive anomaly: (a) mantle thermal anomalies; (b) thermal rejuvenation of the lithosphere and crustal thickening at the ridge-transform intersection; (c) alteration or production of heat within the FZ; and (d) hydrothermal flow.

Mantle Thermal Anomalies
The influence of the nearby Sierra Leone mantle plume along with the proposed equatorial Atlantic mantle "cold spot" (Schilling, 1995) could affect the heat flow of the study area. The effects of these mantle domains can be seen in the bathymetry and basement depth across the St Paul TF and FZ and the adjacent ridge segments, with the warming influence of the mantle plume shallowing the northern MAR segment by ∼300 m compared to the segment south of St Paul. This trend of shallower bathymetry continues along the FZ to our study area. If we assume that the ridge to the north and the south of the FZ had the same depth at the time of formation, we would expect the northern basement to be ∼260 m deeper from plate cooling models. However, after correcting for sediment loading (Sykes, 1996), it is only ∼20 m deeper than the basement depth to the south. Despite this bathymetric effect, the fact that the observed basal heat flow to the north of St Paul matches the predicted values well suggests that, although the mantle regimes may have influenced the bathymetry of the ridge axis, they have had little effect on the surface heat flow of the older lithosphere.

Thermal Rejuvenation of the Crust
The thermal age of the seafloor used to calculate predicted heat flow is derived from the simple geometry of the ridge-transform system, however, this, and the use of standard plate cooling models (e.g., Hasterok, 2013;Stein & Stein, 1992), may not be appropriate. These methods assume that the heat flow within the FZ should, in a normal case, be between the heat flow exhibited by the lithosphere on either side, and should display a similar thermal structure at formation and subsequent thermal evolution with age. However, these cooling models predict a colder temperature structure than more advanced thermal models of TFs (Behn et al., 2007;Grevemeyer et al., 2021;Wang et al., 2022), which may take into account, for example, mantle upwelling from extensional stresses. We note that these effects are greatest in the center of the TF, and thermal structure should return to levels more similar to plate cooling models closer to the fault ends where the FZ begins. Furthermore, it has recently been proposed that TF crust, and therefore FZ crust, forms in a two-stage accretion process involving initial magmatic accretion at one spreading center, a period of stretching and extension along the TF, before another period of heating and magmatism at the opposite RTI where the two plates are welded together to form the FZ . Bathymetric studies have shown evidence in the form of J-shaped ridges for this lateral movement of melt at RTIs from the ridge axis into the TF and even penetrating into the older plate Marjanović et al., 2020). These J-shaped ridges have also been observed at the St Paul FZ in the vicinity of our study area (Growe et al., 2021). This addition of heat and/or melt at the RTI could increase the temperature of the lithosphere, effectively making the lithosphere appear thermally "younger" than its true age when observing its heat flow.
To investigate the effect of melt injection at the RTI, we modeled the intrusion and cooling of a melt sill in a 1D geotherm profile representing the oceanic lithosphere opposite the RTI. After 10 Myr, both a 1 km-thick and 2 km-thick sill inserted into the oceanic crust at a depth of 1 km below surface produce a surface heat flow anomaly of under 1 mWm −2 ( Figure 5). This modeling did not take into account lateral conduction or warming at the RTI, for example, through mantle upwelling, however, thermal models provide little evidence for the significant passive transfer of heat at RTIs (e.g., Roland et al., 2010). We also note that even if lateral conduction or melt injection at the RTI increases the temperature within the FZ, it should not increase the heat flow to greater than that of the adjacent newly formed crust at the ridge axis, which is what we observe around the St Paul FZ with a higher basal heat flow within the FZ than that of the adjacent younger crust. Even if the thermal age of the lithosphere was reset to the same age as the younger lithosphere, this would predict a heat flow of 73 mWm −2 , compared to the observed value of 83 mWm −2 . Using simple 2D analytical plate cooling models, we calculate that the thermal age would need to be reset by an average of ∼11-20 Myr to match the observed heat flow anomaly. In terms of lithospheric thickness, the nascent FZ lithosphere at the RTI would require thinning from a thickness of 32-45 km to a maximum of ∼9.5 km, and a minimum value of thinner than the lithosphere at the adjacent ridge axis, taking the 1260°C isotherm to represent the base of the lithosphere. This would require the heating of the original LAB to mantle potential temperatures (e.g., 1360°C). Therefore, although there is evidence for the addition of melt to the FZ crust when it was at the RTI, we do not consider that thermal rejuvenation can likely explain the observed heat flow anomaly at St Paul, or, at least, the whole of the observed anomaly. Thermal rejuvenation could, however, significantly influence heat flow measurements much closer to the RTI (within ∼1 Myr of passing the intersection) if considerable amounts of melt are added to the crust.

Near-Surface Disturbances or Production of Heat Within the FZ
Here, we first consider the possibility that the slumping events observed in the upper sediment package (Figure 4b) may have disturbed the thermal structure and hence temperature gradients. In general, rapid sedimentation lowers the temperature gradient in the deposited sediments (Wangen, 2010), which would mean that the undisturbed steady state temperature gradients are higher than those measured. Modeling the equilibrium process of the uppermost slump shows that a 100-200 ka, 10 m-thick slump would have equilibrated to within a few percent of the undisturbed temperature profile within this time period, with any remaining effects below the temperature resolution of 1 mK of the heat probe.
We next consider several possible sources of heat within the FZ. Radioactive decay is the main source of heat production within the Earth, however, inputting realistic production values of up to 1 µWm −3 for sediments and lithosphere into numerical models cannot explain the observed anomaly within the FZ, as production is not expected to be higher there than outside the FZ. Alternatively, at slow-spreading ridge environments the exothermic reaction between seawater and mantle peridotite has been shown to produce enough heat to drive low-temperature hydrothermal systems (Früh-Green et al., 2003), and some TFs and FZs have been shown to consist of significant amounts of exhumed peridotite (e.g., Cannat et al., 1991;Gregory et al., 2021). However, a recent tomographic study across our heat flow profile (Growe et al., 2021) does not indicate the presence of meaningful amounts of exhumed or serpentinized peridotite, and the thick sediment cover with a very low permeability (Spinelli et al., 2004) would inhibit the penetration of enough seawater to produce significant hydration of the igneous basement.
Finally, we consider the production of heat through deformation. Although FZs are assumed to be inactive, intraplate discontinuities, they have been observed to host significant global earthquakes (e.g., Robinson, 2011), including a Mb 5.2 event in the Chain FZ, ∼400 km south of St Paul, in 2016 (USGS, 2020). These observations suggest that multiple smaller events, undetectable by land-based global seismometer networks, may occur on FZs. A study of different sites along the Vema FZ found evidence of tectonic activity in crust up to ∼109 Ma (Devey et al., 2018). The analysis of the sediment images (Figure 4) from the St Paul FZ shows minor deformation occurring throughout the lifetime of the FZ up until the present day, both in compressional and extensional senses, as a pure strike-slip movement is difficult to observe due to the orientation of the profile. Recent movement is also visible in discontinuities in the sediment cover and slope changes in the seafloor seen in the bathymetry data along the FZ, suggesting some extensional movement in the northern FZ wall and compressional behavior in the FZ valley ( Figure 6). This deformation could be caused by intraplate stress due to regional plate directional changes ∼11 Ma (Maia et al., 2016), which are responsible for a number of significant bathymetric features at the St Paul TF and the wider equatorial Atlantic region (Bonatti et al., 1994(Bonatti et al., , 2005, including the 4.5 km-high Romanche transform ridge located only ∼150 km to the south of the study area. This plate motion reorganization event may have caused the last major deformation visible in the seismic image, which is estimated to have occurred ∼7-11 Ma (Figure 4a). Furthermore, global bathymetric and gravity data show that the St Paul TF system has evolved from a two-fault system active until ∼20 Ma to a more complex configuration consisting of four faults separating three small intra-transform spreading segments, widening from ∼50 km at our study area to >80 km at present day. This evolution may also have caused some intraplate stresses. Additionally, it has previously been proposed that the thermal differences across FZs, leading to different rates of subsidence across these features, can cause vertical dip-slip motion (De Long et al., 1977). At our heat flow profile, plate cooling models (Hasterok, 2013) would predict a contemporary dip-slip rate of 9 m/Ma (0.009 mm/a), with cumulative dip-slip of ∼1,700 m since the welding of the FZ lithosphere at the eastern RTI to the present day. Furthermore, the active part of the 880 km-long Romanche TF is just 150 km south of our study, which has produced a 20 km-wide and 6,000 m-deep rift valley, and might have induced compressional stress along the St Paul FZ.
To quantify the amount of heat that may be produced by deformation, we use the formula of Leloup et al. (1999) to calculate shear heating, before using a numerical model to determine the resulting surface heat flow contribution. Using a friction coefficient on the order of 0.5 (Byerlee, 1978) and restricting shear heating to the brittle zone (down to 600°C-upper ∼20 km), a 10-km wide zone of shear heating with a steady-state slip rate of 2-3 mm/a is required to produce a heat flow anomaly of 10-15 mWm −2 . This is a generous estimate of the friction coefficient, which could be lower in the fault zone (England, 2018;Fulton et al., 2013;Leloup et al., 1999), resulting in less heat being produced for the same width and slip rate. The result of 2-3 mm/a of slip is a relatively high value that should produce larger, globally observed earthquakes, and subsequently large offsets in bathymetric features, neither of which are observed. If this slip is represented by strike-slip motion along the FZ, it would be similar to observed slip-rates along FZs in the Wharton Basin that have resulted in large (M > 8) earthquakes (Coudurier-Curveur et al., 2020). Furthermore, models of the thermal regime in active TFs have suggested that shear heating has a minimal final effect on the thermal structure (Roland et al., 2010). Therefore, we do not consider that heat produced directly through different forms of deformation, including dip-slip, compression or strike-slip reactivation can explain the observed heat flow anomaly.

Hydrothermal Flow
Although we have explained that the observed deformation within the St Paul FZ is unlikely to be capable of generating significant amounts of heat, this tectonic activity could play a role in enabling or driving fluid circulation and therefore heat advection within the basement. Further to the deformation sources already proposed, different thermal contraction rates and lithospheric density across FZs result in flexural adjustment of the lithosphere in response to the resultant pressure gradients (Sandwell, 1984), which explains the persistent seafloor relief of FZs as they age. This adjustment steepens the relief of the FZ valleys, which may be the cause of the slumping events and some of the deformation seen in the sedimentary sections. Together, these sources of deformation may create fluid pathways within the crust, as well as influencing pressure gradients, which could drive fluid flow. Tomographic studies of TFs have found velocity anomalies interpreted to represent high amounts of fracturing and porosity within the basement Roland et al., 2012). Although this porosity is likely to be reduced over time and may be affected by crustal thickening at the RTI Marjanović et al., 2020), at the St Paul FZ the slightly reduced velocities within the fault zone suggest a porosity increase as compared to the adjacent crust (Growe et al., 2021). Porosity is predicted to be on the order of ∼16% in the top basement rocks, decreasing to ∼5% at 1 km and ∼2% at 2 km below the sediment-basement interface (Growe et al., 2021). Although the relationship between porosity and permeability within the oceanic crust is complex, it is likely that the uppermost 1 km represents a more permeable layer due to its increased porosity, which could enable fluid flow.
Due to the extensive low permeability sediment cover, we do not expect well-ventilated fluid flow, but lateral or vertical circulation within the basement which may be advecting heat into the FZ, such as that observed in other off-axis areas (e.g., Fisher & Von Herzen, 2005). Previous studies at the Vema FZ (Devey et al., 2018) and Southwest Iberian Margin strike-slip faults (Hensen et al., 2022) found evidence for active fluid flow within sedimented seafloor. Our modeling results showed that the small-scale heat flow variation within the FZ can be satisfactorily explained through conductive refraction from changes in the basement and seafloor topography (Figure 2), and does not require very local, shallow heat advection (Fisher & Von Herzen, 2005). Instead, the fluid circulation is required to produce the 10-15 mWm −2 anomaly observed across the FZ valley, which is at least 17 km-wide. We interpret these observations to suggest the presence of larger-scale, deeper hydrothermal circulation within the upper crust, with strong flow channeling controlled by the permeability structure preventing the formation of small-scale convection cells at the basement surface (Fisher & Becker, 2000). The lack of an observed heat flow low either to the north or south of the FZ likely precludes lateral advection across the FZ, unless the circulation cell size is smaller than the spacing between our measurement sites of 50 km, thus we envisage either east-west lateral advection along the FZ, or vertical flow.
If we assume that the conductive contribution to the heat flow within the FZ is as predicted through plate cooling (Hasterok, 2013), we can estimate the vigor of the fluid circulation through calculation of the Nusselt number (Nu), representing the ratio of total heat flow to purely conducted heat . Using a predicted conducted heat flow of 68 mWm −2 and the modeled total basal heat flow of 83 mWm −2 , we estimate the value of Nu as ∼1.2. We can then use Nu to estimate the Rayleigh number (Ra), which indicates both whether convection is able to take place and whether it is steady state. Following the relationships detailed in Wang (2004-Equation 12.24) we find that Ra could be up to ∼50. This is greater than the general critical Ra value for enabling convection within oceanic crust (∼40) , which is likely to be lower in our case due to the significant topography within the FZ that would encourage convection, but relatively low in general, suggesting that convection is present but is limited. Assuming typical values for the physical properties of the oceanic crust and circulating seawater, and a Ra value of 50, we can use Equation 1 (Wang & Davis, 2003) to estimate the permeability of the crust for different convective layer thicknesses.
Where κ is the permeability, h is the layer thickness and ΔT is the temperature difference across it, k is the thermal conductivity of the basement (here we use 2 Wm −1 K −1 ), and ρ, c, Ø, and μ are the density, specific heat, thermal expansion coefficient, and dynamic viscosity of water, respectively. For each permeability value we varied the layer thickness by 100 m until the difference between the calculated ΔT and the temperature difference predicted by the plate cooling model was at a minimum, with the results shown in Table 3.
As the porosity increase of the crust at St Paul is estimated to be greatest within the uppermost ∼1 km (Growe et al., 2021), we consider a layer thickness of 400-1,100 m and corresponding permeability of 10 −11 -10 −12 m 2 to be the most likely. These calculations suggest that the permeability of the upper crust within the St Paul FZ could be reasonably high, compared to the wide possible range of permeability for oceanic crust, from as high as 10 −9 m 2 for the uppermost 100 m  to as low as 10 −22 m 2 calculated from core samples (Fisher, 1998). The upper crust in this location has been shown to likely comprise of extrusive basalts (Growe et al., 2021), which is consistent with the suggested permeability. For example, a permeability of 10 −12 m 2 is similar to that proposed for the top 1 km of the crust at 13°N on the East Pacific Rise (Evans, 1994), and also within the ranges predicted for sedimented, relatively old crust (Fisher & Becker, 2000).
At the St Paul FZ, the observed high heat flow, flanked by conductive regimes to the north and south, suggests that the FZ could act as a higher permeability channel within the lithosphere as compared to the adjacent crust. In general, significant hydrothermal circulation within the oceanic lithosphere is expected to end at an age of ∼65 Ma, due to increased sedimentation and a reduction in permeability and lithospheric heat with age (Stein & Stein, 1994). Crust with >400 m of sediment cover can have a "sealing age" of as young as 25 Ma, which may explain why both the lithosphere to the north and south of the FZ, aged ∼71 Ma and ∼48 Ma, respectively, exhibit conductive heat flow regimes indicative of no heat advection. Increased permeability within the FZ itself could be due to the more intensely fractured fabric inherited from the TF regime, which would form a preferential pathway for fluid as a channelized flow system (e.g., Fisher & Becker, 2000). The continuing minor tectonic activity may aid the higher permeability to persist over time. This excess permeability, coupled with buoyancy forces, could be sufficient to maintain fluid flow. However, circulation could be further encouraged by the significant seafloor topography, pressure gradients, and lithospheric flexure present at the FZ. This likely results in greater pressure gradients than in normal ridge-flank crust, which may be limited to temperature or buoyancy-driven flow (Fisher & Becker, 2000). Thus, the FZ could behave as a vertical conduit for fluid flux, with the width of the observed anomaly at the surface related to the width of the conduit, or it could enable transient flow along the fault (e.g., Wang, 2004). Upwelling fluid flow could be further encouraged due to the warming effect of the thick sedimentary section within the FZ valley .

Do Fracture Zones Have an Inherently Different Thermal Structure to Normal Oceanic Crust?
Throughout this paper, we have compared the observed heat flow at the St Paul FZ with predicted values from plate cooling models, assuming that the heat flow within the FZ should, in a normal case, be between the heat flow exhibited by the lithosphere on either side. However, as discussed previously, FZ crust may have a different formation mechanism involving rejuvenation at the RTI, and therefore thermal structure and evolution to ordinary oceanic lithosphere (e.g., Grevemeyer et al., 2021). Furthermore, a deep low velocity anomaly imaged at the Romanche TF (Wang et al., 2022) potentially suggests thinning of the lithosphere within the transform zone caused by deep hydration and water-induced melting. At the Romanche TF, the LAB shallows by ∼15 km compared to the predicted thickness (i.e., the average thickness of the lithosphere on either side of the transform) or by ∼6 km compared to the thinner, younger lithosphere. If we use plate cooling models and assume the top of the LAB occurs at a temperature of 1260°C (Mehouachi & Singh, 2018), this thinning would be equivalent to a decrease in age of ∼2-12 Myr, in effect making the TF lithosphere appear "younger" than the lithosphere bounding the fault on both sides. Interestingly, this is what the observed heat flow indicates at St Paul, with the anomaly equivalent to an average age reset of ∼11-20 Myr. Both of these recent studies therefore suggest that TF and FZ lithosphere may not be comparable to lithosphere formed at spreading centers, and the standard plate cooling models may not accurately predict the thermal regime in these locations.
Additional indications that FZ crust could be considered in a different class to "standard" oceanic crust include tomographic studies showing significant fracturing of transform crust at a variety of spreading rates Roland et al., 2012;Van Avendonk et al., 1998), which suggest FZs could have heightened permeability down to, and possibly below, the Moho. Also, seismic events have been observed to occur on FZs, such as an event on the Chain FZ in 2016 (USGS, 2020), indicating that some tectonic activity and deformation along FZs may be widespread. The differential temperature and pressure forces which could drive this activity, as well as lithospheric flexure, are also expected to act at all FZs over their lifetime.
These new discoveries suggest that we could perhaps expect heat flow anomalies at all FZs, either as a result of differing initial temperature structure, and/or from advected heat through fluid flow as suggested for the St Paul FZ. The size of anomalies or extent of fluid flow could be related to parameters such as the size or age-offset of the FZ, which has been found to correlate with TF morphology (Ren et al., 2022). The St Paul FZ system has a total age-offset of 30 Myr and offset length of ∼560 km (23 Myr and ∼300 km for St Paul FZ-N only), compared to a global average offset of 40 km for oceanic TFs (Bird, 2003). It therefore represents a larger TF system which may exhibit more extreme differences in crustal formation, as well as greater differential stresses between the juxtaposed sections of lithosphere. At the location of the only other cross-FZ heat flow study (Kolandaivelu et al., 2017), the Ecuador FZ in the Pacific, the authors found anomalous heat flow and suggested significant fluid flow within the basement to explain the deficit, requiring a permeability of 10 −12 m 2 for a 1,000 m-thick basement aquifer, which matches our estimated permeability for the St Paul FZ. The Ecuador FZ has a small age-contrast of 4.5 Myr, but the exposed basement outcrops on either side of the FZ valley could promote vigorous, ventilated fluid circulation without significant tectonic driving forces. An along-FZ and TF study at the Vema system found heat flow ranging from 66 to 170 mWm −2 , with an average of 124 mWm −2 , in the western FZ valley from the RTI to ∼90 km along the FZ (Langseth & Hobart, 1976). Compared to conductive cooling estimates, these values give a spread of both positive and negative heat flow anomalies, suggestive of significant advection of heat. However, the lack of geophysical data allowing sediment thickness and basement topography to be mapped in the study area prevented full modeling of basement heat flow and heat advection. Similarly, within the global heat flow database (Lucazeau, 2019), there are only a few measurements made within TFs and FZs. These data provide very scattered values suggesting both positive and negative heat flow anomalies, but as they are often isolated measurements with little-to-no information about sediment thickness, basement topography, or heat flow on either side of the FZ, it is not possible to compare these data effectively with the St Paul results. Further comprehensive heat flow studies across both TFs and FZs are needed to fully investigate this hypothesis.

Conclusions
We have observed a positive 10-15 mWm − 2 heat flow anomaly within the SPFZ, when compared to conductive cooling models, as well as evidence for continuous deformation within the FZ valley. After considering the possible causes for the anomaly, we conclude: • The most likely cause for the anomaly is heat advected by fluid flow within a confined basement, with a potential basement permeability of 10 −12 m 2 , assuming a 1,000 m-thick permeable layer representing the basaltic upper crust. • The large age-offset of the FZ and recent regional tectonic stress help to drive the fluid flow, creating an ideal, higher permeability environment to channel substantial, though not vigorous, basement fluid flow. • We cannot discount possible contribution to the heat flow anomaly from thermal rejuvenation at the RTI, or from a different temperature structure within FZs caused by their different formation mechanism. • FZ lithosphere could therefore need to be regarded differently to standard oceanic lithosphere formed at the spreading center when considering its structure, evolution with age, and ability to host hydrothermal circulation.