1. SIO 226: Introduction to Marine Geophysics Heat Flow LeRoy Dorman Scripps Institution of Oceanography March, 2006

2. Introduction From the early days, miners noticed that the temperature increased with increasing depth, so they deduced that the interior of the earth was hot. This observation leads to a way to measure heat flow, that of measurement of the the temperature difference required to drive heat through a solid. This is expressed by Fourier's law, which describes conductive heat flow: In one dimension this is Here k is thermal conductivity in So if we can measure the temperature gradient over some (short) distance, and we know the thermal conductivity, we can calculate the heat flow.

3. Simple (1-dimensional) Theory The heat flow equation is The heat flow equation is In steady state, this is or In steady state, this is or In one dimension, it is In one dimension, it is If H = 0 (no sources) If H = 0 (no sources)  x) = linear or constant  x) = linear or constant The boundary conditions (surface temperature and heat flux) determine the solution. At the surface, The boundary conditions (surface temperature and heat flux) determine the solution. At the surface, and from Fourier. and from Fourier. so and measuring temp gradient and k at surface yields heat flow. so and measuring temp gradient and k at surface yields heat flow.

4. Heat Flow at Sea There are two experimental problems: There are two experimental problems: (1)Measure the thermal gradient. (1)Measure the thermal gradient. (2) Measure the thermal conductivity. (2) Measure the thermal conductivity.

5. Types of Probes On both land sea, temperatures at the bottoms drilled holes are used. Thermal conductivity is obtained from cores. On both land sea, temperatures at the bottoms drilled holes are used. Thermal conductivity is obtained from cores. Piston corers can provide temperatures to ~ten meters. Piston corers can provide temperatures to ~ten meters. Short probes allow multiple measurements without running the wire, but no samples. Short probes allow multiple measurements without running the wire, but no samples.

6. Operation of Piston Corer Lowered to seafloor at ~1 m/s or 3600 m/hour (which is slow). Lowered to seafloor at ~1 m/s or 3600 m/hour (which is slow). Operation is triggered by the arrival of the triggering gravity corer at the seafloor, dropping rapidly in free-fall. Operation is triggered by the arrival of the triggering gravity corer at the seafloor, dropping rapidly in free-fall. A wire of appropriate length stops the piston at the seafloor, helping the soft sediments to be sucked into the core barrel and not pushed aside. A wire of appropriate length stops the piston at the seafloor, helping the soft sediments to be sucked into the core barrel and not pushed aside.

7. Hydraulic Piston Corer For REALLY soft sediments, the piston corer does not do a good enough job, so a gentler device, the HPC was developed for use by a drillship. Figure from Kennett. For REALLY soft sediments, the piston corer does not do a good enough job, so a gentler device, the HPC was developed for use by a drillship. Figure from Kennett.

8. Short Probe Data recorded internally. Data recorded internally. No material sample, so conductivity determined by decay of temp rise from a pulse of heat. No material sample, so conductivity determined by decay of temp rise from a pulse of heat. In operation, probe is lowered into seafloor at wire speed, left for a few minutes (10) for temperature to equilibrate, picked up, moved to another site (at about a knot), then the process repeats. E. Davis figure In operation, probe is lowered into seafloor at wire speed, left for a few minutes (10) for temperature to equilibrate, picked up, moved to another site (at about a knot), then the process repeats. E. Davis figure

9. Indirect determination of heatflow: BSR depth We can measure temperature at the seafloor. We can measure temperature at the seafloor. If gas hydrate is present, the increase in temperature with depth will force the hydrate out of its stability field, which is to the left of the phase boundary, producing free gas. If gas hydrate is present, the increase in temperature with depth will force the hydrate out of its stability field, which is to the left of the phase boundary, producing free gas. We can measure the depth of the BSR by seismic reflection, since the presence of gas reduces the compressional velocity by about half, causing a negative-polarity reflection. We can measure the depth of the BSR by seismic reflection, since the presence of gas reduces the compressional velocity by about half, causing a negative-polarity reflection. Then, by Fourier's law, Then, by Fourier's law,

10. Heat flow from BSR depth off Cascadia This allows relatively quick-and-easy determination of heat flow wherever a BSR is present and visible in seismic reflection. This allows relatively quick-and-easy determination of heat flow wherever a BSR is present and visible in seismic reflection.

11. The trend of the heat flow here is downward from the deformation front toward the continent. Causes of this pattern are not clearly understood. Causes of this pattern are not clearly understood. Contributing factors are likely to be: Contributing factors are likely to be: Warm fluid being squeezed out of subducting sediments, which would increase the heat flow, and/or Warm fluid being squeezed out of subducting sediments, which would increase the heat flow, and/or Cooler continental slope sediments being thrust up by the subducting oceanic plate, which would decrease the heat flow. Cooler continental slope sediments being thrust up by the subducting oceanic plate, which would decrease the heat flow.

12. Comparison between BSR-derived heat flow and probe determinations is not perfect. Possible cause is variability of thermal conductivity Possible cause is variability of thermal conductivity Not clear which data are better Not clear which data are better Camparison at right is from Lucazeau, and others, 2004, showing data from the Congo basin. Camparison at right is from Lucazeau, and others, 2004, showing data from the Congo basin.

13. Land Data Depends on tectonic region. Depends on tectonic region. Is correlated with heat generation in the crustal basement (which is higher than heat generation in oceanic crust. Intercept is thought to be heat from mantle. Is correlated with heat generation in the crustal basement (which is higher than heat generation in oceanic crust. Intercept is thought to be heat from mantle. High scatter in basin and range. High scatter in basin and range. Primarily conductive. Primarily conductive.

14. Land Geotherm Land temperature-depth models are constrained to fit the observed heat flow vs basement heat generation in the presence of erosion, a problem not occurring at sea. Land temperature-depth models are constrained to fit the observed heat flow vs basement heat generation in the presence of erosion, a problem not occurring at sea.

15. Oceanic Heat Flow Depends strongly on age. Depends strongly on age. Conductive and convective. Conductive and convective. Conductive heat transfer easiest to understand and model. Conductive heat transfer easiest to understand and model. Figure from K. Becker thesis, 1981. Figure from K. Becker thesis, 1981.

16. Plate models and their evolution McKenzie (1967) figure at upper right. McKenzie (1967) figure at upper right. Parker and Oldenburg (1973) lower right Parker and Oldenburg (1973) lower right Inclusion of effects of fluid flow. Lister (1972) Inclusion of effects of fluid flow. Lister (1972) Stein and Stein (1994), sealing of plate to fluid flow. Stein and Stein (1994), sealing of plate to fluid flow.

17. Convective Cooling Heat flow near ridges was puzzling, much lower than models predicted. Heat flow near ridges was puzzling, much lower than models predicted. Clive Lister (1972) predicted a mechanism, which was adjusted by Stein and Stein, 1994. Clive Lister (1972) predicted a mechanism, which was adjusted by Stein and Stein, 1994.

18. Sealing and sediments Sealing is now thought not to be totally controlled by sedimentation, since sealing age not controlled by sedimentation rate. Sealing is now thought not to be totally controlled by sedimentation, since sealing age not controlled by sedimentation rate.

19. Common Features of Plate Models Age-depth relationship approximates sqrt(t) at young age. Age-depth relationship approximates sqrt(t) at young age. Departure from this for age > 80MY can be due to heat from below the lithosphere. Departure from this for age > 80MY can be due to heat from below the lithosphere. Or from assuming a plate of fixed thickness as by McKenzie. Or from assuming a plate of fixed thickness as by McKenzie.

20. Age Map Compare map of age with map of water depth. Compare map of age with map of water depth. The depth- relationship means that we can use depth to infer age. The depth- relationship means that we can use depth to infer age.

21. A Mystery These depth profiles show interesting complexities. These depth profiles show interesting complexities. What has happened here? What has happened here? From Sclater, Anderson, Bell, 1971 From Sclater, Anderson, Bell, 1971

22. The Answer

23. Summary: The cooling of the lithosphere is the major factor determining the form of the seafloor in the ocean basins. The cooling of the lithosphere is the major factor determining the form of the seafloor in the ocean basins. Water depth can be used as a proxy for age. Water depth can be used as a proxy for age. Cooling is conductive for ages greater than about 65 My but convection is dominant mechanism before then, especially near the ridges. Cooling is conductive for ages greater than about 65 My but convection is dominant mechanism before then, especially near the ridges.