SIO 226: SIO 226: Introduction to Introduction to

Marine GeophysicsMarine GeophysicsHeat FlowHeat Flow

LeRoy DormanLeRoy DormanScripps Institution of Scripps Institution of

OceanographyOceanographyFebruary, 2011February, 2011

IntroductionIntroductionFrom the early days, miners noticed that the From the early days, miners noticed that the temperature increased with increasing depth, temperature increased with increasing depth, so they deduced that the interior of the earth so they deduced that the interior of the earth was hot. This observation leads to a way to was hot. This observation leads to a way to measure heat flow (actually flux), that of measure heat flow (actually flux), that of measurement of the the temperature measurement of the the temperature difference required to drive heat through a difference required to drive heat through a solid. “New” units are solid. “New” units are

This is expressed by Fourier's law, which This is expressed by Fourier's law, which describes conductive heat flow: describes conductive heat flow: In one dimension this is Here In one dimension this is Here kk is thermal conductivity in is thermal conductivity in

So if we can measure the temperature gradient So if we can measure the temperature gradient over some (short) distance, and we know the over some (short) distance, and we know the thermal conductivity, we can calculate the thermal conductivity, we can calculate the heat flow. heat flow.

Q=−k ∇ TQ=−k dT

dxW m−1 K−1°

W /m2

Simple (1-dimensional) Simple (1-dimensional) TheoryTheory

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 isIn one dimension, it is If If H = 0 H = 0 (no sources)(no sources) x) = x) = linear or constantlinear or constant The boundary conditions (surface temperature and heat The boundary conditions (surface temperature and heat

flux) determine the solution. At the surface,flux) determine the solution. At the surface, and from and from

Fourier.Fourier.

so and measuring temp gradient and k at so and measuring temp gradient and k at surface yields heat flow.surface yields heat flow.

∇2T=∂T∂ t

− Hc

∂2T∂ x2 =−H k−1

∇2T=−Hc ∇2T=−H k−1

∂2T∂ x2 =0

T=T s∂T∂ x

∂T∂ x

=Qk

= heatfluxconductivity

Q=k ∂T∂ x

Heat Flow at Heat Flow at SeaSea

There are two There are two experimental experimental problems:problems:

(1)Measure the (1)Measure the thermal gradient.thermal gradient.

(2) Measure the (2) Measure the thermal thermal conductivity.conductivity.

Types of Types of ProbesProbes

On both land sea, On both land sea, temperatures at the temperatures at the bottoms drilled holes are bottoms drilled holes are used. Thermal used. Thermal conductivity is obtained conductivity is obtained from cores.from cores.

Piston corers can provide Piston corers can provide temperatures to ~ten temperatures to ~ten meters.meters.

Short probes allow multiple Short probes allow multiple measurements without measurements without running the wire, but no running the wire, but no samples. samples.

Operation of Piston Operation of Piston CorerCorer

Lowered to seafloor at ~1 Lowered to seafloor at ~1 m/s or 3600 m/hour (which m/s or 3600 m/hour (which is slow).is slow).

Operation is triggered by Operation is triggered by the arrival of the the arrival of the triggering gravity corer at triggering gravity corer at the seafloor, dropping the seafloor, dropping rapidly in free-fall.rapidly in free-fall.

A wire of appropriate A wire of appropriate length stops the piston at length stops the piston at the seafloor, helping the the seafloor, helping the soft sediments to be soft sediments to be sucked into the core barrel sucked into the core barrel and not pushed aside.and not pushed aside.

Hydraulic Hydraulic Piston Piston CorerCorer

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

Short Short ProbeProbe

Data recorded internally.Data recorded internally. No material sample, so No material sample, so

conductivity determined by conductivity determined by decay of temp rise from a decay of temp rise from a pulse of heat.pulse of heat.

In operation, probe is In operation, probe is lowered into seafloor at lowered into seafloor at wire speed, left for a few wire speed, left for a few minutes (10) for minutes (10) for temperature to equilibrate, temperature to equilibrate, picked up, moved to picked up, moved to another site (at about a another site (at about a knot), then the process knot), then the process repeats. E. Davis figurerepeats. E. Davis figure

CapstanCapstan• Used for mechanical Used for mechanical

assistance in pulling assistance in pulling heavy loads on a line heavy loads on a line (rope).(rope).

• The capstan is turned The capstan is turned by an electric motor by an electric motor controlled by the sailor controlled by the sailor manipulating the manipulating the orange handle.orange handle.

• The tension on the line The tension on the line is being controlled by is being controlled by the sailor in the center, the sailor in the center, who is not having to who is not having to work very hard.work very hard.

Trawl/dredge winch with traction engine

Indirect determination of heatflow: Indirect determination of heatflow: BSR depthBSR depth

We can measure temperature at We can measure temperature at the seafloor.the seafloor.

If gas hydrate is present, the If gas hydrate is present, the increase in temperature with depth increase in temperature with depth will force the hydrate out of its will force the hydrate out of its stability field, which is to the left of stability field, which is to the left of the phase boundary, producing the phase boundary, producing free gas.free gas.

We can measure the depth of the We can measure the depth of the BSR by seismic reflection, since BSR by seismic reflection, since the presence of gas reduces the the presence of gas reduces the compressional velocity by about compressional velocity by about half, causing a negative-polarity half, causing a negative-polarity reflection.reflection.

Then, by Fourier's law,Then, by Fourier's law,

Q=kT bsr−T seazbsr

Heat flow from BSR depth off CascadiaHeat flow from BSR depth off Cascadia This allows relatively quick-This allows relatively quick-

and-easy determination of and-easy determination of heat flow wherever a BSR is heat flow wherever a BSR is present and visible in seismic present and visible in seismic reflection.reflection.

The trend of the heat The trend of the heat flow here is downward flow here is downward from the deformation from the deformation

front toward the front toward the continent.continent.

Causes of this pattern are not Causes of this pattern are not clearly understood.clearly understood.

Contributing factors are likely Contributing factors are likely to be:to be:

Warm fluid being squeezed out Warm fluid being squeezed out of subducting sediments, which of subducting sediments, which would increase the heat flow, would increase the heat flow, and/orand/or

Cooler continental slope Cooler continental slope sediments being thrust up by sediments being thrust up by the subducting oceanic plate, the subducting oceanic plate, which would decrease the heat which would decrease the heat flow.flow.

Comparison between BSR-derived Comparison between BSR-derived heat flow and probe determinations is heat flow and probe determinations is

not perfect.not perfect. Possible cause is variability Possible cause is variability of thermal conductivityof thermal conductivity

Distance in box is between Distance in box is between probe and BSR probe and BSR measurement.measurement.

Not clear which data are Not clear which data are betterbetter

Comparison at right is from Comparison at right is from Lucazeau, and others, G3, Lucazeau, and others, G3, 2004, showing data from 2004, showing data from the Congo basin.the Congo basin.

Land DataLand Data

Depends on tectonic Depends on tectonic region.region.

Is correlated with heat Is correlated with heat generation in the crustal generation in the crustal basement (which is basement (which is higher than heat higher than heat generation in oceanic generation in oceanic crust. Intercept is thought crust. Intercept is thought to be heat from mantle.to be heat from mantle.

High scatter in basin and High scatter in basin and range.range.

Primarily conductive.Primarily conductive.

Land GeothermLand Geotherm

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

Oceanic Heat Oceanic Heat FlowFlow

Depends strongly Depends strongly on age.on age.

Conductive and Conductive and convective.convective.

Conductive heat Conductive heat transfer easiest to transfer easiest to understand and understand and model.model.

Figure from K. Figure from K. Becker thesis, Becker thesis, 1981.1981.

Cooling and water depthCooling and water depthAs cooling occurs, isostasy (the concept that columns must As cooling occurs, isostasy (the concept that columns must contain equal mass down to some depth where the earth is more contain equal mass down to some depth where the earth is more or less fluid) requires that the plate sink deeper into the or less fluid) requires that the plate sink deeper into the asthenosphere.asthenosphere.One way of looking at this process is considering that the mean One way of looking at this process is considering that the mean density of the plate and the water above is must equal the density of the plate and the water above is must equal the density of the asthenosphere.density of the asthenosphere.

Common Features of Plate Common Features of Plate ModelsModels

Age-depth relationship approximates sqrt(t) at young Age-depth relationship approximates sqrt(t) at young age.age.

Departure from this for age > 80MY can be due to heat Departure from this for age > 80MY can be due to heat from below the lithosphere.from below the lithosphere.

Or from assuming a plate of fixed thickness as by Or from assuming a plate of fixed thickness as by McKenzie.McKenzie.

Plate models and their Plate models and their evolutionevolution

McKenzie (1967) McKenzie (1967) figure at upper figure at upper right.right.

Parker and Parker and Oldenburg (1973) Oldenburg (1973) lower rightlower right

Inclusion of effects Inclusion of effects of fluid flow. Lister of fluid flow. Lister (1972)(1972)

Stein and Stein Stein and Stein (1994), sealing of (1994), sealing of plate to fluid flow.plate to fluid flow.

Heat flow from modelsHeat flow from models

The McKenzie's (1967) calculations were done using The McKenzie's (1967) calculations were done using trigonometric series, giving answers which were correct, trigonometric series, giving answers which were correct, but not easy to remember and contained no hint of but not easy to remember and contained no hint of dependence on dependence on √√tt..

Neglecting horizontal heat flow and considering small age Neglecting horizontal heat flow and considering small age only lead to solutions in only lead to solutions in √√t, as shown by Parsons and t, as shown by Parsons and Sclater (1977) who transformed the series solutions into Sclater (1977) who transformed the series solutions into that form.that form.

But the plate and Davis and Lister's 1974 half-space model But the plate and Davis and Lister's 1974 half-space model predict infinite heat flow at the origin and all of those predict infinite heat flow at the origin and all of those models predict more heat flow near the ridge crest than is models predict more heat flow near the ridge crest than is observed.observed.

Convective Convective CoolingCooling

Heat flow Heat flow near ridges near ridges was puzzling, was puzzling, much lower much lower than models than models predicted.predicted.

Clive Lister Clive Lister (1972) (1972) predicted a predicted a mechanism, mechanism, which was which was adjusted by adjusted by Stein and Stein and Stein, 1994.Stein, 1994.

Sealing Sealing and and

sedimentssediments Sealing is now Sealing is now

thought not to thought not to be totally be totally controlled by controlled by sedimentation, sedimentation, since sealing since sealing age not age not controlled by controlled by sedimentation sedimentation rate.rate.

Age MapAge Map

Compare map Compare map of age with of age with map of water map of water depth.depth.

The depth- The depth- relationship relationship means that we means that we can use depth can use depth to infer age.to infer age.

tt

A MysteryA Mystery These depth These depth

profiles show profiles show interesting interesting complexities.complexities.

What has What has happened here?happened here?

From Sclater, From Sclater, Anderson, Bell, Anderson, Bell, 19711971

The AnswerThe Answer

Plate thickness from seismologyPlate thickness from seismology

From surface From surface wave wave tomography, it is tomography, it is possible to possible to extract models extract models for various age for various age ranges.ranges.

This procedure This procedure reveals reveals reasonable reasonable agreement with agreement with the cooling of a the cooling of a plate.plate.

Summary:Summary: The cooling of the lithosphere is the major factor The cooling of the lithosphere is the major factor

determining the form of the seafloor in the ocean basins.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 Cooling is conductive for ages greater than about 65 My

but convection is dominant mechanism before then, but convection is dominant mechanism before then, especially near the ridges.especially near the ridges.