lecture 16 heat - ernet
TRANSCRIPT
Lecture 16
Heat
Pollack et al. (1993) Source: Peter Bird
3090 STEIN AND STEIN: CONSTRAINTS ON HYDROTHERMAL HEAT FLOW
250] • • • ] 250] • • •-, 200 t Anderson and Skilbeck [1981] t 200 Pacific Ocean _
• 150 I•••, [] Aflanfic x Galapagos ]J 150 I+\\• PSM o ,n,on . , _
I I + + O/ I ! I I O/ I I I 0 •0 100 1 s0 o so 1 oo 1 so
! , , I , , , "• /•X • GDH1 / I X• • GDH1
___ , ___ -
I•- •,••• - [ I• o o ••o o Oooo o _o o O O O
0/ I I / o I I I 0 50 100 150 0 50 100
AGE (Ma) AGE (Ma) Fig. 6. Observed and predicted heat flow versus age for the ocean basins. (top left) Summary of results from earlier study [Anderson and Skilbeck, 1981]. In their figure, the predicted curve is schematic. Other panels show results for our larger data set, compared to predictions of reference models GDH1 and PSM [Parsons and Sclater, 1977]. We find that the seal- ing age for the Pacific is comparable to that for the other ocean basins, in contrast to the earlier result showing a much younger sealing age.
150
The linear fitting approach characterizes simply the presum- ably complex age and site dependence of the heat flow fraction. The scattered data appear inadequate to characterize the age dependence beyond a linear trend. The heat flow fraction might be expected to increase most rapidly for the younger (0-4 Ma) ages and more slowly near the sealing age, as perhaps suggested by the data.
Our Pacific sealing age differs from that of Anderson and Skilbeck [1981] because their data were compared to the predictions of a thermal model with an 80-km-thick lithosphere, a 1200øC basal temperature, and a thermal conductivity of 6.15 x10 -3 cal *C -I cm -I s -l' This model predicts too low heat flow in older lithosphere, which was not apparent because they had only data for 0-50 Ma lithosphere [Anderson and Hobart, 1976], whereas our data extend to older ages. As a result, their model at 20 Ma predicts heat flow -29 mW in -2 lower than GDH1 and hence implies a younger sealing age. Thus global hydrothermal heat flux estimates using this young sealing age [Wolery and Sleep, 1976, 1988; Anderson eta/., 1977; Sleep and Wolery, 1978] are significantly lower than ours.
It is not clear how much significance to ascribe to the scatter in the heat flow fraction for ages exceeding the nominal sealing
age. Some of the scatter presumably reflects the noise in the data, both from measurement uncertainties and topographic effects [e.g., Lachenbruch, 1968; Noel, 1984]. There also appear to be sites in relatively old lithosphere where heat flow studies indicate the water circulation occurs, such as the 80 Ma site dis- cussed by Ernbley et al. [1983]. The limited number of sufficiently dense heat flow surveys on old lithosphere suggest that such water flow is not common. Considerably more such surveys would be required for any meaningful generalization about water flow. The heat flow data presently available indicate only that any water flow in older lithosphere is not transporting significant amounts of heat through the seafloor.
MECHANISM OF SEALING
The mechanisms which cause the heat flow discrepancy, and hence presumably hydrothermal circulation, to decrease with lithospheric age have long been of interest. Two primary effects, both of which may be present, are thought to contribute. Ander- son and Hobart [ 1976] proposed that the heat flow fraction was low for young, unsedimented, crust and rose to about one once the basement rock was covered by 150-200 m of sediment. In
3090 STEIN AND STEIN: CONSTRAINTS ON HYDROTHERMAL HEAT FLOW
250] • • • ] 250] • • •-, 200 t Anderson and Skilbeck [1981] t 200 Pacific Ocean _
• 150 I•••, [] Aflanfic x Galapagos ]J 150 I+\\• PSM o ,n,on . , _
I I + + O/ I ! I I O/ I I I 0 •0 100 1 s0 o so 1 oo 1 so
! , , I , , , "• /•X • GDH1 / I X• • GDH1
___ , ___ -
I•- •,••• - [ I• o o ••o o Oooo o _o o O O O
0/ I I / o I I I 0 50 100 150 0 50 100
AGE (Ma) AGE (Ma) Fig. 6. Observed and predicted heat flow versus age for the ocean basins. (top left) Summary of results from earlier study [Anderson and Skilbeck, 1981]. In their figure, the predicted curve is schematic. Other panels show results for our larger data set, compared to predictions of reference models GDH1 and PSM [Parsons and Sclater, 1977]. We find that the seal- ing age for the Pacific is comparable to that for the other ocean basins, in contrast to the earlier result showing a much younger sealing age.
150
The linear fitting approach characterizes simply the presum- ably complex age and site dependence of the heat flow fraction. The scattered data appear inadequate to characterize the age dependence beyond a linear trend. The heat flow fraction might be expected to increase most rapidly for the younger (0-4 Ma) ages and more slowly near the sealing age, as perhaps suggested by the data.
Our Pacific sealing age differs from that of Anderson and Skilbeck [1981] because their data were compared to the predictions of a thermal model with an 80-km-thick lithosphere, a 1200øC basal temperature, and a thermal conductivity of 6.15 x10 -3 cal *C -I cm -I s -l' This model predicts too low heat flow in older lithosphere, which was not apparent because they had only data for 0-50 Ma lithosphere [Anderson and Hobart, 1976], whereas our data extend to older ages. As a result, their model at 20 Ma predicts heat flow -29 mW in -2 lower than GDH1 and hence implies a younger sealing age. Thus global hydrothermal heat flux estimates using this young sealing age [Wolery and Sleep, 1976, 1988; Anderson eta/., 1977; Sleep and Wolery, 1978] are significantly lower than ours.
It is not clear how much significance to ascribe to the scatter in the heat flow fraction for ages exceeding the nominal sealing
age. Some of the scatter presumably reflects the noise in the data, both from measurement uncertainties and topographic effects [e.g., Lachenbruch, 1968; Noel, 1984]. There also appear to be sites in relatively old lithosphere where heat flow studies indicate the water circulation occurs, such as the 80 Ma site dis- cussed by Ernbley et al. [1983]. The limited number of sufficiently dense heat flow surveys on old lithosphere suggest that such water flow is not common. Considerably more such surveys would be required for any meaningful generalization about water flow. The heat flow data presently available indicate only that any water flow in older lithosphere is not transporting significant amounts of heat through the seafloor.
MECHANISM OF SEALING
The mechanisms which cause the heat flow discrepancy, and hence presumably hydrothermal circulation, to decrease with lithospheric age have long been of interest. Two primary effects, both of which may be present, are thought to contribute. Ander- son and Hobart [ 1976] proposed that the heat flow fraction was low for young, unsedimented, crust and rose to about one once the basement rock was covered by 150-200 m of sediment. In
3090 STEIN AND STEIN: CONSTRAINTS ON HYDROTHERMAL HEAT FLOW
250] • • • ] 250] • • •-, 200 t Anderson and Skilbeck [1981] t 200 Pacific Ocean _
• 150 I•••, [] Aflanfic x Galapagos ]J 150 I+\\• PSM o ,n,on . , _
I I + + O/ I ! I I O/ I I I 0 •0 100 1 s0 o so 1 oo 1 so
! , , I , , , "• /•X • GDH1 / I X• • GDH1
___ , ___ -
I•- •,••• - [ I• o o ••o o Oooo o _o o O O O
0/ I I / o I I I 0 50 100 150 0 50 100
AGE (Ma) AGE (Ma) Fig. 6. Observed and predicted heat flow versus age for the ocean basins. (top left) Summary of results from earlier study [Anderson and Skilbeck, 1981]. In their figure, the predicted curve is schematic. Other panels show results for our larger data set, compared to predictions of reference models GDH1 and PSM [Parsons and Sclater, 1977]. We find that the seal- ing age for the Pacific is comparable to that for the other ocean basins, in contrast to the earlier result showing a much younger sealing age.
150
The linear fitting approach characterizes simply the presum- ably complex age and site dependence of the heat flow fraction. The scattered data appear inadequate to characterize the age dependence beyond a linear trend. The heat flow fraction might be expected to increase most rapidly for the younger (0-4 Ma) ages and more slowly near the sealing age, as perhaps suggested by the data.
Our Pacific sealing age differs from that of Anderson and Skilbeck [1981] because their data were compared to the predictions of a thermal model with an 80-km-thick lithosphere, a 1200øC basal temperature, and a thermal conductivity of 6.15 x10 -3 cal *C -I cm -I s -l' This model predicts too low heat flow in older lithosphere, which was not apparent because they had only data for 0-50 Ma lithosphere [Anderson and Hobart, 1976], whereas our data extend to older ages. As a result, their model at 20 Ma predicts heat flow -29 mW in -2 lower than GDH1 and hence implies a younger sealing age. Thus global hydrothermal heat flux estimates using this young sealing age [Wolery and Sleep, 1976, 1988; Anderson eta/., 1977; Sleep and Wolery, 1978] are significantly lower than ours.
It is not clear how much significance to ascribe to the scatter in the heat flow fraction for ages exceeding the nominal sealing
age. Some of the scatter presumably reflects the noise in the data, both from measurement uncertainties and topographic effects [e.g., Lachenbruch, 1968; Noel, 1984]. There also appear to be sites in relatively old lithosphere where heat flow studies indicate the water circulation occurs, such as the 80 Ma site dis- cussed by Ernbley et al. [1983]. The limited number of sufficiently dense heat flow surveys on old lithosphere suggest that such water flow is not common. Considerably more such surveys would be required for any meaningful generalization about water flow. The heat flow data presently available indicate only that any water flow in older lithosphere is not transporting significant amounts of heat through the seafloor.
MECHANISM OF SEALING
The mechanisms which cause the heat flow discrepancy, and hence presumably hydrothermal circulation, to decrease with lithospheric age have long been of interest. Two primary effects, both of which may be present, are thought to contribute. Ander- son and Hobart [ 1976] proposed that the heat flow fraction was low for young, unsedimented, crust and rose to about one once the basement rock was covered by 150-200 m of sediment. In
5
EPS 122: Lecture 19 – Geotherms
The ocean basins Depth distribution
Depth distribution is related to age
ie the time available for cooling
Good approximation to observation out to ~70 Ma
squares: North Atlantic circles: North Pacific
EPS 122: Lecture 19 – Geotherms
Depth and heat flow – observations
Stei
n &
Ste
in, 1
994
…works best till ~70 Ma
for greater ages depth decreases more slowly
Depth
Heat flux
for greater ages Q decreases more slowly
initially…
5
EPS 122: Lecture 19 – Geotherms
The ocean basins Depth distribution
Depth distribution is related to age
ie the time available for cooling
Good approximation to observation out to ~70 Ma
squares: North Atlantic circles: North Pacific
EPS 122: Lecture 19 – Geotherms
Depth and heat flow – observations
Stei
n &
Ste
in, 1
994
…works best till ~70 Ma
for greater ages depth decreases more slowly
Depth
Heat flux
for greater ages Q decreases more slowly
initially…
(i) Depth increases more slowly with increasing age (ii) Heat flow decreases with increasing age
1. Half space cooling model
2. Plate model
∂T
∂t
=k
rC
p
—2T +
A
rC
p
∂T
∂t
=k
rC
p
—2T +
A
rC
p
�u ·—T
3
Half space cooling model:
Assumptions: (i) temperature is in equilibrium (ii) horizontal advection >>
horizontal conduction
6
EPS 122: Lecture 19 – Geotherms
A simple half-space model T
= T
a
T = 0
ridge
3D convection and advection equation
Assume: •� temperature field is in equilibrium •� advection of heat horizontally is
greater than conduction
Also, t = x/u i.e. distance and time related by the spreading rate
z
x
We have already seen the solution….
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Surface heat flow
…differentiate T-gradient
The observed heat flux was:
� this simple model provides the t1/2 relation
6
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
3D convection and advection equation
Assume: •� temperature field is in equilibrium •� advection of heat horizontally is
greater than conduction
Also, t = x/u i.e. distance and time related by the spreading rate
z
x
We have already seen the solution….
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Surface heat flow
…differentiate T-gradient
The observed heat flux was:
� this simple model provides the t1/2 relation
6
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
3D convection and advection equation
Assume: •� temperature field is in equilibrium •� advection of heat horizontally is
greater than conduction
Also, t = x/u i.e. distance and time related by the spreading rate
z
x
We have already seen the solution….
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Surface heat flow
…differentiate T-gradient
The observed heat flux was:
� this simple model provides the t1/2 relation
6
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
3D convection and advection equation
Assume: •� temperature field is in equilibrium •� advection of heat horizontally is
greater than conduction
Also, t = x/u i.e. distance and time related by the spreading rate
z
x
We have already seen the solution….
EPS 122: Lecture 19 – Geotherms
A simple half-space model T
= T
a
T = 0
ridge
z
x Temperature gradient
Surface heat flow
…differentiate T-gradient
The observed heat flux was:
� this simple model provides the t1/2 relation
7
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Estimate the lithospheric thickness…
T at base of lithosphere: 1100 °C and Ta = 1300 °C
look up inverse error function
if � = 10-6 m2 s-1
L in km, t in Ma � 10 Ma � L = 35 km � 80 Ma � L = 98 km reasonable?
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Column of lithosphere at the ridge
=
Rearrange
Need �(z) …density as a function of T
coefficient of thermal expansion
…and T as a function of age
Substitute…
Ta = 1300oC T = 1100oC
7
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Estimate the lithospheric thickness…
T at base of lithosphere: 1100 °C and Ta = 1300 °C
look up inverse error function
if � = 10-6 m2 s-1
L in km, t in Ma � 10 Ma � L = 35 km � 80 Ma � L = 98 km reasonable?
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Column of lithosphere at the ridge
=
Rearrange
Need �(z) …density as a function of T
coefficient of thermal expansion
…and T as a function of age
Substitute…
7
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Estimate the lithospheric thickness…
T at base of lithosphere: 1100 °C and Ta = 1300 °C
look up inverse error function
if � = 10-6 m2 s-1
L in km, t in Ma � 10 Ma � L = 35 km � 80 Ma � L = 98 km reasonable?
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Column of lithosphere at the ridge
=
Rearrange
Need �(z) …density as a function of T
coefficient of thermal expansion
…and T as a function of age
Substitute…
L in kms and t in My
What about depth? ……Apply principle of isostacy
7
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Estimate the lithospheric thickness…
T at base of lithosphere: 1100 °C and Ta = 1300 °C
look up inverse error function
if � = 10-6 m2 s-1
L in km, t in Ma � 10 Ma � L = 35 km � 80 Ma � L = 98 km reasonable?
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Column of lithosphere at the ridge
=
Rearrange
Need �(z) …density as a function of T
coefficient of thermal expansion
…and T as a function of age
Substitute…
7
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Estimate the lithospheric thickness…
T at base of lithosphere: 1100 °C and Ta = 1300 °C
look up inverse error function
if � = 10-6 m2 s-1
L in km, t in Ma � 10 Ma � L = 35 km � 80 Ma � L = 98 km reasonable?
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Column of lithosphere at the ridge
=
Rearrange
Need �(z) …density as a function of T
coefficient of thermal expansion
…and T as a function of age
Substitute…
7
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Estimate the lithospheric thickness…
T at base of lithosphere: 1100 °C and Ta = 1300 °C
look up inverse error function
if � = 10-6 m2 s-1
L in km, t in Ma � 10 Ma � L = 35 km � 80 Ma � L = 98 km reasonable?
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Column of lithosphere at the ridge
=
Rearrange
Need �(z) …density as a function of T
coefficient of thermal expansion
…and T as a function of age
Substitute…
8
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Approximate L � �
Rearrange…
Appropriate values: �w = 1.0 x 103 km m-3
�a = 3.3 x 103 km m-3
� = 3 x 10-5 °C-1
� = 10-6 m2 s-1
Ta = 1300 °C t in Ma and d in km
Observed…
The simple half-space cooling model matches ocean depths out to ~70 Ma i.e. lithosphere cools, contracts and subsides
EPS 122: Lecture 19 – Geotherms
The “plate” model
T =
Ta
T = 0
ridge
z
x
Simple half-space model
T =
Ta
T = 0
ridge
z
x
T = Ta
The lithosphere has a fixed thickness at the ridge and cools with time
The asthenosphere below is constant temperature
…asymptotic values of Q, depth etc. …cools and thickens for ever
ρa = 3300 kg/m3
ρw = 1000 kg/m3
α = 3×10-5 oC-1
κ = 10-6 m2s-1
Ta = 1300 oC dr = 2.5 km
8
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Approximate L � �
Rearrange…
Appropriate values: �w = 1.0 x 103 km m-3
�a = 3.3 x 103 km m-3
� = 3 x 10-5 °C-1
� = 10-6 m2 s-1
Ta = 1300 °C t in Ma and d in km
Observed…
The simple half-space cooling model matches ocean depths out to ~70 Ma i.e. lithosphere cools, contracts and subsides
EPS 122: Lecture 19 – Geotherms
The “plate” model
T =
Ta
T = 0
ridge
z
x
Simple half-space model
T =
Ta
T = 0
ridge
z
x
T = Ta
The lithosphere has a fixed thickness at the ridge and cools with time
The asthenosphere below is constant temperature
…asymptotic values of Q, depth etc. …cools and thickens for ever
10
EPS 122: Lecture 19 – Geotherms
A hybrid?
“Plate” model fits depth and Q best
but there is other geophysical evidence for a thickening lithosphere
•� increasing elastic thickness •� increasing depth to low velocity asthenosphere
� thermal boundary layer with small-scale convection
crust
litho
sphe
re
crust
litho
sphe
re
Continents
•� thicker crust
•� similar lithosphere
(cratons?)
EPS 122: Lecture 19 – Geotherms
The mantle geotherm convection rather than conduction
� more rapid heat transfer
Adiabatic temperature gradient
Raise a parcel of rock…
If constant entropy: lower P � expands larger volume � reduced T
This is an adiabatic gradient
Convecting system � close to adiabatic
7
EPS 122: Lecture 19 – Geotherms
A simple half-space model
T =
Ta
T = 0
ridge
z
x Temperature gradient
Estimate the lithospheric thickness…
T at base of lithosphere: 1100 °C and Ta = 1300 °C
look up inverse error function
if � = 10-6 m2 s-1
L in km, t in Ma � 10 Ma � L = 35 km � 80 Ma � L = 98 km reasonable?
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Column of lithosphere at the ridge
=
Rearrange
Need �(z) …density as a function of T
coefficient of thermal expansion
…and T as a function of age
Substitute…
Plate cooling model:
8
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Approximate L � �
Rearrange…
Appropriate values: �w = 1.0 x 103 km m-3
�a = 3.3 x 103 km m-3
� = 3 x 10-5 °C-1
� = 10-6 m2 s-1
Ta = 1300 °C t in Ma and d in km
Observed…
The simple half-space cooling model matches ocean depths out to ~70 Ma i.e. lithosphere cools, contracts and subsides
EPS 122: Lecture 19 – Geotherms
The “plate” model
T =
Ta
T = 0
ridge
z
x
Simple half-space model
T =
Ta
T = 0
ridge
z
x
T = Ta
The lithosphere has a fixed thickness at the ridge and cools with time
The asthenosphere below is constant temperature
…asymptotic values of Q, depth etc. …cools and thickens for ever
8
EPS 122: Lecture 19 – Geotherms
A simple half-space model Ocean depth …apply isostasy
Approximate L � �
Rearrange…
Appropriate values: �w = 1.0 x 103 km m-3
�a = 3.3 x 103 km m-3
� = 3 x 10-5 °C-1
� = 10-6 m2 s-1
Ta = 1300 °C t in Ma and d in km
Observed…
The simple half-space cooling model matches ocean depths out to ~70 Ma i.e. lithosphere cools, contracts and subsides
EPS 122: Lecture 19 – Geotherms
The “plate” model
T =
Ta
T = 0
ridge
z
x
Simple half-space model
T =
Ta
T = 0
ridge
z
x
T = Ta
The lithosphere has a fixed thickness at the ridge and cools with time
The asthenosphere below is constant temperature
…asymptotic values of Q, depth etc. …cools and thickens for ever ...cools and thickens for ever ...asymptotic values of Q, depth
∂T
∂z
=∂∂z
T0er f
✓z
2p
kt
◆�=
T0ppkt
e
�z
2/4kt
∂T
∂t
=k
rC
p
1r
2∂∂r
✓r
2 ∂T
∂r
◆+
A
rC
p
T =A
6k
(a2 � r
2)
�k
dT
dr
=Ar
3
T =�Q
b
b
2
k
✓1a
� 1r
◆
0 =k
r
2∂∂r
✓r
2 ∂T
∂r
◆+A
T = T
a
✓z
L
+•
Ân=1
2np
sin
✓npz
L
◆exp
✓�n
2p2kt
L
2
◆◆
4
9
EPS 122: Lecture 19 – Geotherms
Depth and heat flow – observations
Stei
n &
Ste
in, 1
994
Which model(s) fit the data? HS – Half-space model GDH1 – plate model PSM – plate model
All fit the heat flow data (within error)
The GDH1 “plate” model does a better job of fitting the depth data (which is better constrained)
EPS 122: Lecture 19 – Geotherms
The ocean basins Depth distribution
Depth distribution is related to age
ie the time available for cooling
Good approximation to observation out to ~70 Ma
squares: North Atlantic circles: North Pacific
Plate model:
There is a limit to the lithospheric thickness available for cooling
10
EPS 122: Lecture 19 – Geotherms
A hybrid?
“Plate” model fits depth and Q best
but there is other geophysical evidence for a thickening lithosphere
•� increasing elastic thickness •� increasing depth to low velocity asthenosphere
� thermal boundary layer with small-scale convection
crust
litho
sphe
re
crust
litho
sphe
re
Continents
•� thicker crust
•� similar lithosphere
(cratons?)
EPS 122: Lecture 19 – Geotherms
The mantle geotherm convection rather than conduction
� more rapid heat transfer
Adiabatic temperature gradient
Raise a parcel of rock…
If constant entropy: lower P � expands larger volume � reduced T
This is an adiabatic gradient
Convecting system � close to adiabatic
Small scale convection
Source: Peter Bird
globally and also are corrected for convective effects.
Fig 3.6 Two different ways of averaging continental heat low data. The first (a) is by the age ofthe last major tectonic event and (b) is by the radiometric date of crustal age. The width of eachbox represents one standard deviation
Fig 3.7 Locations of heat flow measurements in both oceans and continents
87
Continental Heat Flow
Sclater et al., 1981