e global hf reyes - university of california, san diego
TRANSCRIPT
Global Oceanic heat flow es1mates by
Valeria Reyes Ortega
November 2nd, 2016
Scripps Ins1tu1on of Oceanography UC San Diego
(Wei and Sandwell, 2006)
Outline
• Introduc1on • Objec1ve • Theory • Examples • Limita1ons
Introduc1on
Total heat output of the Earth
Heat flow from the core Radiogenic heat
produc1on in the mantle
Secular cooling of the Earth
Radiogenic heat produc1on in the con1nental crust
• Total surface heat output à 42 – 44 TW (Sclater et al., 1980; Pollack et al., 1993)
• However, this es1mate has been ques1oned by Hofmeister and Criss, 2005.
• Taking conduc1ve ocean heat flow measurements at face values leads to a global heat output of only 31 TW.
• The 13 TW difference is related to Cenozoic oceanic lithosphere (0-‐66 Ma) heat flow.
• Lithospheric cooling models predict high heat flow values at ridges and on young ridge flanks
(Müller, et al., 1997)
Objec1ves
• Derive the local heat loss using the depth d and age A of the seafloor assuming conserva1on of energy and local isostasy.
• Compare the solu1on with Half-‐space cooling model and conduc1ve heat flow measurements.
Theory
• Conserva)on of Energy
−∇ ∙ k ∇ T+ ! c!! ∙ ! T+ ! c! ! !! ! = !(1)
−∇ ∙ k ∇ T+ ! c!! ∙ ! T = 0(2)
Assuming steady state spreading and no internal heat genera1on:
! ∙ ! T = !! !!
∇ ∙ ! (3)q
1 2
Depth of compensa1on
ρw
ρm
ρ=ρm [1-‐α(T-‐Tm)]
• Isostacy balance
water
lithosphere
mantle
v
1 2=
! (!) = ! ! !! (!!! !!)
(! − !!!! )!"(4)
! ∙ ∇!(!) = ! ! !! (!!! !!)
! ∙ ∇ !!! !"(5)
Taking the gradient and then the dot product with the plate velocity
0
L
x
x
+z
By neglec1ng lateral transport
!"(!)!"!! !" = ! ! − ! ! = !! − !!(7)
Basal heat flow Surface heat flow Subs1tu1ng Eq. (7) into Eq. (6):
! ∙ ∇! ! = ! ! (!!! !!) !!
(!! − !!) (8)Scalar subsidence rate
! ∙ ∇!(!) = ! ! (!!! !!)!!
∇ ∙ !!! !"(6)
! = ∇!∇!∙∇! (9)
Given a grid of seafloor age A(x) the local fossil spreading velocity is:
The final expression becomes: ∇!∙∇! !∇!∙∇! = ! !
(!!! !!) !!(!! − !!) (10)
To calculate the surface heat flow:
!! = !! + ! ! (!!! !!) !!
∇!∙∇! !∇!∙∇! (11)General assump1ons
α = 3.85 x 10-‐5 °C-‐1 Cp = 1124 kg-‐1°C-‐1 ρm = 3330 kg m-‐3
ρw = 1025 kg m-‐3
(Doin and Fleitout, 1996)
Mid-‐Atlan1c Ridge example
(Wei and Sandwell, 2006)
!! − !! a) Should not be computed
across ridges or transform faults
b) Omit < 0.5 Ma young seafloor within a 20 km distance
c) Constant heat flow 38 mW m-‐2 was added to account for the basal heat input
∇!
Surface heat flow (mW m-‐2)
Reproduced from Wei and Sandwell (2006)
0 10 20 30 40 50 60 70Age (Ma)
-6000
-5000
-4000
-3000
-2000
Dep
th (m
)
Half-space coolingAveraged Seafloor depth
0 10 20 30 40 50 60 70Age (Ma)
0
50
100
150
200
250
300
350
Hea
t flo
w (m
W m
-2) Half-space cooling
Estimation based on subsidence ratePollack et al. data
! = 480/ !
-‐ Basal heat flow of 38 mW m-‐2
-‐ 3 Ma age bins
! = 2500+ 350/ !
Mid-‐Atlan1c Ridge example
Reproduced from Wei and Sandwell (2006)
0 10 20 30 40 50 60 70Age (Ma)
-6000
-5000
-4000
-3000
-2000
Dep
th (m
)
Half-space coolingAveraged Seafloor depth
0 10 20 30 40 50 60 70Age (Ma)
0
50
100
150
200
250
300
350
Hea
t flo
w (m
W m
-2) Half-space cooling
Estimation based on subsidence ratePollack et al. data
Global Analysis example
! = 480/ !
! = 2500+ 350/ !-‐ Basal heat flow
of 38 mW m-‐2
-‐ 3 Ma age bins
0 10 20 30 40 50 60 70Age (Ma)
4
6
8
10
Area
(m2 )
#1012 Area varies with age
0 10 20 30 40 50 60 70Age (Ma)
0
2
4
6
Inte
rval
hea
t flo
w (W
)
#1012
0 10 20 30 40 50 60 70Age (Ma)
0
1
2
3
Accu
mul
ated
hea
t flo
w (W
) #1013
20.4 TW
66
Cenozoic Heat output
5 TW contribu1on (0-‐3 Ma)
• Q con1nents and older oceans: 23.6 TW • QT is close to the 44 TW value
Heat flow in each age bin 1mes the area of the bin
Limita1ons • Since the age gradient is discon1nuous across plate boundaries,
the method fails over very young seafloor. • The model assumes local isosta1c balance, so 20 km of the
ridge axis have to be omined.
• The results show excellent agreement with the cooling model if a basal heat flux of 38 mW m-‐2 is added.
• The method relies on the HSC cooling model to es1mate 5-‐TW contribu1on to the heat flow over the spreading ridges
Thank you!
References
Doin, M.P., Fleitout, L., 1996. Thermal evolu1on of the oceanic lithosphere: an alterna1ve view. Earth Planet. Sci. Len. 142, 121–136.
Hofmeister, A.M., Criss, R.E., 2005. Earth's heat flux revised and linked to
chemistry. Tectonophysics 395, 159–177. Müller, R. D., Roest, W. R., Royer, J. Y., Gahagan, L. M., & Sclater, J. G. (1997).
Digital isochrons of the world's ocean floor. Journal of Geophysical Research: Solid Earth, 102(B2), 3211-‐3214.
Wei, M., & Sandwell, D. (2006). Es1mates of heat flow from Cenozoic seafloor
using global depth and age data. Tectonophysics, 417(3), 325-‐335.