Chapter
26
Terrestrial
heat
flow
During
the
thirty-five
years
which
have
passed
since
I
gave
this
wide-ranged
estimate
[of
20-400
million
years]
experimental
investigation
has
supplied
much
of
the
knowledge
then
wanting
regarding
the
thermal
properties
of
rocks
to
form
a
closer
estimate
of
the
time
which
has
passed
since
the
consolidation
of
the
earth,
we
have
now
good
reason
for
judging
that
it
was
more
than
20,000,000
and
less
than
40,000,000
years
ago,
and
probably
much
nearer
20
than
40.
Lord
Kelvin
He
at
losses
The
nature
of
the
surface
boundary
condition
of
the
mantle
changes
with
time.
Currently,
the
mantle
has
a
conduct
i
on
b o
undary
layer
with
a
thickness
that
averages
100-200
km.
The
boundary
layer
is
assumed
to
start
out
at
zero
thickness
at
volcanic
ridges;
it
is
pierced
in
places
by
volcanoes
that
deliver
a
small
fraction
of
the
Earth's
heat
to
the
surface
via
magma,
and
it
may
be
invaded
at
greater
depths
by
sills
and
dikes
that
affect
the
bathymetry
and
heat
flow
.
Ridges
also
jump
around,
migrate
or
start
on
a
pre-existing
TBL.
The
cooling
of
the
mantle
is
mainly
accomplished
by
the
cooling
of
the
sur-
face
plates
.
In
early
Earth
history
a
transient
magma
ocean
allowed
magmas
to
transfer
their
heat
directly
to
the
atmosphere.
As
buoyant
mate-
rial
collected
at
the
top,
the
partially
molten
inte-
rior
became
isolated
from
the
surface.
Magma,
however,
could
break
through
a
possibly
thick
buoyant
layer
and
create
'heat
pipes'
to
carry
magma
and
heat
to
the
surface
. Io,
Venus
and
early
Mars
are
objects
that
may
utilize
this
mech-
anism
of
heat
transfer
.
It
is
also
an
alternative
to
plate
tectonics
on
early
Earth
.
The
surface
bound-
ary
condition
in
these
cases
can
be
viewed
as
a
permeable
plate.
Intrusion
affects
the
topog-
raphy
and
heat
flow,
maldng
these
parameters
non-unique
functions
of
age.
The
Earth's
interior
is
cooling
off
by
a
combi-
nation
of
thermal
conduction
-
and
intrusion
-
through
the
surface
boundary
layer
and
the
deliv-
ery
of
cold
material
to
the
interior
by
slabs,
a
form
of
advection
.
An
unknown
amount
of
heat
is
transferred
to
the
surface
by
hydrothermal
circulation
.
The
delamination
of
the
bottom
of
over-thickened
crust
also
cools
off
the
underly-
ing
mantle
.
The
heat
generated
in
the
interior
of
the
Earth,
integrated
over
some
delay
time,
is
transferred
to
the
surface
conduction
boundary
layer
by
a
combination
of
solid-state
convection
,
fluid
flow
,
radiation
and
conduction.
The
con-
ducted
heat
through
the
surface
TBL
(there
may
be
deeper
ones
as
well)
can
be
decomposed
into
a
steady-state
(or
declining)
background
term,
a
transient
term,
and
a
crustal
contribution.
In
334
TERR
E
STRIAL
H
EAT
FLOW
I
I
I
120
I-
-
100
I-
-
c::J
E
80
~
1----
'+
-
.s
:;;
60
0
;;:::
+
r-
t
(ij
Ql
40
:r:
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20
f="""
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I
I
I
2
3
4
Crustal
age
(1
0
9
yr)
th
e
continents,
heat
flow
is
often
plotted
as
a
function
of
age
(Figure
26.1)
or
the
time
since
th
e
last
tectonic
or
igneous
event
and
the
long-
term
asymptotic
value
is
taken
to
be
the
back-
ground
heat
flow.
The
transient
effect
has
a
time
constant
of
more
than
200
Myr
and
this
is
stretched
out
further
by
erosion,
which
strips
off
the
radioactive-rich
outer
layers.
In
some
compi-
lations,
the
transient
effect
is
discounted
in
esti
-
mating
continental
and
global
heat
flow
.
Crustal
radioactivity
is
a
major
contributor
to
continen-
tal
heat
flow
and
lateral
variations
in
this
heat
flow.
In
the
ocean
basins
the
main
contribution
to
th
e
observed
heat
flow
is
the
transient
effect
,
the
formation
of
the
oceanic
crust
itself.
Theo-
retically
,
heat
flow
should
die
off
as
the
s
quare-
root
of
age
but
it
is
nearly
constant
after
the
ini-
tial
transient
(see
Fi
g
ure
26.1)
.
The
background
oc
e
anic
heat
flow
is
nearly
the
same
as
under
con-
tinents
,
perhaps
slightly
larg
er.
There
is
lit-
t l e
evidence
t h a t
ho
t
spo
t s
or
swel
l s
are
associated
with
h
igh
h
ea
t
flow.
In
co
n
trast
to
predictions
from
the
plate
and
cool-
in
g
half-space
models
there
is
little
correlation
of
heat
flow
with
age
or
depth
(Figure
26.2)
. Mea-
sured
heat
flow
is
not
a
unique
function
of
age
.
This
indicates
that
the
mantle
is
not
isothermal
(characterized
by
a
single
p
otential
te
m
per-
ature
)
or
homogenous
(in
composition
and
ther-
mal
properties).
c:
0
·
-g
<1l
L.t
Global
heat
flow
data
Ob
served
/GDH
1:
Global
data
50
100
150
Age
(My
)
Measured
heat
fl
ow
and
cumu
lative
heat
flow
as
a
function
of
age
.
If
the
shallow
mantle
is
at
the
melting
point
,
or
if
there
are
fertile
bl
obs
in
the
mantle
with
l
ow
melting
points
,
then
intrusion
by
dikes
and
sills
may
modify
the
heat
flow
.
T he
top
panel
shows
heat
fl
ow
vs
age
with
one-standard
deviations
(Stein
and
Stein
,
1994)
.
[
constr
a
in
t s
on
h
yd
r
otherma
l
heat
flu
x ]
The
cold
outer
shell
of
the
Earth
is
not
simply
a
coolin
g
boundar
y
layer
of
uniform
composition
and
conductivity
,
losing
heat
by
conduction
alone
.
Ocean
bathymetry
is
more
uniquely
a func-
tion
of
square-root
age,
s
uggesting
that
som
e
process
affe
cts
the
near-surface
thermal
g
radient
without
affectin
g
the
integrated
density
of
th
e
outer
layers.
Glob
al
heat
flow
Global
heatflow
compilat
i o n s
are
read-
ily
available
(www
.
heatflow.und.edu)
(http
://
www.geo.lsa
.
umich.edu
/IHFCjheatflow.html).
The
total
heat
flow
through
the
surface
of
the
Earth
from
the
interior,
based
on
me
asu
re
d
he
at
flow,
is
about
30
TW.
Various
corrections
and
adjustments
are
made
to
the
data
and
som
e
workers
think
the
adjusted
total
heat
flow
may
be
closer
to
44
TW
but
this
is
based
on
assumption
s.
Table
26.1
I
Summary
of
heat
flow
observa-
tions
I
nput
Potential
energy
co
n
tr
i
but
ions
Mant
le
differentiat
ion
and
co
ntractio
n
H eat
fr
o m
co
re
Core
differe
nt iation
Cond
uction
down
ad
iabat
Inne
r
core
growt
h
E
art
hqu
akes
T idal
fr iction
Current
rad
iogenic
(B
SE)
De
layed
radioge
ni
c (
1-2
Gyr)
Secular
cool
ing
(50-80
K!Gy
r)
Total
Radiogenic
+
other
Output
G loba
l heatf
l
ow
(observed)
Cool
i
ng
plate
mode
l
(t
heoretica
l)
Regions
of
excess
mag
mati
sm
1W
3
8
1
.2
6
0.5
2
I
28
5-
15
9-
14
42
-
57
56-7
1
30-32
44
2.4
-
3.5
About
28
TW
are
generated
by
radioactive
decay
in
the
interior
.
There
are
about
10
TW
of
non-
radiogenic
heat
sources
such
as
cooling
and
differentiation
of
the
core
,
contraction
of
the
mantl
e ,
tidal
friction
and
so
on
.
On
a
convecting
planet
one
expects
temporal
variations
in
heat
flow
of
at
least
10
%.
The
secular
cooling
of
the
Earth
contributes
somewhere
between
30-60
%
of
the
measured
heat
flow
.
Thus
,
there
is
either
a
good
match
between
heat
production
and
heat
flow,
or
there
is
a
deficit
or
a
surplus
of
heat
.
Some
workers
have
declared
an
energy
crisis
,
or
a
missing
heat-source
problem.
TI1is
crisis
is
simi-
lar
to
the
crisis
precipitated
by
Lord
Ke
l v i n
and
h i s
age
of
t h e
E
art
h .
A
summary
of
the
energy
inputs
and
outputs
of
the
mantle
and
core
are
given
in
Table
26
.
1.
The
total
radiogenic
and
secular
cooling
amounts
to
42-57
TW,
while
the
current
radiogenic
pro-
duction
is
only
28
TW.
The
observed
conducted
heat
flow
loss
is
30-32
TW
.
Of
this,
about
2.4-3
.5
TW
is
from
the
vicinity
of
hotspots.
An
unlmown
amount
of
heat
loss
is
due
to
hydrothermal
cir-
culation.
A
generous
allowance
for
this
brings
HEAT
LOSSES
335
the
heat
loss
through
the
surface
to
44
TW
[m
a
ntl
e
plum
es
heat
fl
ow
].
TI1e
local
heat
flow
from
the
interior
is
esti-
mated
by
drilling
holes
and
measurin
g
tem-
perature
gradients
and
thermal
conductivity
.
Clearly,
the
surface
of
the
Earth
is
not
densely
or
uniformly
covered
by
such
holes
.
TI1e
most
straightforward
way
of
estimating
the
global
ter-
restrial
heat
flow
is
simply
to
average
the
data
in
an
appropriate
way.
A
spherical
harmonic
expan-
sion
of
heat
flow
data
smooths
it
,
and
serves
as
an
interpolation
scheme;
however,
it
is
not
nec-
essarily
appropriate
for
heat
flow,
tomography,
bathymetry
or
other
functions
that
are
not
poten-
tial
functions.
Data
can
be
binned
(by
region,
age
,
tectonomagmatic
age
and
so
on)
to
minimize
the
uneven
spatial
distributions
of
the
measure-
ments.
In
practice,
averages
are
calculated
in
var-
ious
tectonic
provinces
since
the
global
dataset
is
not
uniformly
dense.
Various
'corrections
'
are
applied
to
the
raw
data
so
that
estimates
of
global
power
are
model
dependent
.
Examples
of
these
corrections
are
:
replacing
oceanic
mea-
surements
with
predictions
from
a
theoretical
cooling
model,
adding
in
an
arbitrary
or
the-
oretical
amount
of
hydrothermal
heat
flow
-
which
is
well
known
only
near
ridges,
remov-
ing
transient
effect
s
from
tectonic
or
magmatic
events,
and
eliminating
data
from
areas
thought
to
be
affected
by
hotspo
t
s.
Some
workers
ar
g
ue
that
it
is
preferab
l e
to
base
s u
rface
h
eat
f
low
a n
alys
i s
not
only
on
the
exten-
sive
m
easureme
n
ts
but
also
on
processes
that
are
thought
to
bias
the
measurements
. This
has
become
a
contentious
issue
.
Global
h
eat
f l
ow
ma p s
show
a
strong
age
dependency
that
is
lacking
in
the
data
;
this
is
a
result
of
the
correction.
The
dramatic
effects
of
hydrothermal
circu-
lation
on
surface
heat
flux
have
been
exten-
sively
documented
on
young
(
<
20
My)
seafloor
but
theory
and
data
are
lacldng
for
old
seafloor.
The
magnitude
of
the
assumed
hydrothermal
correction
to
measured
values
of
heat
flow
is
essentially
the
same
as
the
so-called
missing
heat
source
.
Co
n
ti
n e n t
al
an
d
ocea
n
ic
heat
flow
dat
a
are
treated
differently.
The
secular
decay
of
the
heat
flow
in
continents
is
often
considered
336
TERRESTRIAL
HEAT
FLOW
Average
Continent
Stable
Platform
0
20
40
60
80
Heat
flow
(mW
/m
2
)
100
to
be
noise
(erosion,
tectonomagmatic
heating)
while
it
is
the
main
signal
in
oceanic
areas
(the
plate
creation
process
itself).
Histograms
of
heat
flow
data
are
far
from
Gaussian
(Fig-
ure
26.3)
so
median
values
are
often
tabulated.
The
uncorrected
continental
and
oceanic
heat
flow
histograms
have
similar
means
and
medi-
ans.
Nevertheless,
the
mean
heat
flux
through
the
seafloor
may
be
substantially
higher
than
that
through
continents
.
It
may
be
just
coin-
cidental
that
the
most
frequent
values
and
means
of
the
two
datasets
are
so
close
to
each
other.
The
non-uniform
spatial
distributions
of
both
continental
and
oceanic
data
are
partly
the
result
of
an
emphasis
on
geothermally
active
and
other
anomalous
areas,
and
sedimentary
basins.
The
continental
histogram
is
more
peaked
than
the
oceanic
one.
This
is
expected
if
vigorous
hydrothermal
circulation
occurs
on
the
seafloor.
120
Number
4405
140
Continental
heat
Histogram
comparisons
can
be
misleading.
Data
are
often
edited
to
eliminate
unusual
environ-
ments,
or
to
force
agreement
with
some
the-
oretical
expectation.
This
is
quite
common
in
geochemistry;
the
impressive
chemical
unifor-
mity
of
MORB
is
partially
the
result
of
avoiding
anomalous
areas,
and
removing
data
thought
to
be
influenced
by
plumes.
Oceanic
heat
flow
and
bathymetry
is likewise
biased
by
ignoring
or
elim-
inating
data
thought
to
be
influenced
by
hotspots.
Unbiased
sampling
of
a
heterogenous
popu
l
ation
requires
that
sampling
be
as
uniform
as
possi-
ble
in
order
that
statistics
can
be
done
.
One
can-
not
test
a
hypothesis
if
a
hypothesis
was
used
to
select
and
prune
the
data.
Means
and
stan-
dard
deviations
have
no
meaning
if
a
hypothesis-
dependent
filtering
of
the
data
has
taken
place
prior
to
the
application
of
the
statistics.
In
spite
of
data
processing
and
data
sel
ection,
regions
that
have
been
designated
as
hotspots
appear
not