Heat-producing crust regulation of subsurface temperatures: A stochastic model re-evaluation of the geothermal potential in southwestern Queensland, Australia

Abstract

A large subsurface, elevated temperature anomaly is well documented in Central Australia. High heat producing granites (HHPGs) intersected by drilling at Innamincka are often assumed to be the dominant cause of the elevated subsurface temperatures, although their presence in other parts of the temperature anomaly has not been confirmed. Geological controls on the temperature anomaly remain poorly understood. Additionally, methods previously used to predict temperature at 5 km depth in this area are simplistic and possibly do not give an accurate representation of the true distribution and magnitude of the temperature anomaly. Here we re-evaluate the geological controls on geothermal potential in the Queensland part of the temperature anomaly using a stochastic thermal model. The results illustrate that the temperature distribution is most sensitive to the thermal conductivity structure of the top 5 km. Furthermore, the results indicate the presence of silicic crust enriched in heat producing elements between 5 and 40 km.

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Geothermics
51
(2014)
182–200
Contents
lists
available
at
ScienceDirect
Geothermics
jo
ur
nal
homep
age:
www.elsevier.com/locate/geothermics
Heat-producing
crust
regulation
of
subsurface
temperatures:
A
stochastic
model
re-evaluation
of
the
geothermal
potential
in
southwestern
Queensland,
Australia
C.
Siégela,b,∗,
C.E.
Schranka,c,
S.E.
Bryana,b,
G.R.
Beardsmored,
D.J.
Purdye
aSchool
of
Earth,
Environmental
and
Biological
Sciences,
Queensland
University
of
Technology,
Gardens
Point
Campus,
2
George
Street,
Brisbane,
QLD
4001,
Australia
bQueensland
Geothermal
Energy
Centre
of
Excellence,
The
University
of
Queensland,
St
Lucia,
QLD
4072,
Australia
cSchool
of
Earth
and
Environment,
The
University
of
Western
Australia,
35
Stirling
Highway,
Crawley,
WA
6009,
Australia
dHot
Dry
Rocks
Pty
Ltd,
36
Garden
Street,
South
Yarra,
VIC
3141,
Australia
eGeological
Survey
of
Queensland,
Level
10,
119
Charlotte
Street,
Brisbane,
QLD
4000,
Australia
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
22
August
2013
Accepted
14
January
2014
Keywords:
Geothermal
Australia
Heat
flow
Thermal
conductivity
Stochastic
modelling
Inversion
modelling
a
b
s
t
r
a
c
t
A
large
subsurface,
elevated
temperature
anomaly
is
well
documented
in
Central
Australia.
High
heat
producing
granites
(HHPGs)
intersected
by
drilling
at
Innamincka
are
often
assumed
to
be
the
dominant
cause
of
the
elevated
subsurface
temperatures,
although
their
presence
in
other
parts
of
the
tempera-
ture
anomaly
has
not
been
confirmed.
Geological
controls
on
the
temperature
anomaly
remain
poorly
understood.
Additionally,
methods
previously
used
to
predict
temperature
at
5
km
depth
in
this
area
are
simplistic
and
possibly
do
not
give
an
accurate
representation
of
the
true
distribution
and
magnitude
of
the
temperature
anomaly.
Here
we
re-evaluate
the
geological
controls
on
geothermal
potential
in
the
Queensland
part
of
the
temperature
anomaly
using
a
stochastic
thermal
model.
The
results
illustrate
that
the
temperature
distribution
is
most
sensitive
to
the
thermal
conductivity
structure
of
the
top
5
km.
Fur-
thermore,
the
results
indicate
the
presence
of
silicic
crust
enriched
in
heat
producing
elements
between
5
and
40
km.
©
2014
Elsevier
Ltd.
All
rights
reserved.
1.
Introduction
Elevated
geothermal
gradients
have
long
been
recognised
in
the
Great
Artesian
Basin
(GAB)
of
central-eastern
Australia
(Polak
and
Horsfall,
1979,
and
references
therein)
(Fig.
1a).
More
recently,
a
regional
map
estimating
the
temperature
at
5
km
depth
has
been
generated
(Oztemp)
(Somerville
et
al.,
1994;
Chopra
and
Holgate,
2005;
Gerner
and
Holgate,
2010)
as
a
basis
for
assessing
the
geothermal
energy
potential
in
Australia.
The
depth
of
5
km
was
chosen
as
a
cut-off
for
the
economic
extraction
of
geothermal
energy
(Chopra
and
Holgate,
2005).
The
map
suggests
the
pres-
ence
of
a
large
(ca.
800,000
km2)
subsurface
temperature
anomaly
(Oztemp
anomaly)
across
central
Australia
and
SW
Queensland
(Fig.
1b),
with
estimated
temperatures
greater
than
235 ◦C
at
5
km
depth,
ca.
85 ◦C
(i.e.,
ca.
57%)
higher
than
predicted
from
the
∗Corresponding
author
at:
School
of
Earth,
Environmental
and
Biological
Sci-
ences,
Queensland
University
of
Technology,
Gardens
Point
Campus,
2
George
Street,
Brisbane,
QLD
4001,
Australia.
Tel.:
+61
449807464.
E-mail
addresses:
c.siegel@qut.edu.au,
coralie
s@hotmail.fr
(C.
Siégel).
average
geothermal
gradient
for
the
upper
continental
crust
(Somerville
et
al.,
1994;
Chopra
and
Holgate,
2005).
It
is
estimated
that
rocks
in
the
Cooper
Basin
region,
shal-
lower
than
5
km,
hold
ca.
7.8
million
PJ
available
heat
(Somerville
et
al.,
1994;
Bahadori
et
al.,
2013)
(Fig.
1b).
Across
the
continent,
Geoscience
Australia
has
estimated
that
the
crust
shallower
than
5
km
contains
thermal
energy
equivalent
to
2,500,000
years
worth
of
the
total
2004–2005
energy
consumption
in
Australia
(Budd
et
al.,
2006).
Accordingly,
geothermal
exploration
and
development
attracted
multi-billion
dollar
work
commitments
from
industry
in
Australia,
with
more
than
400
geothermal
tenements
so
far
granted
since
2001
(Dowd
et
al.,
2011).
To
date,
generation
of
electricity
from
geothermal
energy
in
cen-
tral
Australia
and
SW
Queensland
is
limited
to
the
80
kWe
(net)
Birdsville
geothermal
plant
(Bahadori
et
al.,
2013)
operating
since
1992,
a
20
kWe
plant
that
operated
on
Mulka
cattle
station
in
South
Australia
(Lund
and
Boyd,
1999)
for
a
short
time
from
1987,
and
a
1
MWe
pilot
plant
commissioned
by
Geodynamics
Ltd
at
Innam-
incka
in
May
2013.
Recently,
larger-scale
projects
have
focused
on
Engineered
Geothermal
System
(EGS)
development
at
Innam-
incka,
South
Australia
(Fig.
1b),
where
high
heat
producing
granites
http://dx.doi.org/10.1016/j.geothermics.2014.01.005
0375-6505/©
2014
Elsevier
Ltd.
All
rights
reserved.

Author's personal copy
C.
Siégel
et
al.
/
Geothermics
51
(2014)
182–200
183
Fig.
1.
Summary
of
the
geological
features
of
the
area
of
study
in
SW
Queensland.
The
scale
is
the
same
for
(b–d).
(a)
Outline
of
the
study
area;
GAB
is
Great
Artesian
Basin,
WA
is
West
Australia,
SA
is
South
Australia,
QLD
is
Queensland,
NSW
is
New
South
Wales,
VIC
is
Victoria,
NT
is
Northern
Territory
and
ACT
is
Australian
Capital
territory;
(b)
Oztemp
map
with
towns
and
locations
referred
to
in
text;
after
Holgate
and
Gerner
(2011);
SA
and
QLD
indicates
the
state
border
between
South
Australia
and
Queensland.
(c)
Nature
of
the
intersected
basement
using
data
from
Brown
et
al.
(2012)
for
Queensland
and
available
information
from
https://sarig.pir.sa.gov.au/Map
for
South
Australia;
(d)
depth
to
basement
(modified
after
Purdy
et
al.,
2013)
and
location
of
new
data
generated
in
this
study.
Purple
crosses
indicate
the
location
for
new
thermal
conductivity
and
heat
production
values
and
grey
points
correspond
to
new
temperature
and
heat
flow
data
at
5
km
depth.
(HHPGs)
are
intersected
at
3–5
km
depth.
In
particular,
heat
flow
studies
indicate
that
the
high
temperatures
observed
at
Innam-
incka
are
related
to
release
of
heat
generated
by
radioactive
decay
within
HHPGs
at
depth,
below
a
thermally
insulating
sedimen-
tary
cover
(Middleton,
1979;
Gallagher,
1987;
Beardsmore,
2004).
It
has
thus
been
similarly
predicted
that
anomalously
high
tem-
peratures
in
SW
Queensland
(Fig.
1b)
also
result
from
subsurface
HHPGs
(e.g.,
Chopra
and
Holgate,
2005;
Draper
and
D’Arcy,
2006).
However,
heat
production
values
estimated
from
limited
whole-
rock
chemical
data
for
the
few
granites
(Champion
et
al.,
2007)
intersected
in
petroleum
wells
to
depths
of
ca.
3
km
are
substan-
tially
lower
(1.6–4.2
!W
m−3)
than
those
estimated
for
granites
at
Innamincka
(9.7
!W
m−3for
the
Big
Lake
Suite
Granite;
Middleton,
1979).
Given
the
apparent
absence
of
HHPGs
(at
<5
km
depth)
beneath
large
tracts
of
the
Oztemp
anomaly,
an
important
issue
for
geother-
mal
energy
assessment
across
this
region
is
a
critical
appraisal
of
the
quality
of
data
upon
which
the
temperature
map
was
based.
Important
issues
with
the
current
Oztemp
map
are
the
use
of:
(1)
linear
extrapolations
of
borehole
temperature
measurements,
as
this
may
introduce
errors
because
a
conductive
steady
state
temperature
profile
of
continental
crust
must
be
non-linear
in
the
presence
of
radiogenic
material;
(2)
unreliable,
shallow
(e.g.,
<500
m)
temperature
measurements
extrapolated
to
5
km
depth,
because
shallow
temperatures
could
be
affected
by
past
climatic
variations
(e.g.,
Bauer
and
Chapman,
1986);
and
(3)
tempera-
ture
extrapolations
without
considering
material
properties
of
the
intersected
lithologic
formations,
in
particular,
thermal
conductiv-
ity
and
heat
production
of
the
rocks
(e.g.,
Chapman,
1986).
The
availability
of
heat
flow
data
in
Australia
and
across
the
GAB
are
limited
with
only
two
heat
flow
values
reported
for
the
Queens-
land
part
of
the
Oztemp
anomaly
(Gallagher,
1987;
Goutorbe
et
al.,
2008).
Additional
heat
flow
data
have
been
measured
at
the
continental
scale
using
a
linear
relationship
between
the
silica
geothermometer
and
heat
flow
(Pirlo,
2002).
However,
the
distribu-
tion
of
these
values
is
heterogeneous
across
SW
Queensland.
Other
heat
flow
determinations
across
the
Oztemp
anomaly
are
restricted
to
the
South
Australian
part
of
the
Cooper
Basin
(Beardsmore,
2004;
Meixner
et
al.,
2012).
Consequently,
the
foundations
of
the
Oztemp
anomaly
for
SW
Queensland
are
based
on
sparse
surface
heat
flow
data
and
currently,
little
evidence
for
buried
high
heat
producing
granitic
rocks
at
depth.

Author's personal copy
184
C.
Siégel
et
al.
/
Geothermics
51
(2014)
182–200
Fig.
2.
Available
information
on
basement
structure.
Image
in
the
bottom
hand
left
corner
is
the
C-seismic
horizon,
corresponding
to
the
top
of
the
Early-Cretaceous
Cadna-Owie
formation
(after
Fig.
5
of
Radke,
2009)
of
the
Great
Artesian
Basin
(Cook
et
al.,
2013).
Black
lines
indicate
the
location
of
deep
crustal
seismic
transects.
Blue
contours
correspond
to
Tertiary
intraplate
volcanic
fields
where
xenoliths
were
found
(after
O’Reilly
and
Griffin,
1990).
Note
that
xenoliths
are
only
located
on
the
eastern
side
of
the
study
area.
Information
on
the
basement
structure
of
the
study
area
is
derived
primarily
from
deep
crustal
seismic
transects
and
seismic
horizons
(e.g.,
C-seismic
horizon
depicted
in
the
bottom
hand
left
corner
image).
(For
inter-
pretation
of
the
references
to
color
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)
The
aim
of
this
paper
is
to
provide
an
improved
understanding
of
the
nature
and
origin
of
the
thermal
regime
in
SW
Queensland
as
well
as
a
re-assessment
of
the
geothermal
potential,
both
of
which
are
crucial
for
the
development
of
geothermal
energy
and
to
reduce
exploration
and
development
costs.
This
study
provides
163
new
heat
flow
data
and
temperature
estimates
at
5
km
depth.
A
new
temperature
map
at
5
km
depth
is
presented
to
serve
as
a
guide
for
more
focused
geothermal
exploration
studies.
This
map
is
based
on
stochastic
thermal
modelling,
which
permits
a
quantification
of
uncertainties
of
our
estimates,
and
includes
new
thermal
conduc-
tivity
and
heat
production
measurements
on
subsurface
granitic
rocks.
2.
Geological
background
A
large
part
of
the
Oztemp
anomaly
correlates
with
the
extent
of
the
Thomson
Orogen;
a
poorly
understood
tectonic
element
in
east-
ern
Australia
that
separates
Precambrian
cratonic
regions
of
central
Australia
from
Phanerozoic
fold
belts
developed
along
the
east-
ern
margin
(Fig.
1c)
(see
recent
reviews
Fergusson
and
Henderson,
2013;
Purdy
et
al.,
2013).
Through
much
of
its
extent,
the
Thomson
Orogen
is
concealed
by
thick
sedimentary
cover
(Fig.
1d)
and
as
a
result,
tectonic
interpretations
are
still
debated.
In
particular,
the
nature
of
the
underlying
lower
crust
is
disputed
with
some
authors
proposing
it
is
oceanic
crust
(Harrington,
1974;
Glen
et
al.,
2013),
whereas
others
have
argued
that
it
is
Precambrian
(Henderson,
1980;
Finlayson,
1990)
and
silicic
continental
crust
(O’Reilly
and
Griffin,
1990).
Information
on
the
nature
of
the
Thomson
Orogen
basement
derives
from
drilling
(Fig.
1c),
outcrops
located
outside
the
Oztemp
anomaly
in
the
Anakie
Inlier
and
Charter
Towers
area
(e.g.,
Fergusson
and
Henderson,
2013;
Purdy
et
al.,
2013),
and
from
geophysical
methods
such
as
gravity,
magnetic
and
deep
crustal
seismic
transects
(Fig.
2).
Across
the
Oztemp
anomaly,
ca.
780
drill
holes
intersect
Thomson
orogen-related
rocks
at
1–4
km
depth
(Brown
et
al.,
2012)
(Fig.
1c).
Information
from
these
holes
suggests
that
the
uppermost
structural
levels
are
primarily
composed
of
low-grade
metasedimentary
rocks,
lesser
granitic
intrusions
(ca.
52
intersections)
and
volcanic
rocks
(ca.
15
intersections).
The
thick-
ness
of
the
lower
crust
is
revealed
by
deep
crustal
seismic
transects
that
indicate
the
Moho
is
located
at
ca.
40
km
depth
(Finlayson
et
al.,
1990).
Along
the
Brisbane–Eromanga
transect
(a
1100
km
long
E-W
geophysical
transect
in
southern
Queensland;
Fig.
2),
the
crust
is
considered
to
be
more
silicic
to
the
west
based
on
low
magnetisation
and
low
Bouguer
anomalies
(O’Reilly
and
Griffin,
1990).
Additional
information
on
the
nature
of
the
crust
derives
from
extrapolation
of
xenolith
studies
in
Eastern
Australia
(O’Reilly
and
Griffin,
1990)
(Fig.
2)
and
an
exposed
crustal
profile
in
the
Arunta
and
Musgrave
Inliers
of
central
Australia
(Sandiford
et
al.,
2001).
Within
this
exposed
crustal
profile,
the
abundance
of
high
heat
producing
rocks
varies
with
depth.
Importantly,
the
crust
between
6
and
10
km
depth
is
highly
enriched
in
heat
produc-
ing
elements.
For
example,
the
Teapot
Granite
Complex
has
an
estimated
heat
generation
of
5.9
±
1.7
!W
m−3(Sandiford
et
al.,
2001).
The
lack
of
recent
magmatic
activity
and
seismicity
across
the
Oztemp
anomaly
suggests
that
the
area
is
tectonically
stable.
The
youngest
known
intrusive
rocks
are
the
Permo-Carboniferous
Big
Lake
Suite
granodiorites
at
Innamincka
(Gatehouse
et
al.,
1995;
Marshall,
2013).
Additionally,
only
23
earthquakes
were
detected
in
the
Queensland
part
of
the
Oztemp
anomaly
during
the
last
cen-
tury
and
of
those,
only
two
are
of
magnitude
>4
(GA
Earthquake
Database
http://www.ga.gov.au/earthquakes/searchQuake.do).
Deep
HHPGs
serve
as
a
potential
reservoir
for
EGS
development.
Consequently,
if
appropriate
drilling
targets
are
to
be
identified,
it
is
crucial
to
understand
the
distribution
and
character
of
the
sub-
surface
granitic
rocks.
Across
the
Queensland
part
of
the
Oztemp
anomaly,
the
52
granitic
intrusions
intersected
in
drill
holes
are
distributed
heterogeneously
(Fig.
1c)
and
vary
in
composition
from
syenogranite
to
monzogranite,
from
I
to
S-type,
and
from
fresh
(LOL
Stormhill
1)
to
strongly
altered
(DIO
Wolgolla
1)
(Murray,
1994a,b).
Limited
data
indicate
low
heat
production
(<5
!W
m−3)
(Champion
et
al.,
2007)
and
crystallisation
ages
from
400
to
860
Ma,
with
two
clusters
at
ca.
420–430
Ma
SE
of
Innamincka
and
ca.
470
Ma
near
Longreach
(Murray,
1994a,b
and
references
therein;
Draper,
2006).
In
contrast,
the
adjacent
Big
Lake
Suite
intrusions
that
are
the
focus
of
EGS
development
in
Australia
have
emplacement
ages
of
ca.
310–330
Ma
(Gatehouse
et
al.,
1995;
Marshall,
2013)
and
higher
heat
production
values
(ca.
7–9.7
!W
m−3)
(Middleton,
1979).
East
of
the
Oztemp
anomaly,
in
the
Roma
Shelf
area
(north
and
south
of
Roma,
Fig.
1b
and
c)
intrusive
rocks
are
extensive
below
the
sedi-
mentary
cover.
These
are
known
as
the
‘Roma
Granites’
and
have
emplacement
ages
ranging
from
320
to
350
Ma
(Murray,
1994a,b)
but
lack
the
geochemical
data
needed
to
calculate
heat
production
values.
High
thermal
resistance
due
to
thick
and/or
low
conduc-
tive
sedimentary
blanketing
can
effectively
trap
heat
(e.g.,
thick
formations
enriched
in
low
conductive
materials
like
coal
and
shale)
(Mildren
and
Sandiford,
1995),
and
is
thus
another
key
parameter
for
EGS
exploration.
In
central
western
Queensland,
episodes
of
repeated
basin
subsidence
and
sediment
accumula-
tion
have
occurred
since
the
early
Paleozoic,
resulting
in
a
series
of
stacked
basins
(Fig.
3)
and
sediment
thicknesses
up
to
4
km
(Fig.
1d)
(e.g.,
west
of
Bayrick
and
beneath
the
Cooper
Basin).
Major
basin
systems
include:
(1)
the
Devonian
Adavale
Basin,
Warrabin
Trough
and
Barrolka
Trough;
(2)
the
Late
Devonian–Early
Carboniferous
Drummond
Basin;
(3)
the
mid
Carboniferous
to
mid
Triassic
Galilee
Basin;
(4)
the
early
Permian
to
mid
Triassic
Cooper
Basin;
and
(5)
the
very
extensive
Jurassic
to
Cretaceous
Eromanga
and
Surat
basins,
components
of
the
Great
Australian
Superbasin
(Cook
et
al.,
2013).

Author's personal copy
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/
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51
(2014)
182–200
185
Fig.
3.
Distribution
of
sedimentary
basins
in
SW
Queensland
that
can
provide
ther-
mal
insulator
cover
to
heat-producing
basement
rocks
(Fergusson
and
Henderson,
2013).
The
thick
solid
line
corresponds
to
the
extent
of
the
Eromanga
Basin.
(For
interpretation
of
the
references
to
color
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)
3.
Methodology
3.1.
Approach
and
limits
To
re-evaluate
the
geothermal
potential
in
western
Queensland,
heat
transfer
mechanisms
across
the
intersected
formations
must
be
evaluated.
Most
geothermal
studies
assessing
surface
heat
flow
assume
dominantly
vertical
conduction
(Ricard
and
Chanu,
2013
and
references
therein),
and
in
this
study,
we
have
adopted
this
assumption.
However,
if
thick,
permeable
sedimentary
sequences
are
present,
advection
and
convection
can
affect
heat
transfer
in
the
continental
crust
significantly,
as
shown
for
example,
in
the
Perth
Basin,
WA
(Sheldon
et
al.,
2012;
Schilling
et
al.,
2013).
Previous
studies
have
used
a
wide
range
of
methods
to
estimate
heat
flow,
depending
on
the
quality,
quantity
and
type
of
data
available.
These
include
methods
based
on
thermal
conductivity
and
temperature
gradient
measurements
(for
a
review,
see
Beardsmore
and
Cull,
2001).
While
the
most
direct
methods
to
determine
the
surface
heat
flow
are
based
on
the
product
of
thermal
conductivity
and
temper-
ature
gradient,
other
methods
such
as
inversion
methods,
assume
a
set
of
thermal
conductivity
characteristics
and
determine
a
heat
flow
value
to
minimise
error
between
the
modelled
and
observed
temperature
profiles
(Matthews,
2009;
Kirkby
and
Gerner,
2010;
Korsch
et
al.,
2011).
In
this
study
we
use
this
latter
approach.
We
used
163
wells
in
the
study
area
(ca.
1300
km
×
850
km;
Fig.
1d),
in
which
temperature,
thermal
conductivity
and
heat
pro-
duction
data
were
recorded
(refer
to
Section
3.2
for
details).
For
these
wells
a
conductive
temperature
profile
was
calculated
to
best
fit
the
observed
temperature
measurements,
using
a
one-
dimensional
inversion
model.
Subsequently,
the
temperature
was
extrapolated
to
a
depth
of
5
km
as
detailed
in
Appendix
A.
Table
1
provides
the
list
of
parameters
used
in
the
thermal
modelling.
Wells
were
selected
according
to
the
following
criteria:
(1)
geographical
location
to
provide
sufficient
spatial
coverage
for
data
interpolation
maps;
and
(2)
quantity
and
quality
of
available
information;
lithologic
descriptions
and
reliable
temperature
mea-
surements
(e.g.,
Horner
plots
and/or
including
drill
stem
tests).
Table
1
Nomenclature.
Symbol
Parameter
K
Thermal
conductivity
[W
m−1K−1]
A
Heat
production
[!
W
m−3]
T
Temperature
[◦C]
TBTemperature
at
5
km
depth
[◦C]
z
Depth
[m]
zBDepth
of
the
bottom
of
the
layer
[m]
zTDepth
equivalent
to
5
km
[m]
C1and
C2Constants
derived
from
integration
Q
Heat
flow
[mW
m−2]
QBHeat
flow
at
the
bottom
of
the
layer
[mW
m−2]
QTHeat
flow
at
5
km
depth
[mW
m−2]
!ε
Mean
squared
temperature
error
!ε%Derivative
of
the
mean
squared
temperature
error
Pj(QTj/!εj) Point
Pjwith
attribute
QTj and
!εjused
to
determine
coefficients
of
the
quadratic
function
N
Number
of
observed
temperatures
TiMeasured
temperature
at
a
given
depth
[◦C]
tiPredicted
temperature
at
a
given
depth
[◦C]
TTEstimated
temperature
at
5
km
depth
[◦C]
!TiDifference
between
measured
and
predicted
temperature
at
a
given
depth
[◦C]
KbBulk
thermal
conductivity
[W
m−1K−1]
KmMatrix
conductivity
[W
m−1K−1]
∅
Porosity
[vol%]
K
(25) Thermal
conductivity
at
25 ◦C
[W
m−1K−1]
TB∞True
formation
temperature
[◦C]
TB(t)
Temperature
at
the
bottom
of
the
hole
at
a
particular
time
[◦C]
tcCirculation
time
[s]
teTime
elapsed
since
the
fluids
circulated
[s]
C
Slope
determined
by
the
BHT
measurements
CUBulk
rock
concentration
of
Uranium
[ppm]
CTh Bulk
rock
concentration
of
Thorium
[ppm]
CK2OBulk
rock
concentration
of
Potassium
oxide
[wt%]
#
Density
[kg
m−3]
3.2.
Input
parameters
3.2.1.
Stratigraphy
The
stratigraphy
of
the
basins
must
be
taken
into
account
for
determining
the
material
properties
of
intersected
sedimen-
tary
formations.
The
stratigraphy
for
each
well
was
established
using
the
most
recent
stratigraphic
constraints
(Cook
et
al.,
2013;
Fergusson
and
Henderson,
2013;
Withnall
and
Hutton,
2013),
infor-
mation
from
well
completion
reports
and
an
unpublished
compiled
database
from
the
Geological
Survey
of
Queensland.
The
general
stratigraphy
for
each
basin
is
reported
in
Table
2.
Additional
details
for
each
well
are
available
in
Supplement
1
(also
publically
available
at
http://eprints.qut.edu.au/63373/).
3.2.2.
Thermal
conductivities
Surface
heat
flow
is
a
function
of
thermal
conductivity
(Fourier,
1822).
Thermal
conductivity
of
a
rock
depends
on
several
physical
parameters
such
as
lithology,
porosity,
pore
fluids,
temperature,
the
nature
and
proportion
of
its
constituents
and
its
microstruc-
ture
(for
a
review,
see
Clauser
and
Huenges,
1995).
The
general
range
of
thermal
conductivities
for
geomaterials
covers
about
one
order
of
magnitude,
with
values
from
ca.
0.2
W
m−1K−1for
coal
to
ca.
5.5
W
m−1K−1for
dolomite
and
quartzite
(Beardsmore
and
Cull,
2001).
Porosity
can
have
a
strong
control
on
the
thermal
conduc-
tivity
of
a
sedimentary
formation,
with
values
ranging
from
ca.
2.3
to
6
W
m−1K−1in
sandstone,
for
>25%
and
0%
porosity,
respectively
(Gallagher,
1987).
The
effect
of
temperature
on
thermal
conductiv-
ity
is
relevant
in
areas
where
the
temperature
varies
significantly
(for
most
crystalline
rocks,
a
decrease
of
ca.
10–50%
occurs
from
0◦C
to
about
300 ◦C,
Seipold,
1998).
Lithology,
porosity
and
tem-
perature
should
therefore
be
taken
into
account
when
estimating
thermal
conductivity
for
thermal
modelling.

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Table
2
Summary
of
stratigraphy
encountered
in
the
study
area,
listing
the
sedimentary
formations
for
each
basin,
their
stratigraphic
age,
approximate
thickness
range
and
estimated
and
measured
thermal
conductivities.
Formation
name Formation
age Thickness
range
(m) Estimated
thermal
conductivity
(W
m−1K−1)
naMeasured
thermal
conductivity
(W
m−1K−1)
(RSDd)
naThermal
conductivity
references
All
wells
This
study
(na=
163)
Surface
deposits
Quaternary
–
2–247
2.30
±
2.00b–
–
–
–
Tertiary
volcanics
Tertiary
–
10–44
1.73
±
0.21c–
–
–
–
Eromanga
basin
Winton
formation Late
cretaceous 16–1030 34–1166 2.78
±
0.22 3
1.48
±
0.06
(04) 2
b
Mackunda
formation
Early
cretaceous
31–1030
34–257
2.90
±
0.14
3
1.35
±
0.25
(19)
1
b
Allaru
mudstone Early
cretaceous 2–453 31–360 2.52
±
0.51 3
1.39
±
0.32
(23) 10
a;
b;
d;
f
Toolebuc
formation
Early
cretaceous
1–23
1–173
2.48
±
0.51
3
1.06
±
0.29
(27)
4
e;
f
Walumbilla
formation Early
cretaceous 0.1–1552 23–499 2.51
±
0.46 7
1.43
±
0.42
(29) 22
a;
d;
e;
f
Cadna-Owie
formation
Early
cretaceous
3–1090
26–267
3.03
±
0.33
4
1.86
±
0.23
(12)
6
a;
b;
c
Hooray
sandstone Late
jurassic–early
cretaceous
13–462 38–211 3.10
±
0.42 4
2.59
±
0.74
(29) 2
e;
d
Westbourne
formation
Late
jurassic
4–3273
3–382
3.31
±
0.66
7
2.92
±
0.91
(31)
10
b;
c;
e;
d
Adori
sandstone Late
jurassic 2–126 5–119 3.48
±
0.91 4
4.63
±
0.35
(8)
2
b
Birkhead
formation
Middle
jurassic
3–451
10–148
2.28
±
0.68
4
3.90
±
1.28
(33)
9
a;
b
Hutton
sandstone Middle
jurassic 1–680 11–294 3.27
±
0.46 7
4.67
±
0.83
(18) 14
a;
b;
c
Poolowanna
formation
Early
jurassic
4–371
10–220
3.28
±
0.55
3
3.94
±
2.11
(54)
4
b
Precipice
sandstone
Early
jurassic
1–1447
4–122
3.94
±
1.38
3
–
–
–
Surat
basin
Griman
creek
formation
Early
cretaceous
13–397
167–307
2.78
±
0.22
3
–
–
–
Surat
siltstone
Early
cretaceous
14–391
97–155
2.90
±
0.07
3
–
–
–
Walumbilla
formation
Early
cretaceous
0.1–1552
23–499
2.51
±
0.46
7
–
–
–
Bungil
formation
Early
cretaceous
1–702
35–287
3.25
±
0.29
3
–
–
–
Mooga
sandstone Late
jurassic–early
cretaceous
5–902 33–310 3.33
±
0.29
3
–
–
–
Orallo
formation
Late
jurassic
4–385
101–266
3.40
±
0.18
3
1.99
±
0.16
(08)
7
e
Gubberamunda
sandstone
Late
jurassic
7–488
35–259
3.65
±
0.06
3
2.58
±
0.17
(07)
1
e
Westbourne
formation
Late
jurassic
4–3273
3–382
3.05
±
0.24
7
–
–
–
Springbok
sandstone
Middle
jurassic
2–338
25–112
3.56
±
0.24
3
–
–
–
Walloon
coal
measures
Middle
jurassic
31–861
114–446
2.82
±
0.16
3
–
–
–
Eurombah
formation Middle
jurassic 3–337 25–79
3.49
±
0.11
3
–
–
–
Hutton
sandstone
Middle
jurassic
1–680
11–294
3.30
±
0.21
7
4.67
±
0.83
(18)
14
a;
b;
c
Evergreen
formation
–
upper
unit
Early
jurassic
10–271
15–181
2.85
±
0.13
3
–
–
–
Boxvale
sandstone
Early
jurassic
1–129
1–81
3.26
±
0.68
3
–
–
–
Evergreen
formation
–
lower
unit Early
jurassic 2–127 19–195 3.16
±
0.13 3
–
–
–
Precipice
sandstone
Late
triassic–early
jurassic
1–1447
4–122
3.94
±
1.38
3
–
–
–
Cooper
basin
Nappamerri
group
Late
permian–middle
triassic
3–494
23–460
3.11
±
0.18
3
3.42
±
1.11
(32)
9
a;
b;
c
Gidgealpa
group
Toolachee
formation Middle–late
permian
3–367 8–145 2.70
±
0.74 3
2.93
±
1.32
(45)
11
a;
b;
c
Daralingie
formation
Early
permian
6–96
8–96
2.42
±
0.27
3
2.80
±
1.19
(43)
8
b;
c
Roseneath
shale
Early–middle
permian
2–183
3–98
2.45
±
0.46
3
1.90
±
0.40
(21)
4
a;
b;
c

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187
Epsilon
formation
Early
permian
2–265
5–90
2.46
±
0.72
3
2.44
±
1.55
(64)
5
a;
b;
c
Murteree
shale
Early
permian
3–521
4–59
2.63
±
1.00
3
2.59
±
0.85
(33)
4
a;
b
Patchawarra
formation
Early
permian
1–404
3–383
2.61
±
0.91
3
3.62
±
1.61
(44)
11
a;
b;
c
Tirrawarra
sandstone
Early
permian
31–88
33–40
5.14
±
0.80
3
3.95
±
1.07
(27)
6
b;
c
Merrimelia
formation
Early
permian
9–201
9–70
3.21
±
0.58
3
3.60
±
0.86
(24)
6
a;
b;
c
Galilee
basin
Moolayember
formation
Late
triassic
2–1063
9–602
2.94
±
0.59
4
–
–
–
Warang
sandstone
Early–middle
triassic
394
149
3.57
±
1.35
3
–
–
–
Betts
creek
beds
Late
permian
21–215
111–253
2.65
±
0.96
3
–
–
–
Clematis
sandstone
Early–middle
triassic
4–581
1–190
3.45
±
0.32
4
–
–
–
Rewan
group
Late
permian–early
triassic
2–1302
43–591
2.87
±
0.15
3
–
–
–
Bandanna
formation
Late
permian
1–1036
12–818
2.88
±
0.54
4
–
–
–
Back
creek
group
Black
alley
shale
Late
permian
5–373
11–191
3.43
±
1.00
3
1.73
±
0.23
(13) 2g
Peawaddy
formation
Late
permian
5–349
21–188
3.03
±
0.25
3
Catherine
sandstone
Middle
permian
2–178
27–131
3.88
±
0.90
3
Ingelara
formation
Late
permian
10–309
32–173
2.96
±
0.25
3
Freitag
formation
Late
permian
4–214
17–127
3.76
±
1.04
3
Aldebaran
formation
Early–middle
permian
11–908
183–1086
3.98
±
0.92
3
Cattle
creek
formation
Early
permian
17–891
85-829
3.11
±
0.22
3
–
–
–
Reids
dome
beds
Early
permian
63–1263
26–667
2.80
±
0.49
3
–
–
–
Colinlea
sandstone
Late
permian
2–966
13–91
3.72
±
0.15
3
–
–
–
Aramac
coal
measures
Early
permian
18–333
18–232
3.29
±
0.44
3
–
–
–
Jochmus
formation
–
upper
unit
Late
carboniferous–early
permian
287
17–319
3.71
±
1.04
4
–
–
–
Eddie
tuff
member
Early
permian
85–125
21–125
3.38
±
1.41
3
–
–
–
Jochmus
formation
–
lower
unit
Late
carboniferous–early
permian
341–400
12–341
3.06
±
0.33
3
–
–
–
Jericho
formation
–
upper
unit
Late
carboniferous–early
permian
200
63–400
2.98
±
0.57
3
–
–
–
Oakleigh
siltstone
member
Late
carboniferous–early
permian
46–167
69–167
2.62
±
0.79
3
–
–
–
Jericho
formation
–
lower
unit
Late
carboniferous–early
permian
–
126–386
3.03
±
0.48
3
–
–
–
Lake
Galilee
sandstone
Late
carboniferous–early
permian
287
85–287
4.21
±
0.53
3
–
–
–
Drummond
basin
Ducabrook
formation
Early
carboniferous
12–43
1025
3.59
1
–
–
–

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188
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/
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(2014)
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Table
2
(Continued)
Formation
name Formation
age Thickness
range
(m) Estimated
thermal
conductivity
(W
m−1K−1)
naMeasured
thermal
conductivity
(W
m−1K−1)
(RSDd)
naThermal
conductivity
references
All
wells
This
study
(na=
163)
Natal
formation Early
carboniferous 206–384 385
2.85 1
–
–
–
Bulliwallah
formation
Early
carboniferous
43–657
656
3.02
1
–
–
–
Star
of
hope
formation Early
carboniferous 377–890 890
3.24 1
–
–
–
Raymond
formation
Early
carboniferous
264–417
417
3.05
1
–
–
–
Scartwater
formation Early
carboniferous 441
442
3.08 1
–
–
–
Saint
annes
formation
Late
devonian–early
carboniferous
214
214
3.47
1
–
–
–
Ukalunka
beds Early
devonian –
395
3.04
1
–
–
–
Adavale
basin
Buckabie
formation
Late
devonian–early
carboniferous
37–1743
8–1251
3.21
±
0.17
3
–
–
–
Etonvale
formation
Middle
devonian
12–704
5–415
3.52
±
1.04
3
–
–
–
Cooladdi
formation
Middle
devonian
6–64
16
4.15
±
0.19
3
–
–
–
Lissoy
sandstone
Middle
devonian
31–53
44
3.90
±
0.86
3
–
–
–
Bury
limestone Middle
devonian 217–328 253–301 3.01
±
0.63 3
–
–
–
Log
creek
formation
Middle
devonian
59–263
317–657
3.28
±
0.36
3
–
–
–
Georgina
basin
Toko
group
Ordovician
–
220–1190
3.84
±
0.70
3
–
–
–
Cockroach
group
Late
cambrian–early
ordovician
–
146–1135
4.03
±
0.46
3
–
–
–
Narpa
group
Early–late
cambrian
–
209–1283
3.19
±
0.78
3
–
–
–
Shadow
group
Middle
cambrian–proterozoic
–
7–513
3.57
±
0.57
3
–
–
–
a:
Gallagher
(1987);
b:
Hot
Dry
Rocks
Pty
Ltd,
G.E.C.
(2011);
c:
Weber
and
Kirkby
(2011);
d:
Brown
et
al.
(2012);
e:
Faulkner
et
al.
(2012);
f:
Fitzell
et
al.
(2012);
g:
Troup
et
al.
(2012).
an
is
the
number
of
samples.
bSurface
deposits
are
considered
as
typical
sediments
(from
Beardsmore
and
Cull,
2001;
refer
to
Electronic
Appendix
A).
cTertiary
volcanics
are
considered
as
basalt
(from
Beardsmore
and
Cull,
2001;
refer
to
Electronic
Appendix
A).
dRSD
is
relative
standard
deviation.

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(2014)
182–200
189
To
limit
the
uncertainty
of
thermal
conductivity
for
a
particular
formation,
thermal
conductivity
measurements
of
representative
samples
are
desirable.
In
general,
thermal
conductivity
measure-
ments
are
preferred
within
single
wells
to
determine
the
surface
heat
flow.
Samples
are
selected
for
different
lithologies
within
the
section
and
used
in
association
with
knowledge
of
the
rela-
tive
percentage
of
those
lithologies.
However,
the
selection
of
a
representative
sample
can
be
difficult
due
to
large
vertical
litho-
logical
variations
within
some
formations,
and
because
not
all
lithologies
within
a
formation
have
always
been
sampled
(Meixner
et
al.,
2012).
A
review
of
publically
available
data
for
the
studied
area
indicates
a
generally
large
standard
deviation
for
the
measured
thermal
conductivity
(Table
2).
For
example,
among
25
measured
average
thermal
conductivity
values,
9
have
a
relative
standard
deviation
>30%,
with
a
maximum
of
64%
for
the
Early
Permian
Epsilon
Formation
(Cooper
Basin).
Additionally,
thermal
conductiv-
ity
measurements
are
not
available
for
all
sedimentary
formations
encountered
in
SW
Queensland.
Available
thermal
conductivity
measurements
are
concentrated
for
formations
within
the
Ero-
manga
and
Cooper
basins,
but
data
are
sparse
for
the
Surat
basin,
and
none
have
been
reported
from
the
Galilee,
Drummond,
Adavale
and
Georgina
basins.
The
available
measurements
are
thus
not
nec-
essarily
representative
(Meixner
et
al.,
2012).
Our
study
is
at
a
regional
scale
and
therefore
it
is
desirable
to
use
representative
thermal
conductivities
for
each
formation.
Thermal
conductivities
were
estimated
for
all
formations
encoun-
tered
in
this
study,
using
an
average
thermal
conductivity
for
a
particular
lithology,
correcting
for
porosity
and
saturation
when
information
is
available
and
also
correcting
for
temperature.
Meth-
ods
to
estimate
the
average
thermal
conductivity
of
a
formation
include
the
use
of:
(1)
geophysical
logs
(Goutorbe
et
al.,
2006);
(2)
a
compaction
model
based
on
the
concept
of
loss
of
porosity
with
depth
(Yorath
and
Hyndman,
1983);
and
(3)
lithologic
descriptions
and
applying
corrections
for
temperature,
porosity
and
the
nature
of
the
saturants
(Beardsmore,
2004).
In
this
study,
we
used
the
approach
of
Beardsmore
(2004).
To
account
for
lithologic
variations
within
a
sedimentary
formation,
detailed
lithologic
descriptions
(based
on
reports
of
ditch
cutting
and
core
compositions)
for
three
wells
were
used
to
estimate
an
arithmetic
mean
thermal
conduc-
tivity
(i.e.,
an
upper-bound
estimate,
e.g.,
Maze
and
Wagner,
2009)
and
a
standard
deviation.
For
formations
where
lithologic
propor-
tions
where
reported
in
comparative
terms,
we
used
the
following
to
convert
to
percentage:
“dominant”
=
80%;
“minor”
=
20%;
“occa-
sional”
or
“grading”
or
“contains”
=
10%;
“very
minor”
=
5%,
“rare”
or
“traces”
=
1%
and
“interbedded”
=
equal
proportions
(Beardsmore,
2004).
The
effect
of
porosity
and
volumetric
percentage
of
the
nature
of
the
saturants
(oil,
gas,
of
water)
on
the
bulk
thermal
con-
ductivity,
when
available,
were
corrected
using
the
geometric
mean
model
(Eq.
(1);
Gallagher,
1987).
Kb=
(Km)1−∅(Ks)∅,
(1)
where
Kbis
the
bulk
thermal
conductivity,
Kmthe
matrix
conduc-
tivity
and
∅
is
the
porosity.
The
matrix
conductivities
were
taken
from
Beardsmore
and
Cull
(2001).
In
cases
where
no
porosity
information
was
available,
the
thermal
conductivity
was
estimated
using
average
lithologic
values
(Beardsmore
and
Cull,
2001).
Where
the
nature
of
the
saturants
was
unknown,
the
formations
were
assumed
to
be
100%
water
saturated.
Once
a
mean
thermal
conductivity
was
estimated
for
a
for-
mation,
it
was
subsequently
corrected
for
temperature.
Several
empirical
relationships
have
been
proposed
for
the
temperature
dependence
of
thermal
conductivity
(for
a
review,
see
Clauser
and
Huenges,
1995).
The
empirical
relationship
proposed
by
Birch
and
Clark
(1940)
was
successfully
tested
by
Sass
et
al.
(1992)
on
an
independent
dataset.
This
correction
was
adopted
here:
K(T)
=K(0)
1.007
+
T(0.0036
−
(0.0072/K(0))),
(2)
where:
K(0)
=
K(25)[1.007
+
25(0.0037
−
(0.0074/K(25)))].
The
temperature
(T)
for
the
mean
depth
of
the
sedimen-
tary
formation
interval
was
determined
by
linear
interpolation
of
all
reliable
temperature
measurements
from
each
well.
Further
details
on
the
estimation
of
thermal
conductivities
are
available
in
Supplements
1
and
2
(also
publically
available
at
http://eprints.qut.edu.au/63373/).
Eight
new
thermal
conductivity
measurements
on
granitic
rock
sampled
from
drill
cores
were
performed
for
this
study
and
are
reported
in
Table
3
and
discussed
in
Section
4.2.
For
each
sample,
two
or
three
thermal
conductivity
measurements
were
undertaken
at
room
temperature
(25 ◦C)
along
the
core
axis
of
each
sample
using
a
steady
state
divided
bar
apparatus.
The
instrument
was
calibrated
for
the
range
of
thermal
conductivity
0.4–12
W
m−1K−1.
Three
cylindrical
specimens
(each
specimen
1/3
to
1/2
its
diam-
eter
in
thickness)
of
each
granitic
sample
were
cut,
ground
flat
and
polished
to
a
standardised
flatness
and
grit
(except
for
the
TEP
Jandowae
West
1
sample,
from
which
only
two
specimens
could
be
prepared).
The
specimens
were
evacuated
under
vacuum
for
a
min-
imum
of
3
h,
then
submerged
in
water
and
subsequently
returned
to
atmospheric
pressure.
Water
saturation
continued
under
atmo-
spheric
pressure
for
a
minimum
of
16
h
prior
to
the
conductivity
measurement.
Thermal
conductivity
measurements
reported
in
Table
3
correspond
to
the
harmonic
mean
(i.e.,
the
lower-bound
estimate)
and
standard
deviation
of
the
analyses
performed
on
the
2–3
measurements.
Granitic
intrusions
in
the
study
area
rarely
display
the
same
degree
of
vertical
lithologic
variation
as
sedimen-
tary
units.
They
are
typically
more
homogeneous
with
depth,
and
thus
thermal
conductivity
measurements
of
the
granitic
bodies
are
considered
regionally
representative.
3.2.3.
Temperature
Fourier’s
first
law
(1822)
shows
that
heat
flow
depends
as
much
on
the
geothermal
gradient
as
thermal
conductivity.
Temperatures
recorded
by
the
petroleum
industry
are
usually
of
two
types:
bot-
tom
hole
temperature
measurements
(BHTs)
acquired
near
the
bottom
of
the
hole
during
geophysical
logging,
and
temperature
of
the
reservoir
fluids
measured
during
drill
stem
tests
(DST).
It
is
well
recognised
that
BHTs
are
recorded
under
transient
ther-
mal
conditions.
BHTs
are
primarily
affected
by
the
cooling
effect
of
the
circulating
drilling
fluids
and
thus
generally
underestimate
the
true
formation
temperature
by
ca.
10 ◦C
(Goutorbe
et
al.,
2007).
To
estimate
the
true
formation
temperature,
a
wide-range
of
correc-
tions
have
been
proposed
(for
review,
see
Goutorbe
et
al.,
2007).
The
Horner
correction
method
is
the
most
utilised
technique
(Kutasov
and
Eppelbaum,
2009
and
references
therein)
and
has
been
adopted
here
to
correct
BHT
measurements
in
the
study
area.
The
Horner
correction
method
requires
the
use
of
at
least
two,
but
ideally
three
or
more,
BHT
measurements
at
similar
depth
and
different
shut-in
times,
i.e.,
at
a
different
time
after
the
circulation
of
the
fluids.
A
summary
of
this
method
is
available
from
Chapman
et
al.
(1984).
DST
temperatures
are
generally
more
reliable,
less
variable
and
require
no
specific
correction
(Förster
et
al.,
1997).
DSTs
record
the
temperature
of
the
fluids
extracted
from
the
walls
of
the
borehole.
They
are
considered
to
be
at
equilibrium
with
the
surrounding
rocks
and
represent
true
formation
temperatures
(Förster
et
al.,
1997).
The
available
subsurface
temperature
measurements
in
SW
Queensland
have
been
compiled
into
the
single
Oztemp
dataset
(Holgate
and
Gerner,
2011).
Overall,
the
spatial
distribution
of
the
data
is
not
homogeneous
and
the
quality
of
individual
data
points
is
not
always
high.
The
number
of
temperature

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(2014)
182–200
Table
3
Summary
of
analysed
granites
in
this
study,
listing
their
location,
lithological
characteristics,
modal
mineralogy,
and
measured
thermal
conductivities.
Sample
Depth
(m)
Description
Modal
mineralogy
Thermal
conductivity
(W
m−1K−1)
Q
AF
Pl
Ms
Bt
Hb
DIO
Wolgolla
1
2040.4–2041.7
Altered,
leucocratic,
coarse-grained,
porphyritic,
muscovite–biotite
S-type
monzogranite
35
30
30
3
2
3.55
±
0.07
TEA
Roseneath
1
2192–2196
Pale
grey,
medium-grained,
leucocratic,
biotite–muscovite
S-type
monzogranite;
cut
by
black
veins
35
28
30
5
2
3.70
±
0.06
AOD
Budgerygar
1 1621.5–1622.4 Grey,
medium-grained,
equigranular,
hornblende–biotite
I-type
monzogranite
30
25
25
10
10
3.30
±
0.09
LOL
Stormhill
1
1552–1553
Pale
grey,
medium-grained,
equigranular,
biotite
I-type
monzogranite
30
40
25
5
3.40
±
0.04
AOP
Balfour
1
1693–1695
Red,
fine-grained,
equigranular,
I-type
tonalite;
enclaves
and
calcite
veins
30
40
30
2.90
±
0.16
TEP
Jandowae
West
1
467–468
Pale
grey,
medium-grained,
equigranular,
bornblende–biotite
I-type
quartz
monzodiorite
10
10
45
15
20
2.51
±
0.24
Javel
2a1146–1176
Pale
grey
to
pink,
coarse-grained,
porphyritic,
biotite–muscovite
S-type
monzogranite
30
40
20
2
8
3.68
±
0.19
PGA
Bradley
1
890.6–894.4
Red,
medium-grained,
porphyritic,
biotite
I-type
monzogranite
30
30
35
5
3.55
±
0.05
Q
is
Quartz,
AF
is
Alkali
Feldspar,
Pl
is
plagioclase,
Ms
is
Muscovite,
Bt
is
Biotite
and
Hb
is
Hornblende.
aUpper
granite.
measurements
within
individual
boreholes
is
generally
very
limited
with
only
383
wells
amongst
5442
wells
in
Australia
hav-
ing
more
than
two
reliable
temperature
measurements
at
depth
(>1
km).
Additionally,
the
quality
of
the
data
is
yet
to
be
fully
eval-
uated
(Meixner
et
al.,
2012).
We
compared
the
Oztemp
dataset
with
individual
well
completion
reports
and
identified
discrepan-
cies
in
temperature
data
(e.g.,
measured
temperature
and/or
depth
of
measured
temperature,
or
data
not
recorded)
for
ten
wells
among
the
163
wells
studied
(Table
5).
Such
errors
can
be
significant,
and
for
CON
Lynwood
1
(25◦35%25%% E
and
143◦31%36%% E),
a
difference
of
31 ◦C/km
in
the
calculated
average
thermal
gradient
was
discov-
ered
(70 ◦C/km
using
Oztemp
data
versus
39 ◦C/km
from
data
in
the
well
completion
report).
To
ensure
data
quality,
each
temper-
ature
datum
used
in
this
study
was
systematically
cross-checked
against
the
well
completion
reports.
Generally,
several
tempera-
ture
measurements
are
available
at
different
depths
and
are
used
to
predict
the
‘best-fit’
temperature
profile.
In
total,
for
the
163
wells,
464
temperature
measurements
were
used
for
thermal
mod-
elling.
These
are
listed
in
Supplement
2
(also
publically
available
at
http://eprints.qut.edu.au/63373/).
Amongst
the
163
wells,
75
wells
have
both
DST
and
Horner-corrected
data,
33
wells
have
DST,
50
have
Horner
data,
4
are
uncorrected
BHT
and
1
is
unknown.
The
mean
surface
temperature
in
the
area
is
considered
to
be
homogeneous
at
25 ◦C,
consistent
with
a
previous
study
of
the
ther-
mal
state
of
the
Cooper
Basin
(Beardsmore,
2004).
The
impact
of
variation
in
mean
surface
temperature
on
the
predicted
temper-
ature
at
5
km
depth
was
tested
with
the
stochastic
approach.
The
estimated
temperature
at
5
km
depth
only
varied
by
1◦C
for
a
13 ◦C
change
at
the
surface.
3.2.4.
Heat
production
Heat
production
rates
for
basement
granites
was
estimated
from
the
concentration
of
U
(CU),
Th
(CTh)
and
K
(CK2O)
and
a
density,
#,
of
2.65
g/cm3using
the
equation
of
Rybach
and
Buntebarth
(1981):
A
=
10−5#(9.52CU+
2.56CTh +
3.48CK2O).
(3)
Heat
production
of
each
sedimentary
formation
was
considered
constant
with
a
value
of
1.87
!W
m−3,
based
on
average
U,
Th
and
K
concentrations
from
Kamber
et
al.
(2005)
(Table
4).
This
value
was
determined
for
the
volcanogenic
Rolling
Downs
Group
of
the
GAB
and
may
only
be
applicable
to
this
particular
rock
suite.
However,
previous
studies
have
also
used
values
of
this
order
for
sedimentary
rocks.
For
example,
in
Queensland
a
value
of
1
!W
m−3was
used
for
sedimentary
rocks
in
the
Millungera
and
Eromanga
basin
(Korsch
et
al.,
2011),
and
1.2
and
1.4
!W
m−3for
the
Eromanga
and
Cooper
basins,
respectively
(Meixner
et
al.,
2012).
The
adopted
value
of
1.87
!W
m−3represents
an
upper-bound
estimate
and
thus
leads
to
a
more
conservative
estimate
of
heat
flow
contributed
by
radio-
genic
granitic
rock.
Concentrations
of
U,
Th
and
K
for
ten
intersected
granitic
rocks
are
available
from
Champion
et
al.
(2007)
and
the
late
BW
Chappell
(unpublished
data).
They
indicate
heat
production
values
are
low,
ranging
from
1.8
to
4.2
!W
m−3.
Our
new
measurements
(Table
4)
on
an
additional
8
samples
confirm
a
low
to
medium
heat
produc-
tion
capacity
of
intersected
granitic
rocks
in
SW
Queensland.
Where
available,
we
applied
measured
values
for
granite
heat
production.
Otherwise
a
heat
production
value
of
2.5
!W
m−3was
used,
as
estimated
by
Meixner
et
al.
(2012)
using
available
whole-
rock
chemistry
of
Australian
granites
(Champion
et
al.,
2007).
Heat
production
for
other
types
of
basement
rocks
was
consid-
ered
to
be
1.7
!W
m−3(Meixner
et
al.,
2012),
using
global
upper
crustal
averages
of
U,
Th
and
K
concentrations
(Rudnick
and
Gao,
2003).

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191
Table
4
Key
chemical
characteristics
and
heat
production
values
of
basement
granites
from
SW
Queensland
analysed
in
this
study,
and
compared
with
other
crustal
materials.
This
table
also
presents
heat
production
values
for
the
sedimentary
cover
and
other
type
of
basement
rocks.
Lithology
SiO2(wt%)
U
(ppm)
Th
(ppm)
K2O
(wt%)
Heat
production
(!W
m−3)aData
sources
Sediments
65.9 3.27 13.06
1.77
1.87
Kamber
et
al.
(2005)
Felsic
igneous
rocks
–
–
–
–
2.50
Meixner
et
al.
(2012)
Other
basement
rocks
–
–
–
–
1.70
Meixner
et
al.
(2012)
Granites
DIO
Wolgolla
1
77.1
5.13
22.55
3.79
3.17
This
study
TEA
Roseneath
1
77.7
6.41
9.08
4.76
2.67
This
study
AOD
Budgerygar
1 65.5 3.42 9.35 2.25 1.70 This
study
LOL
Stormhill
1 77.2
5.29
16.34
4.71
2.88
This
study
AOP
Balfour
1
64.8
1.82
8.98
2.14
1.27
This
study
TEP
Jandowae
West
1
61.0
1.35
3.80
1.64
0.75
This
study
Javel
2b76.6
10.70
10.13
4.52
3.80
This
study
PGA
Bradley
1
73.0
6.87
36.46
7.18
4.87
This
study
Upper
Continental
Crust
66.6
2.7
10.5
2.8
1.65
Rudnick
and
Gao
(2003)
Middle
Continental
Crust
63.5
1.3
6.5
2.3
0.98
Rudnick
and
Gao
(2003)
Lower
Continental
Crust
53.4
0.2
1.2
0.61
0.19
Rudnick
and
Gao
(2003)
Average
Continental
Crust
60.6
1.3
5.6
1.81
0.87
Rudnick
and
Gao
(2003)
Big
Lake
Suite –
16.5 74
6.0
9.74
Middleton
(1979)
aA
density
of
2.65
is
used
for
the
calculation.
bUpper
granite.
3.3.
Stochastic
approach
Measured
or
estimated
values
of
thermal
conductivity,
tem-
perature
and
heat
production
are
affected
by
a
wide
range
of
parameters,
the
poor
knowledge
of
which
limits
the
capa-
bility
of
determining
accurate
values
of
heat
flow.
Moreover,
insufficient
sampling
across
the
regional
study
area
imposes
a
fundamental
uncertainty
of
material
properties
and
temperature
data.
It
is
therefore
important
to
consider
the
impact
of
vari-
ance
in
these
parameters
on
the
uncertainty
of
the
calculated
heat
flow
and
extrapolated
temperature
at
5
km
depth
(Fig.
4).
Previous
geothermal
studies
have
used
a
stochastic
or
Monte-
Carlo
approach
to
characterise
the
uncertainty
of
the
calculated
output
(e.g.,
Srivastava
and
Singh,
1999;
Ferrero
and
Gallagher,
2002;
Srivastava,
2005;
Meixner
et
al.,
2012).
The
value
of
such
approaches
has
been
pointed
out
by
Korsch
et
al.
(2011)
who
modelled
heat
flow
in
the
Millungera
basin
using
nine
different
scenarios.
The
calculated
heat
flow
varied
by
up
to
20
mW
m−2.
This
large
uncertainty
associated
with
the
estimation
of
thermal
conductivity
and
the
type
of
temperature
correction
justifies
the
use
of
a
Monte-Carlo
approach,
which
has
been
adopted
here.
We
consider
the
following
parameters
as
the
main
sources
for
the
uncertainty
in
our
temperature
estimates:
thermal
conductivity,
volumetric
heat
production
and
temperature
mea-
surements.
These
parameters
were
perturbed
in
our
models
according
to
a
specific
probability
density
function.
For
each
well,
1000
realisations
with
randomly
perturbed
input
parameters
were
calculated.
For
temperature
and
heat
production,
a
normal
dis-
tribution
was
employed
with
a
standard
deviation
of
1.5 ◦C
and
0.5
!W
m−3,
respectively
(Fig.
4).
The
temperature
and
heat
pro-
duction
estimates
obtained
from
the
wells
and
the
laboratory
were
used
as
means
(Supplement
2;
also
publically
available
at
http://eprints.qut.edu.au/63373/).
The
probability
distribution
used
for
the
thermal
conductivity
is
assumed
to
be
lognormal
as
suggested
by
the
compilation
of
existing
thermal
conductivity
data
(Meixner
et
al.,
2012).
The
mean
and
standard
deviation
for
the
log-
normal
distribution
of
thermal
conductivities
are
those
that
have
been
estimated
and
reported
in
Table
2.
For
the
global
model,
all
three
parameters
(heat
production,
thermal
conductivity
and
tem-
perature)
are
perturbed.
The
uncertainty
of
which
of
the
three
parameters
or
their
combinations
has
the
largest
effect
on
heat
flow
estimates
was
also
examined.
To
this
end,
a
well
with
particularly
well-
constrained
temperature
measurements
(DIO
Macadama
1)
was
chosen.
Simulations
of
all
8
possible
permutations
of
keep-
ing
none,
one,
or
more
parameters
fixed
while
perturbing
the
Table
5
List
of
temperature
measurement
discrepancies
between
original
data
derived
from
well
completion
reports
and
the
compiled
database
Oztemp
from
Holgate
and
Gerner
(2011).
Well
name
Depth
(m)
WCR
T
(◦C)
WCR
Depth
(m)
Oztemp
T
(◦C)
Oztemp
Method
AOG
Ferrett
1
1581
71
2017.78
71
DST
UOD
Condamine
1
1394
49
1528.6
60.6
DST
OMN
Scotia
2
2901
108
2774
100
DST
PPC
Waggaba
1
766
43
Not
found
Not
found
DST
PPC
Waggaba
1
994
43
Not
found
Not
found
DST
PPC
Waggaba
1
1104
49
Not
found
Not
found
DST
PPC
Waggaba
1
1152
49
Not
found
Not
found
DST
HEP
Toobunyah
1 Not
found Not
found
1219.2
97.2
Horner
SSL
Clinton
1
2980
160
2804.2
146.66
DST
SSL
Clinton
1
2918
154
2743.8
146.66
DST
CON
Lynwood
1
2480
122
1371.6
121.67
Horner
DIO
Challum
4
2352
128
2351.53
79.86
DST
SSL
Juno
2
2825
149
2825.5
156.66
Horner
LEA
Bodalla
South
3
1715
101
1715
107.8
Horner

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156 158 160 162 164 166
0
50
100
150
200
250
0.02 0.04 0.06 0.08 0.1 0.12 0.14
0
50
100
150
200
250
150 200 250
0
50
100
150
200
250
0
0.5
1
1.5
2
2.5
3
3.5
4
0
50
100
150
200
250
300
1
2
3
4
5
6
7
8
0
50
100
150
200
250
300
350
T
K
A
Q5km
T5km
Temperature (°C)
Thermal conductivity (Wm-1K-1
)
Heat production (μWm-3
)
Temperature (°C)
Heat flow (Wm-2
)
FrequencyFrequencyFrequency
Frequency Frequency
Fig.
4.
Schematic
diagram
illustrating
the
use
of
the
stochastic
approach.
The
uncer-
tainties
of
three
parameters:
temperature
(T),
thermal
conductivity
(K)
and
heat
production
(A),
have
been
considered
to
determine
the
uncertainties
of
the
cal-
culated
heat
flow
(Q)
and
temperature
at
5
km
depth.
The
perturbations
were
performed
randomly
using
a
Gaussian
distribution
for
temperature
and
heat
pro-
duction,
and
a
lognormal
distribution
for
thermal
conductivity.
others
were
run.
The
results
are
presented
and
discussed
in
Section
4.4.
3.4.
Interpolation
techniques
For
visualisation
of
the
results
on
a
map
(Figs.
6,
7
and
8a)
we
used
inverse
distance
weighting
(IDW)
for
interpolation.
More
sophisticated
interpolation
methods
such
as
Kriging
require
that
the
data
are
normally
distributed
(which
is
not
the
case
here),
and
are
thus
not
applicable.
However,
it
must
be
noted
that
interpola-
tions
do
not
represent
geostatistically
thorough
predictions.
The
data
used
for
interpolation
can
be
found
in
Supplement
3
(also
publically
available
at
http://eprints.qut.edu.au/63373/).
4.
Results
The
results
of
the
stochastic
thermal
model,
i.e.,
temperature
and
heat
flow
estimates
at
5
km
depth
can
be
found
in
Supplement
3
(also
publically
available
at
http://eprints.qut.edu.au/63373/).
4.1.
Heat
production
The
intrusive
rocks
sampled
in
this
study
range
from
leucocratic
monzogranite
to
tonalite
and
monzodiorite
and
include
both
S-type
and
I-type
compositions
(Table
3).
Heat
production
values
esti-
mated
for
these
rocks
range
from
0.75
to
4.87
!W
m−3.
Granite
in
TEP
Jandowae
West
1,
located
close
to
Brisbane
and
well
east
of
the
temperature
anomaly
has
the
lowest
heat
production
value
while
granite
intersected
in
PGA
Bradley
1,
located
outside
the
Oztemp
anomaly
to
the
west
has
the
highest
value.
Most
granitic
rocks
analysed
here
have
heat
production
values
greater
than
the
upper
continental
crust.
However,
this
enrichment
is
significantly
lower
than
that
observed
for
the
Big
Lake
Suite
granodiorite
(Table
4)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Heat flow 5 km (mWm-2)
123 4 56 78
a)
b)
1
2
3
4
5
6
7
8
140
160
180
200
220
240
260
Temperature 5 km (ºC)
Fig.
5.
Control
of
input
parameters
(thermal
conductivity,
heat
production
and
tem-
perature)
on
heat
flow
and
temperature
determinations
at
5
km
depth.
(a)
Range
of
estimated
heat
flow
(mW
m−2)
at
5
km
depth.
(b)
Range
of
estimated
temperature
(◦C)
at
5
km
depth.
Simulation
1:
temperature
and
heat
production
are
fixed,
thermal
conductivity
varies;
Simulation
2:
thermal
conductivity
and
temperature
are
fixed,
heat
production
varies;
Simulation
3:
thermal
conductivity
and
heat
production
are
fixed,
temperature
varies;
Simulation
4:
temperature
is
fixed,
thermal
conductivity
and
heat
production
vary;
Simulation
5:
thermal
conductivity
is
fixed,
temperature
and
heat
production
vary;
Simulation
6:
heat
production
is
fixed,
thermal
conduc-
tivity
and
temperature
vary;
Simulation
7:
thermal
conductivity,
heat
production
and
temperature
are
fixed;
Simulation
8:
thermal
conductivity,
heat
production
and
temperature
vary.
The
widest
range
of
uncertainties
is
observed
when
thermal
conductivity
data
are
perturbed
(simulations
1,
4,
6
and
8).
and
confirms
the
lack
of
HHPG
intersected
in
drill
cores
across
the
Oztemp
anomaly
area.
4.2.
Thermal
conductivity
measurements
New
thermal
conductivity
measurements
on
eight
granitic
sam-
ples
range
from
2.5
to
3.7
W
m−1K−1and
are
within
the
range
of
published
values
for
similar
granite
lithologies
(Zoth
and
Haenel,
1988).
Granitic
rocks
generally
exhibit
low
porosities
(Clauser
and
Huenges,
1995);
therefore,
the
variation
of
thermal
con-
ductivity
mainly
depends
on
mineralogy.
The
low
bulk
thermal
conductivity
(2.5
W
m−1K−1)
of
this
monzodiorite
intrusion
(TEP
Jandowae
West
1)
is
explained
by
the
high
abundance
of
plagioclase
(45
vol%),
a
low
conductivity
phase
(ca.
2.1
W
m−1K−1),
and
the
low

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182–200
193
Fig.
6.
Results
of
stochastic
thermal
modelling.
(a
and
b)
Median
estimated
temperature
and
heat
flow
map
at
5
km
depth,
respectively.
(c
and
d)
First
quartile
(25%)
estimated
temperature
and
heat
flow
maps
at
5
km
depth,
respectively.
(e
and
f)
Third
quartile
(75%)
estimated
temperature
and
heat
flow
maps
at
5
km
depth,
respectively.
(g
and
h)
Estimated
temperature
and
heat
flow
maps
at
5
km
depth,
respectively,
using
a
uniform
distribution
of
thermal
conductivity
within
the
interval
0.1–5
W
m−1K−1and
fixed
heat
production
and
temperature
data.
The
4
sets
of
maps
clearly
indicate
a
prominent
SW-NE
trend
of
lower
heat
flow
data.

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abundance
of
highly
conductive
quartz
(10
vol%;
>6
W
m−1K−1)
(Table
3)
(Clauser
and
Huenges,
1995).
4.3.
Stochastic
modelling:
the
effect
of
input
parameter
on
uncertainty
Eight
simulations
were
undertaken
to
examine
the
influence
of
input
parameters
on
the
calculated
heat
flow
and
temperature
at
5
km
depth
(Fig.
5).
We
picked
DIO
Macadama
1
as
an
example
because
it
provides
the
best
temperature
constraints.
The
eight
sim-
ulations
represent
all
possible
permutations
of
perturbed
versus
fixed
input
parameters.
Simulations
1,
4,
6
and
8
all
include
thermal
conductivity
as
a
variable
parameter.
These
simulations
display
a
wide
range
of
uncertainty
(up
to
25
mW
m−2and
20 ◦C)
suggesting
that
thermal
conductivity
has
the
strongest
influence
on
estimated
heat
flow
and
temperature,
in
agreement
with
Meixner
et
al.
(2012).
Simulations
2,
3,
5
and
7,
for
which
thermal
conductivity
is
fixed,
exhibit
small
variability
of
less
than
5
mW
m−2and
5◦C
at
5
km
depth,
and
a
higher
median
than
simulations
1,
4,
6
and
8.
The
dif-
ferences
in
median
heat
flow
and
median
temperature
between
those
two
groups
of
simulations
are
up
to
10–15
mW
m−2and
5◦C,
respectively.
Thermal
conductivity
is
thus
a
crucial
parameter
that
should
be
carefully
constrained
to
minimise
the
uncertainty
of
heat
flow
and
deep
temperature
determination.
4.4.
Stochastic
modelling:
the
effect
of
the
perturbation
distribution
The
stochastic
model
discussed
in
Section
4.3
suggests
that
the
predicted
temperatures
and
heat
flows
at
5
km
depth
vary
widely
depending
on
the
thermal
conductivity
data
(Fig.
5).
The
question
arises
as
to
which
degree
the
choice
of
the
perturbation
distribu-
tion
for
thermal
conductivity
affects
the
model
predictions?
In
the
simulations
described
below,
a
lognormal
distribution
based
on
the
statistical
evaluation
of
existing
material
data
for
the
region
(Meixner
et
al.,
2012)
was
employed.
To
obtain
a
conservative
estimate
of
the
impact
of
the
choice
of
perturbation
function,
a
sim-
ulation
in
which
a
uniform
probability
distribution
with
bounds
of
0.1–5
W
m−1K−1was
used.
This
is
equivalent
to
assuming
that
no
a
priori
knowledge
of
thermal
conductivity
exists
except
for
lower
and
upper
bounds.
1000
model
realisations
were
run
keeping
tem-
perature
and
heat
production
fixed
because
these
two
parameters
have
a
negligible
effect
on
the
results.
The
results
are
illustrated
in
Fig.
6g
and
h.
They
indicate
an
uncertainty
of
ca.
±20%
for
temper-
ature
estimation
at
5
km
depth
and
a
significantly
underestimated
heat
flow
(ca.
−40%)
using
a
uniform
distribution
of
thermal
con-
ductivity
and
fixing
the
other
parameters.
However,
this
result
is
unlikely
to
represent
the
natural
case
because
material
properties
with
lower
and
upper
bounds
thermal
conductivity
values
are
rare.
Our
a
priori
knowledge
of
thermal
conductivities
is
therefore
useful
and
must
be
considered
in
any
quantitative
heat
flow
determina-
tions.
It
is
also
interesting
to
note
that
the
strong
SW-NE
trend
of
lower
heat
flow
is
reproduced
(see
Fig.
6h).
4.5.
New
temperature
and
heat
flow
map
at
5
km
depth
The
new
predicted
temperature
map
for
5
km
depth
(Fig.
6a)
has
significant
differences
compared
to
the
Oztemp
temperature
map
of
Gerner
and
Holgate
(2010).
The
regional
extent
of
the
Oztemp
anomaly
is
much
smaller
with
a
prominent
SW-NE
trend
of
elevated
temperatures
(200–250 ◦C)
(Fig.
6a).
Only
scattered
anomalous
temperatures
are
now
predicted
north
of
the
Roma
Shelf
and
in
the
Georgina
Basin.
A
lower
heat
flow
zone
(Fig.
6b)
with
values
ranging
from
80
to
100
mW
m−2is
observed
between
domains
with
heat
flow
>100
mW
m−2and
is
oriented
along
a
SW-NE
trend.
This
trend
Fig.
7.
Average
thermal
conductivity
(measurement
unit)
of
the
sedimentary
cover.
Areas
of
high
heat
flow
and
lower
temperatures
at
5
km
correspond
to
areas
with
higher
thermal
conductivity
of
the
sedimentary
sequence
(e.g.,
towards
the
Galilee
Basin).
(For
interpretation
of
the
references
to
color
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)
parallels,
and
is
adjacent
to,
the
high
temperature
trend
described
above.
While
the
data
points
are
clustered
along
this
trend,
the
con-
touring
SW-NE
pattern
persists
when
interpolating
more
evenly
distributed
data
points
over
a
smaller
area
(25◦20%0%% E–27◦10%0%% E
and
141◦2%0%% E–144◦2%0%% E).
Therefore
the
contouring
trends
are
not
directly
affected
by
the
distribution
of
the
data
points.
First
quartile
and
third
quartile
maps,
which
correspond
to
25%
and
75%
cumulative
probability,
respectively
(Fig.
6c–f)
are
very
similar
in
terms
of
spatial
distribution,
confirming
the
SW-NE
trend.
The
quartile
maps
provide
an
upper
and
lower
bound
for
the
esti-
mated
temperature
and
heat
flow
at
5
km
depth,
indicating
an
uncertainty
due
to
material
properties
of
ca.
±10%
for
both
param-
eters.
Globally,
areas
with
elevated
heat
flow
at
5
km
depth
are
also
characterised
by
high
temperature
at
5
km
depth.
An
exception
occurs
towards
the
Galilee
Basin
(Figs.
3,
6a
and
b)
where
heat
flow
is
high
(ca.
100
mW
m−2)
and
temperatures
generally
lower
(three
temperature
measurements
below
170 ◦C).
Such
differences
may
result
from
changes
in
the
thermal
conductivity
of
the
sedimentary
cover,
with
higher
thermal
conductivities
(e.g.,
average
sedimen-
tary
pile
conductivity
>2.75
W
m−1K−1)
towards
the
Galilee
Basin
(Fig.
7).
5.
Discussion
Several
key
points
should
be
addressed
when
interpreting
the
data
and
their
implications
as
well
as
model
limitations.
First,
the
validity
of
the
model
assumptions
is
examined.
Subsequently,
top
down
and
bottom
up
effects,
which
may
cause
high
heat
flow,
are
discussed,
followed
by
the
spatial
heat
flow
distribution
and
trends.
5.1.
Validity
of
modelling
assumption:
convection,
advection
or
transient
heat
transfer
Poor
agreement
between
observed
temperature
profiles
and
those
predicted
from
1D
conductive
heat
flow
models
may
indi-
cate
non-conductive
heat
transfer
(e.g.,
Reid
et
al.,
2012),
such
as
convection,
and/or
advection,
or
transient
heat
transfer,
or
geo-
metrical
effects
due
to,
for
example,
significant
lateral
gradients
of
topography,
formation
thickness,
and
material
properties.
Our
results
indicate
that
the
mean
temperature
error
is
generally
low
(≤10 ◦C,
and
in
>50%
of
the
map,
it
is
<5 ◦C,
Fig.
8a
and
b).
In
other
words,
the
model
error
is
on
the
order
of
the
uncertainty
imposed
by
poorly
constrained
material
properties
and
that
of
the
actual
down-hole
temperature
measurements.
Mean
errors
between
10
and
23 ◦C
occur
only
locally
and
may
indicate
areas
that
should
be
reassessed
for
their
thermal
transport
processes.
However,
we

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51
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195
Fig.
8.
Reliability
of
the
temperature
and
heat
flow
maps.
(a)
Mean
temperature
error
map;
(b)
histogram
of
mean
temperature
errors.
The
majority
of
the
wells
studied
have
small
mean
temperature
errors
that
suggest
that
the
assumption
of
1D
steady-state
conduction
is
for
most
cases,
valid.
(For
interpretation
of
the
references
to
color
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)
conclude
that
1D
steady
state
conduction
generally
predicts
the
temperature
data
well
at
the
regional
scale
(Fig.
8a
and
b).
5.2.
Top
down
effects:
sedimentary
blanketing
Poorly
conducting
formations
may
trap
heat
by
thermal
refraction
(e.g.,
Mildren
and
Sandiford,
1995).
Fourier’s
law
of
heat
conduction
(1822)
indicates
a
linear
correlation
between
the
geothermal
gradient
and
the
inverse
of
thermal
conductivity:
dT
dz =Q
K.
(4)
Therefore,
one
may
expect
to
observe
a
positive
correlation
between
the
inverse
of
the
mean
thermal
conductivity
of
the
sedi-
mentary
cover
and
the
predicted
geothermal
gradient.
In
our
data,
the
coefficient
of
correlation
is
low
(0.36)
assuming
a
linear
cor-
relation.
Similarly,
no
correlation
between
high
temperature
areas
and
total
thickness
of
sediments
is
identified
(correlation
coeffi-
cient
is
0.17).
Our
results
suggest
that
high
temperature
areas
are
not
associated
with
areas
of
low
conductivity
(Fig.
9)
and
thus
sed-
imentary
blanketing
is
not
the
cause
of
the
elevated
temperatures,
at
least
not
at
the
regional
scale.
This
finding
concurs
with
the
study
of
Meixner
et
al.
(2012)
in
the
Cooper
Basin,
where
elevated
crustal
or
mantle
inputs
are
required
to
explain
observed
temperatures.
5.3.
Bottom
up
effects:
mantle
versus
crustal
inputs
In
the
previous
sections,
convective,
advective
or
transient
heat
transfer,
and
sedimentary
blanketing
have
been
ruled
out
as
major
contributors
to
elevated
temperatures
in
SW
Queensland.
Conse-
quently,
a
higher
thermal
input
from
depth
is
required,
as
suggested
by
Meixner
et
al.
(2012).
Mantle
heat
flow
and
radiogenic
heat
production
of
rocks
below
5
km
contribute
to
heat
flow
at
5
km
depth.
It
is
difficult
to
distinguish
between
mantle
and
crustal
input
if
no
independent
constraints
on
either
quantity
are
available.
Mantle
heat
flow
can
be
estimated
through
pressure–temperature
estimates
from
xenoliths,
which
provide
the
geothermal
gradient,
and
assuming
a
thermal
conductivity
for
the
mantle
(e.g.,
peri-
dotite).
Alternatively,
if
the
crustal
structure
and
heat
production
of
constituent
rocks
are
known,
the
crustal
contribution
to
heat
flow
at
5
km
depth
can
be
calculated
(Perry
et
al.,
2006).
Since
the
estimated
heat
flow
at
5
km
depth
is
the
sum
of
mantle
and
crustal
contribution,
one
can
be
computed,
if
the
other
is
known:
Q5
km =
QM+
Aave(zM−
z5
km),
(5)
where
Q5
km is
the
heat
flow
at
5
km
depth,
QMis
the
mantle
heat
flow,
z5
km is
5
km
depth,
zMis
the
depth
of
the
Moho
and
Aave is
the
average
radiogenic
heat
production
between
the
Moho
and
z5
km.
Constraints
on
the
crustal
structure
in
the
study
area
are
limited
to
deep
crustal
seismic
transects
including
the
Brisbane–Eromanga
transect
(Fig.
2)
and
for
depths
less
than
ca.
3–4
km
by
drill
holes
interception
that
penetrate
the
basement.
The
distribution
of
U,
Th
and
K
within
the
crust
of
the
study
area
is
largely
unknown.
Pressure
and
temperature
information
from
young
xenoliths
are
only
avail-
able
along
the
Eastern
seaboard
(O’Reilly
and
Griffin,
1990).
Thus,
available
information
to
constrain
the
mantle
heat
flow
across
the
temperature
anomaly
is
very
limited.
The
only
estimated
values
for
the
mantle
heat
flow
are
located
in
South
Australia
and
range
from
25
to
29.5
mW
m−2(Neumann
et
al.,
2000;
McLaren
et
al.,
2003;
Meixner
et
al.,
2012).
Nevertheless,
one
can
narrow
down
the
pos-
sible
range
of
mantle
and
crustal
contributions
to
heat
flow
at
5
km
depth
by
comparing
Q5km predicted
by
our
stochastic
approach
to
standard
crustal
and
mantle
heat
flow
values.
R² = 0.36
10
15
20
25
30
35
40
45
50
55
0.27
0.29
0.31
0.33
0.35 0.37 0.39
dT/dz (ºC/km)
1/K (W-1Km)
Fig.
9.
Geothermal
gradient
determined
using
temperature
determination
at
5
km
depth
versus
inverse
of
the
average
thermal
conductivity
of
the
sedimentary
cover.
This
graph
illustrates
the
lack
of
correlation
between
sedimentary
blanketing
and
geothermal
gradient.

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20 30 40 50 60 70
−1
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Mantle Heat Flow (mW-2)
Average Heat Production (µWm-3)
27 65
Upper CC
Middle CC
Lower CC
Bulk CC
40 mW/m
2
60 mW/m
2
80 mW/m
2
100 mW/m
2
120 mW/m
2
140 mW/m2
Average Continental heat flow
Fig.
10.
Average
heat
production
between
5
and
40
km
depth
versus
mantle
heat
flow.
Isolines
correspond
to
heat
flow
at
5
km
depth
and
dashed
lines
to
standard
crustal
averages
from
Rudnick
and
Gao
(2003).
For
areas
of
high
heat
flow
(>100
mW
m−2),
an
unrealistic
mantle
heat
flow
(>65
mW
m−2)
is
required
for
standard
crustal
heat
production
values.
The
depth
of
the
Moho
is
well-established
from
the
Brisbane–Eromanga
seismic
transect
at
ca.
40
km
(Finlayson
et
al.,
1990).
Using
Eq.
(4),
we
can
determine
the
average
crustal
heat
pro-
duction
required
to
match
the
interpreted
heat
flow
at
5
km
depth
(Q5
km)
given
a
particular
mantle
heat
flow
(Fig.
10).
The
SW
corner
of
Queensland
is
characterised
by
heat
flow
generally
greater
than
100
mW
m−2(Fig.
6b).
Using
Fig.
10
and
considering
a
mantle
heat
flow
of
27
mW
m−2(Neumann
et
al.,
2000;
McLaren
et
al.,
2003;
Meixner
et
al.,
2012),
the
average
heat
production
between
5
and
40
km
is
much
higher
than
crustal
stan-
dards
(e.g.,
ca.
2.1–3.3
!W
m−3compared
to
0.87
and
1.65
!W
m−3
for
the
average
and
upper
continental
crust,
respectively;
Fig.
10)
suggesting
that
higher
radiogenic
crustal
input
is
required.
It
has
recently
been
suggested
that
this
region
is
characterised
by
a
higher
mantle
heat
flow,
based
on
He
isotope
analyses
of
arte-
sian
water
(Uysal
et
al.,
2012).
We
can
evaluate
the
mantle
heat
contribution
by
considering
an
extreme
situation
or
environment
such
as
a
hot
spot
where
mantle
heat
flow
is
expected
to
be
the
main
contributor
to
the
measured
surface
heat
flow.
Across
the
Hawaiian,
hot
spot
for
example,
surface
heat
flow
does
not
exceed
65
mW
m−2
(Stein
and
Stein,
1993).
Using
this
value
as
the
mantle
heat
flow
still
requires
higher
than
average
crustal
heat
production
values
in
the
5–40
km
interval
(e.g.,
ca.
1–2.2
!W
m−3versus
0.87
!W
m−3
for
the
average
continental
crust)
(Fig.
10).
In
addition,
such
high
mantle
heat
flow
would
result
in
Moho
temperatures
in
excess
of
1000 ◦C,
which
would
lead
to
substantial
melting
of
the
lower
crust
(e.g.,
Thompson
and
Connolly,
1995)
and
drastic
mechanical
consequences.
It
is
also
inconsistent
with
Mareschal
and
Jaupart’s
(2012)
recent
global
analysis
of
the
thermal
regime
of
the
conti-
nents,
which
predicts
maximum
Moho
temperatures
on
the
order
of
800 ◦C
for
crust
of
40
km
thickness.
The
lower
crust
in
the
western
part
of
the
Eromanga
transect
is
interpreted
to
be
silicic
(O’Reilly
and
Griffin,
1990).
It
is
well
recognised
that
silicic
rocks
have
higher
heat
producing
capac-
ity
than
mafic
rocks
(Turcotte
and
Schubert,
2002).
Consequently,
our
finding
contradicts
models
that
propose
SW
Queensland
and
the
Thomson
Orogen
are
underlain
by
oceanic
crust
(Harrington,
1974;
Glen
et
al.,
2013).
We
alternatively
conclude
that
areas
of
high
crustal
temperature
in
SW
Queensland
require
a
silicic
lower
to
middle
crust
located
between
5
and
40
km
depth
and
relatively
enriched
in
heat
producing
elements.
It
is
well
accepted
that
heat
production
becomes
more
depleted
in
the
lower
crust
as
a
result
of
chemical
differentiation
of
the
continental
crust
through
granitic
magmatism
(e.g.,
Taylor
and
McLennan,
1995;
Rudnick
and
Gao,
2003;
Hawkesworth
and
Kemp,
2006).
Accordingly,
models
proposing
an
exponential
decrease
of
heat
production
with
depth
(Lachenbruch,
1968)
are
some-
times
invoked.
These
simple
models
are,
however,
in
contradiction
with
heat
production
studies
of
drilled
or
exposed
crustal
pro-
files.
Geochemical
and
geobarometric
data
indicate
an
exponential
decrease
of
heat
production
with
depth
is
rarely,
if
ever,
valid,
with
high
heat
producing
material
often
occurring
at
greater
depth
(Ashwal
et
al.,
1987;
Hart
et
al.,
1990;
Clauser
et
al.,
1997;
Brady
et
al.,
2006;
He
et
al.,
2008).
Such
a
crustal
profile
is
exposed
in
the
Arunta
and
Musgrave
Inliers
of
central
Australia
where
high
heat
producing
material,
characterised
by
the
Mesoproterozoic
Teapot
Granite
Complex
(5.9
±
1.7
!W
m−3),
is
abundant
between
pre-exhumation
depths
of
6–10
km
(Sandiford
et
al.,
2001).
The
deformation
of
Proterozoic
crust
during
the
Petermann
and
the
Alice
Springs
orogenies
(Sandiford
et
al.,
2001)
have
led
to
exhumed
blocks
in
the
Musgrave
and
Arunta
Inlier,
and
to
buried
and
thrust
downwards
crustal
material.
Such
high
heat
producing
crustal
Fig.
11.
Geologic
origin
for
the
SW-NE
trend
of
lower
heat
flow
and
temperatures
at
5
km
depth
in
SW
Queensland.
(a)
Close-up
of
median
heat
flow
at
5
km
depth
as
illustrated
in
Fig.
6b
with
a
slightly
different
colour
scale.
(b)
The
lower
median
heat
flow
SW-NE
trend
corresponds
to
basement
structure
and
a
depression
indicated
by
the
top
of
Cadna-Owie
formation
as
delineated
by
the
C
seismic
horizon
and
top
of
the
Cadna-Owie
formation
(after
Radke,
2009).
(For
interpretation
of
the
references
to
color
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)

Author's personal copy
C.
Siégel
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al.
/
Geothermics
51
(2014)
182–200
197
material
may
therefore
extend
in
the
subsurface
beneath
the
Thom-
son
orogen
at
depth
>5
km
and
is
thus
a
likely
candidate
to
explain
the
silicic
and
heat
producing
crust
the
model
indicates.
5.4.
SW-NE
trend
The
predicted
heat
flow
map
at
5
km
depth
(Figs.
6b
and
11a)
indicates
a
narrow
SW-NE
trending
zone
of
lower
heat
flow
with
values
ranging
from
80
to
100
mW
m−2.
In
response
to
the
linear
relationship
between
the
average
heat
production
at
5–40
km
and
heat
flow
(Eq.
(5)),
this
trend
also
corresponds
to
heat
production
at
5–40
km
that
are
lower
than
average.
This
zone
of
lower
heat
flow
seems
to
coincide
remarkably
well
with
structural
trends
observed
in
seismic
horizons
(Fig.
11b)
related
to
the
top
of
the
Cadna-Owie
formation
(Radke,
2009)
and
to
thick
sedimentary
cover
(Fig.
3).
Specifically,
the
low
heat
flow
trend
corresponds
to
the
Arraburry
and
Windorah
troughs
and
the
Ullenbury
and
Thomson
depres-
sions
(Fig.
2).
A
lower
heat
flow
value
in
this
area
could
result
from
localised
lower
mantle
heat
flow
or
a
local
decrease
in
radiogenic
heat
production.
The
latter
case
would
occur
if
the
depressions
were
related
to
a
more
mafic
crust
or
to
thinned
continental
crust.
The
latter
is
consistent
with
the
observed
increase
in
sedimentary
infill
in
the
troughs.
Tectonic
extension
will
reduce
the
vertical
extent
of
crystalline
basement,
which
is
potentially
enriched
in
high
heat
producing
elements,
and
thus
the
local
crustal
contribution
to
heat
flow.
6.
Conclusions
This
study
has
re-evaluated
the
geothermal
potential
in
SW
Queensland
and
has
confirmed
the
generally
high
subsurface
tem-
peratures
observed
in
Oztemp.
A
new
temperature
map
at
5
km
depth
reveals
a
strong
SW-NE
trend
of
elevated
(200–250 ◦C)
tem-
peratures.
This
study
has
also
investigated
the
geological
controls
on
the
elevated
geothermal
gradients
using
a
stochastic
approach.
Estimated
temperature
and
heat
flow
at
5
km
depth
are
most
sen-
sitive
to
the
thermal
conductivity
of
the
strata.
A
poor
correlation
between
thickness
and
average
thermal
conductivity
of
the
sedi-
mentary
pile
and
estimated
temperature
at
5
km
depth
suggests
that
thermal
blanketing
is
not
the
sole
cause
of
high
geother-
mal
gradients.
In
addition,
the
small
mean
temperature
errors
between
modelled
and
observed
temperature
profiles
indicate
that
the
assumption
of
steady
state,
purely
conductive
heat
transfer
may
be
valid
and
that
effects
of
advective,
convective
or
transient
heat
transfer
are
likely
to
be
minor
at
the
regional
scale
of
this
study.
Consequently,
elevated
subsurface
temperatures
must
result
from
bottom
up
contributions.
Estimations
of
the
relative
contrib-
utions
of
mantle
versus
crustal
heat
input
from
below
5
km
depth
suggest
that
the
observed
high
geothermal
gradients
are
unlikely
to
be
generated
by
elevated
mantle
heat
flow
alone.
Consequently,
we
conclude
that
the
crust
between
5
and
40
km
depth
is
relatively
high
heat
producing
in
the
region
of
anomalously
high
crustal
tem-
peratures.
Our
study
supports
the
existence
of
silicic
continental
lower
to
middle
crust
enriched
in
heat
producing
elements
beneath
the
region
of
elevated
temperature
and
for
much
of
the
Thomson
orogen.
A
SW-NE
trend
of
lower
heat
flow
and
inferred
average
heat
production
through
the
study
area
correlates
with
structural
trends
and
may
relate
to
zones
of
thinned
continental
crust
and
therefore
lower
total
crustal
heat
production.
Acknowledgements
C.
Siégel
is
supported
by
the
QUT
Postgraduate
Research
Award.
C.
Siégel
acknowledges
support
from
QGECE
and
IFE
for
funding
analytical
experiments.
We
thank
A.
Antriasian
and
S.
Egan
for
thermal
conductivity
measurements,
A.
Greig
for
ICPMS
analysis
of
U,
Th
and
K
and
ALS
for
XRF
analysis
of
K2O.
O.
Gaede,
T.
Uysal,
A.
Kirkby
and
T.
Meixner
are
thanked
for
discussions.
Two
anony-
mous
reviewers
and
the
editor
J.
Moore
are
thanked
for
providing
comments
that
have
significantly
improved
the
manuscript.
Appendix
A.
Theoretical
approach
Our
approach
follows
a
modified
version
of
Chapman
(1986),
with
a
different
choice
of
boundary
conditions.
Like
Chapman
(1986),
we
assume
a
thermal
steady
state
and
treat
each
well
as
a
1D
multi-layer
diffusion
problem.
In
the
study
area,
most
tempera-
ture
data
are
located
at
a
depth
>1
km,
with
very
few
data
towards
the
surface
of
the
Earth.
We
judge
that
the
deeper
temperature
data
are
more
reliable
than
the
estimated
surface
temperature.
There-
fore,
we
calculate
the
temperature
profiles
stepwise
from
bottom
to
top
rather
than
top
to
bottom
as
in
Chapman
(1986).
Constant
material
properties
are
assumed
in
each
layer.
The
only
source
term
is
radiogenic
heat
production.
Conductive
heat
transfer
through
a
single
layer
with
a
constant
source
term
is
described
by
the
following
ordinary
differential
equation
(Chapman,
1986),
also
called
Poisson’s
equation:
Kd2T
dz2=
−A,
(A.1)
where
K
is
the
thermal
conductivity
(W
m−1K−1),
T
is
the
tem-
perature
(◦C),
z
denotes
depth
(m),
and
A
is
the
volumetric
heat
production
(!W
m−3).
Integrating
Eq.
(A.1)
twice
yields
the
tem-
perature
profile,
a
quadratic
function:
KT(z)
=
−1
2Az2+
zC1+
C2,
(A.2)
where
C1and
C2denote
the
integration
constants.
Because
heat
production
is
constant
in
the
layer
under
consideration,
the
constants
of
this
1D
equation
can
be
solved
for
with
the
following
boundary
conditions:
Q(z
=
zB)
=
QB
T(z
=
zB)
=
TB
,
(A.3)
where
zBdenotes
the
vertical
position
of
the
layer
bottom,
QBis
heat
flow
at
the
layer
bottom,
and
TBis
temperature
at
the
bottom.
Thus,
the
temperature
profile
in
the
layer
is:
T(z)
=
−A
2K(z2+
z2
B)
+
zQB+
AzB
K+
TB−zBQB
K.
(A.4)
The
temperature
profile
through
a
multi-layer
stack
can
now
be
computed
easily
by
a
piecewise
(i.e.,
layer
by
layer)
upward
prop-
agation
of
Eq.
(A.4)
with
updated
material
properties
and
bottom
temperature
as
well
as
heat
flow.
In
other
words,
the
temperature
and
heat
flow
at
a
layer
interface
are
calculated
for
the
lower
layer
with
Eq.
(A.4).
They
serve
as
starting
parameters
for
the
tempera-
ture
profile
in
the
overlying
layer,
which
is
also
calculated
with
Eq.
(A.4)
using
updated
material
properties.
This
procedure
requires
that
the
temperature
and
heat
flow
at
the
bottom
(or
top)
of
the
stack
are
known.
In
this
study,
we
estimated
the
temperature
TTand
heat
flow
QT
at
a
depth
of
zT=
5
km
for
each
well.
No
well
in
the
study
area
has
penetrated
the
crust
to
this
depth,
and
the
maximum
well
depth
is
3.9
km
(PPC
Lissoy
1).
However,
for
each
well,
the
number
of
inter-
sected
formations
and
their
respective
thicknesses,
conductivities
and
heat
production
rates
are
known
or
can
be
estimated
(see
Sec-
tion
3.2
for
discussion
of
material
properties
and
their
derivation)
to
a
certain
depth
zC<
zT.
Well
logs
also
provide
often
sparse
temper-
ature
measurements,
which
provide
an
estimated
true
formation
temperature
when
corrected
(see
Section
3.2.3
for
a
discussion
of
temperature
methods
and
corrections).
Assuming
that
the
material

Author's personal copy
198
C.
Siégel
et
al.
/
Geothermics
51
(2014)
182–200
5 km TT
25 ˚C T(5 km)
∆ε
Depth (km)
Temperature (˚C)
Heat Flow - 5 km - QB (mWm-2
)
∆ε’ = 0
∆T
a)
b
)
Fig.
A1.
Schematic
model
to
determine
heat
flow
at
5
km
depth.
(a)
Modelled
temperature
profile
using
observed
temperatures
(stars)
and
a
constant
thermal
conductivity.
It
must
be
noted
that
this
temperature
profile
is
a
simple
illustration
and
will
vary
with
depth
depending
on
thermal
conductivity
variations
of
the
sedi-
mentary
cover.
!T
is
the
difference
between
observed
and
modelled
temperature.
TTis
the
shift
of
the
temperature
profile
from
0
to
the
best
fit
TT(refer
to
text).
(b)
The
mean
square
temperature
error
(!ε)
is
a
quadratic
function
of
heat
flow
at
5
km
QT(Eq.
(A.11))
and
is
used
to
determine
the
best
fit
TT.
The
best
fit
QTcorresponds
to
the
smaller
mean
squared
errors
(!ε%=
0),
i.e.,
the
lowest
point
of
the
quadratic
function.
TTis
computed
using
QTand
Eq.
(A.9).
between
the
deepest
observation
in
the
well
and
zTremains
iden-
tical,
TTand
QTcan
be
inverted
by
minimising
the
mean
squared
temperature
error
of
the
calculated
temperature
profile
(Fig.
A1):
!ε
=
N

i=1
(Ti−
ti)2
N,
(A.5)
where
N
denotes
the
number
of
actual
temperature
observations
in
the
well,
Tiis
the
measured
temperature
at
a
given
depth,
and
tiis
the
predicted
temperature
at
that
depth.
For
a
given
QT,
it
is
straightforward
to
calculate
the
best-fit
TT.
Eq.
(A.4)
indicates
that
the
choice
of
the
initial
TBcontrols
the
position
of
the
temperature
profile
(it
is
a
simple
summand)
and
thermal
conductivity
controls
the
shape
of
the
temperature
pro-
file
(it
affects
the
slope
of
the
linear
part
of
Eq.
(A.4)).
A
change
of
TTwould
therefore
simply
shift
the
temperature
profile
by
its
magnitude
along
the
temperature
axis
(Fig.
A1).
Thus,
TTcan
be
computed
by
minimising
the
mean
squared
temperature
error
(Fig.
A1):
!ε
=
N

i=1
(Ti−
(ti+
X))2
N,
(A.6)
and
with
!Ti=
(Ti−
ti):
!ε
=
X2−2
NX
N

i=1
!Ti+1
N
N

i=1
!T2
i.
(A.7)
Eq.
(A.7)
has
the
minimum:
!ε%=
2X
−2
N
N

i=1
!Ti=
0.
(A.8)
Therefore,
the
following
solution
for
TTis
obtained:
X
=
N

i=1
!Ti
N.(A.9)
The
minimised
square
temperature
error
can
hence
be
expressed
using
Eqs.
(A.7)
and
(A.9):
!ε
=
N

i=1
(Ti−
(ti+N
i=1!Ti/N))2
N.
(A.10)
This
procedure
requires
that
QTis
known,
which
is
not
the
case.
Eq.
(A.10)
shows
that
!ε
is
a
quadratic
function
of
QT:
f
(QT)
=
!ε
=
aQ2
T+
bQT+
c.
(A.11)
Given
three
points,
Pj(QTj/!εj),
the
coefficients
a,
b
and
c
of
this
quadratic
function
can
be
calculated
empirically
and
the
best
fit
QT
determined
by
minimisation.
Thus,
both
the
best-fit
temperature
profile
and
the
respective
temperature
and
heat
flow
at
5
km
depth
are
determined
in
a
three
step
process
for
any
given
well:
first,
three
arbitrary
QTare
assumed
(0,
50,
and
100
!W
m−3).
For
each
one,
the
corresponding
best-fit
TTand
its
mean
squared
temperature
error
are
calculated
analytically
with
Eqs.
(A.9)
and
(A.10).
This
yields
the
desired
three
pairs
of
QTand
!ε
data
needed
to
calculate
the
coefficients
of
Eq.
(A.11).
The
best-fit
QTis
simply
the
minimum
of
Eq.
(A.11):
−b(2a)−1.
In
the
third
step,
the
corresponding
TTis
computed
for
the
best-fit
QTwith
Eq.
(A.9).
Appendix
B.
Supplementary
data
Supplementary
material
related
to
this
article
can
be
found,
in
the
online
version,
at
doi:10.1016/j.geothermics.2014.01.005.
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