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Pressure—Temperature—Time
Paths of Regional Metamorphism
I. Heat Transfer during the
Evolution of Regions of Thickened
Continental Crust
Journal Article
Author(s):
England, Philip C.; Thompson, Alan Bruce
Publication date:
1984
Permanent link:
https://doi.org/10.3929/ethz-b-000422845
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
Journal of Petrology 25(4), https://doi.org/10.1093/petrology/25.4.894
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Pressure-Temperature-Time
Paths
of
Regional
Metamorphism
I.
Heat Transfer during the Evolution
of
Regions
of
Thickened
Continental Crust
by
PHILIP
C.
ENGLAND
1
AND ALAN BRUCE THOMPSON
2
'Department of Geological Sciences, Harvard University, Cambridge, MA 02138 U.SA.
2
Institutfiir Mineralogie und Petrographie, ETH Zurich, CH 8092 Zurich, Switzerland
(Received 20 June 1982; in revised form 15 April 1984)
ABSTRACT
The development
of
regional metamorphism
in
areas
of
thickened continental crust
is
investigated
in
terms
of the
major controls
on
regional-scale thermal regimes. These
are: the
total radiogenic heat
supply within
the
thickened crust,
the
supply
of
heat from
the
mantle,
the
thermal conductivity
of the
medium
and the
length
and
time scales
of
erosion
of the
continental crust.
The
orogenic episode
is
regarded
as
consisting
of a
relatively rapid phase
of
crustal thickening, during which little temperature
change occurs
in
individual rocks, followed
by a
lengthier phase
of
erosion,
at the end of
which
the
crust
is at its
original thickness.
The
principal features
of
pressure-temperature-time
{PTt)
paths
followed
by
rocks
in
this environment
are a
period
of
thermal relaxation, during which
the
temperature
rises towards
the
higher geotherm that would
be
supported
by the
thickened crust, followed
by a
period
of cooling
as the
rock approaches
the
cold land surface.
The
temperature increase that occurs
is
governed
by the
degree
of
thickening
of
the crust,
its
conductivity
and the
time that elapses before
the
rock
is
exhumed sufficiently
to be
affected
by the
proximity
of
the cold upper boundary.
For
much
of
the parameter range considered,
the
heating phase encompasses
a
considerable portion
of the
exhumation (decompression) part
of
the
PTt
path.
In
addition
to the
detailed calculation
of PTt
paths
we present
an
idealized model
of
the thickening
and
exhumation process, which
may be
used
to
make
simple calculations
of
the amount
of
heating
to be
expected during
a
given thickening
and
exhumation
episode
and of the
depth
at
which
a
rock will start
to
cool
on its
ascent path.
An
important feature
of
these
PTt
paths
is
that most
of
them
lie
within
50 °C of the
maximum temperature attained
for one
third
or
more
of the
total duration
of
their burial
and
uplift,
and for a
geologically plausible range
of
erosion rates
the
rocks
do not
begin
to
cool until they have completed
20 to 40 per
cent
of
the total
uplift they experience. Considerable melting
of the
continental crust
is a
likely consequence
of
thickening
of
crust with
an
average continental geotherm.
A
companion paper discusses these results
in
the
context
of
attempts
to use
metamorphic petrology data
to
give information
on
tectonic
processes.
1. INTRODUCTION
Observations of metamorphic rocks exposed over regional extents form one of the
important classes of data on which our present understanding of the evolution of orogenic
belts is based. This understanding is at best patchy, owing to the many combinations of
horizontal and vertical motions that may occur during the lifetime of an orogenic belt and to
the complex, or sometimes merely insensitive, response to these processes of the geological
indicators from which histories of strain, deviatoric stress, pressure or temperature may be
inferred. In this paper we discuss the problems of inferring one class of these histories, the
pressure-temperature-time (PTt) path followed by a rock during regional metamorphism;
more specifically, we concentrate on the PTt paths resulting from the burial and exhumation
of rocks during episodes of continental thickening.
UournaJ
of
Petrotojy. VoL
25, Pin 4,
pp. 894-928,
1984]
PRESSURE-TEMPERATURE-TIME
PATHS. I 895
Heat
and
mass transfer during
the
development
of an
orogenic belt may involve
the
thickening
of
continental crust
by
thrusting
or
magma addition,
the
thinning
of
crust
by
intra-plate rifting or the sliding of nappes under gravity; heat may be supplied to the crust by
magmas generated from partial melting of the mantle, may be transferred within the crust by
conduction or by the motion
of
fluids, and is generated to
a
significant extent by the decay of
radioactive isotopes within
the
continental crust.
In
understanding
the
development
of
an
individual orogenic belt, and the evolution of the continental crust as a whole, it is desirable to
know the extent
to
which these, and other, processes have influenced the thermal history of
the rocks that are now exposed in regional metamorphic terrains.
It has long been recognized that
PT
data derived from mineral assemblages are, on their
own, of limited use in this endeavour, and certainly cannot be used to infer directly, say, the
ambient geothermal gradient during metamorphism. Thus
the
problem divides into
two
portions,
of
which the first
is to
determine the likely PTt paths that rocks may experience in
given tectonic environments, and the second is to find, if possible, features of these paths that
are diagnostic of particular processes and are likely to be recorded in the mineral assemblages
when the rock finally reaches the surface.
Rocks that record mineral geobarometric pressures
of
several kilobars are widespread on
the surface
of
crust
of
normal continental thickness; this, with geophysical evidence
for
greatly thickened crust
in
regions
of
present
day
orogenic activity implies that crustal
thickening
is of
major importance
in
orogenic evolution. Several models,
of
varying
complexity, have been constructed
to
describe the thermal regimes
of
regions
of
thickened
continental crust (e.g. Oxburgh
&
Turcotte, 1974; Bickle
et
al., 1975; Bird
et al,
1975;
England & Richardson, 1977; Toksoz & Bird, 1977; England, 1978; Richardson & England,
1979) but most of these have been tied to specific geological areas and often the full range of
variability of the parameters to the models has not been considered.
In the following sections we construct
a
system that we believe may contain the principal
elements dictating the thermal development of thickened continental crust and investigate the
PTt paths that may
be
followed
by
rocks undergoing burial
and
exhumation during
an
orogenic episode.
A
companion paper (Thompson & England, 1984, hereafter referred to
as
Part II) deals with the petrological problems of inferring such paths from the rocks preserved
at the land surface.
2.
PHYSICAL MODEL
As has been established in previous work (Clark & Jager, 1969; Bickle et
al,
1975; England &
Richardson, 1977; England, 1978) the apparently insuperable complexity
of
treating the thermal
development of a continental collision zone can be overcome by the recognition that there are only
a
few major controls on the kinds of thermal profile developed and
a
host of minor controls. The major
controls are enumerated below, and regional geotherms and PTt paths are calculated for cases in which
these controls are varied over their geologically interesting ranges.
The
use of
systems such
as
these may seem undesirable,
in
that they are
not
attached
to a
recognizable geological history
for
one specific terrain and have
a
somewhat abstract
flavour.
We
cannot emphasize too strongly our belief that
an
understanding
of
the major factors that govern
regional metamorphism is not achieved by the construction of detailed numerical analogues to specific
complex geological terrains; in contrast, the kind of simple numerical experiments to be described herp
can give valuable insights into heat transfer processes during metamorphism on
a
regional scale (s~e
also section 4).
2.1.
Assumptions
2.1.a. Heat sources
We assume that the major sources
of
heat
in
regional metamorphism are the decay
of
radioactive
elements
in the
continental crust and
the
heat transferred
to the
base
of
the crust from
the
upper
896
P. C.
ENGLAND
AND
A. B.
THOMPSON
mantle. Metamorphic reactions within the crust may be local sources
or
sinks of heat, but the amounts
of heat involved are generally much less than the total heat flowing through the system. This assump-
tion, and the quantities involved, are discussed in subsection 3.3.
2.1.b. Mechanism of heat transfer
Heat transfer
is
assumed
to be
predominantly
by
conduction and,
for
lack
of
any better general
relation, the crust
is
assumed
to
have constant thermal conductivity.
In
subsection 3.1 we discuss our
reasons for making this assumption.
2.I.e. Initial conditions
Before orogeny, the continental crust
is
assumed
to
have
a
conductive steady state profile with
a
given heat flux,
Q*,
from
the
uppermost mantle
and
a
given internal heat production distribution.
Specifically, we assume radiogenic heat production to be constant
at
a rate
A
to depth
D
and to be zero
elsewhere. Then the temperature, V
c
,
at
any depth
z
is given by:
Az
Q+z
V
e
(z) =
(D-z/2) + -— 0<7<Z)
K K
(i)
AD
1
Q*z
=
+ z
>
D
IK
K
where Q+ is
the
heat flow from
the
upper mantle
to
the
crust,
K is
the
thermal conductivity
of
the
medium, and the surface temperature is taken
to
be zero—an adequate assumption
for
the centigrade
scale used here.
A
special case, which may well be
of
considerable geological importance—that of the
telescoping
of
passive continental margins
(e.g.
Helwig,
1976;
Jackson, 1980)—is considered
separately (see section 4). There, the initial condition
is
given by equation 1, but
a
period
of
extension
and subsidence precedes the compressional phase.
2.1.d.
Geometry of thickening
Thickening
of
the crust
in
orogeny
is
assumed
to
occur without change
in
the heat supplied
to the
base
of
the continental lithosphere. Such
a
change
by its
nature
is
long term
and
thus impossible
to observe directly;
it
would also
be
very hard
to
demonstrate from geological observations.
We
chose three geometries
of
thickening which reasonably represent
the
great variety
of
processes that
may be involved in continental thickening (Fig.
1).
In the first case (Figs,
la, Id,
\g)
the thickening
is
assumed
to
be the result
of
the emplacement of
a single thrust sheet
of
thickness
5
onto
the
continental section whose temperature
is
given
by
equation 1; this gives an initial temperature distribution
of:
V(z,0)=V
c
(z)
0<z<5
(2a)
V{z,
0)
=
V
t
{z
-S)
z>S (2b)
In
the
second case (Figs.
\b, le,
\h)
the thickening
is
assumed
to
occur
by
homogeneous horizontal
shortening
of
the entire crust
by
continental collision. Thus
if
the crustal thickness
is
multiplied
by
a
factor of/(>1) then
V(z,0)=V
c
{z/f) 0<z//<C
(3a)
(z>0
for
Figs.
lc,f,i)
V(z,0)
=
V
c
(z
- (/-
1)C)
z/f
>
C (3b)
where
C is
the initial crustal thickness, taken
to be
greater than the heat production scale length,
D.
In all the systems described below
C
is taken to be 35 km. In the third case, the thickening takes place
throughout the entire lithosphere (Figs,
lc,
If, 1/)
and the temperature
is
given
by
equation (3a)
for
all values of depth.
The first
two
cases correspond
to
crustal shortening without disturbance
to
the
mantle thermal
regime, and they represent reasonable end members
of
the geometries
of
crustal thickening. The third
case,
involving thickening
of
the lithosphere
as
a
whole represents
a
possible geometry
of
continental
thickening in. which
the
sub-crustal thermal gradients are reduced due
to
the compression,
and
this
differs importantly from
the
other two cases.
In all
cases, though,
the
heat flow
at
the base
of
the
PRESSURE-TEMPERATURE-TIME PATHS.
I 897
lithosphere remains constant.
The
geological relevance
of
these geometries
is
considered further
in
section
4.
The initial internal heat production distribution H(z) is given in the case of thickening by thrusting by:
H(z)=A 0<z<min(S,D)
=
0
D <z^S if S > D
(4)
=
0
z> S
+
D
or in the case of thickening by homogeneous compression by:
H(z)=A
= 0
z/f>D
(5)
2.I.e. Erosional parameters
We assume that the continental lithosphere
is
always close
to
isostatic equilibrium and thus that
at
some time after thickening
the
crust will have returned close
to its
original thickness through
the
agency
of
erosion acting on its elevated surface. Thus the depth, E
mtx
of
the erosion is defined to be
S
(equations 2),
or (/
—
1)C
(equations 3),
and it
remains
to
choose
a
time scale. Erosional time and
length scales are discussed in subsection 3.4.
2.1.
f. One-dimensionality
Throughout this paper
we
consider
the
transfer
of
heat
in the
vertical direction only.
On a
local
scale there
is
frequently evidence
of
appreciable lateral heat transfer,
for
example
in the
neighbour-
hood
of
intrusive bodies, but
on a
regional scale we should expect horizontal thermal gradients
to be
much less than vertical ones. Even were
we
willing
to
consider lateral heat transfer,
the
absence
of
adequate constraints on the boundary conditions would make such
an
enterprise fruitless in the general
case.
2.2.
Method of solution
The equation
of
heat transfer
in a
constant-conductivity moving medium, with heat transfer only
in
the
z
direction
is
\dv
d
1
v
u(z,t)dv h(z,t)
Kdt~
dz
2
K ~dz
+
K
where
v
is the temperature,
K
is the thermal diffusivity,
K
is the thermal conductivity,
h
the rate of heat
generation
and u is
the vertical velocity of the medium relative
to
the plane
z =
0. Equation (6a) may
be written in
a
non-dimensional form:
do'
<9V u
o
l do'
=
—u'(z',t')
+
h'(z',t') (6b)
df
dz'
1
K dz'
where
z' = z/l, v' = v/o
0
, t' =
Kt/l
2
and h' =
hl
2
/Ko
0
and
/ is a
characteristic length
of
the system
(e.g.
the
lithospheric thickness),
o
0
is a
characteristic temperature
and u
0
is a
characteristic velocity
(see section 5.2).
We shall assume that there
is no
shortening
or
extension after time
( = 0, so
that the velocity
is
simply the rate at which the medium is eroded,
=
0
t> T
We discuss
in
section 3.3 the role
of
endothermic and exothermic metamorphic reactions, but make
no detailed calculations concerning them, so the heat production distribution is given by
h(z,t)=H{z + E(Q)
(8)
where
H is
calculated from equation (4)
or (5) as
appropriate, and E(t) is the amount
of
erosion that
has occurred at time
t.