EPSL
ELSEVIER
I
Earth and Planetary Science Letters 124 (1994) 95-103
The effect of lithospheric phase transitions on subsidence
of extending continental lithosphere
Yu.Yu. Podladchikov
a,
A.N.B. Poliakov
b,
D.A. Yuen
Department of Sedimentary Geology, Vrije Uniusrsiteit, 1081 HVAmsterdam, The Netherlands
HLRZ, KFA-Jiilich, Postfach 1913, 0-52425 Jiilich, Germany
" Department of Geology and Geophysics and Minnesota Supercomputer Institute, Uniuersity of Minnesota, Minneapolis,
MN 55415, USA
I
I
~
1
Received November 9, 1993; revision accepted April 6,1994
Abstract
A new simple model for sedimentary basin formation, which combines both stretching and phase transitions
occurring together in the lithosphere, is proposed, and two important aspects in sedimentary basin formation are
addressed: (1) the explanation of the domal uplift preceding rifting, and (2) the ability of the model to explain the
contradiction between a small amount of crustal stretching and the large amount of thermal subsidence without the
need to invoke differential stretching between the crust and mantle.
Relationships for synrift initial and thermal post-rift subsidence are derived. The model predicts that extension of
continental lithosphere could produce synrifting uplift up to a threshold amount of extension and then subsidence
for greater extension. Three dimensionless parameters quantify the contribution of the phase transition to the
subsidence history: (1) the Clapeyron slope normalized to the initial geothermal gradient, (2) the ratio of depth of
phase transition to the thickness of the lithosphere, and (3) the ratio of density effect due to phase transition to the
change in density due to thermal expansion. An evaluation of these parameters has been carried out by using
thermodynamical data for the garnet-spinel transition for upper mantle rocks. Our simple model shows that by
including the effects of lithospheric phase transition in existing stretching models of sedimentary basin formation we
can obtain an extra significant parameter controlling the subsidence and the entire extensional tectonics of such
basins.
1. Introduction
Any movement of lithospheric material is accompanied by changes in the pressure P and
temperature T. This results in multiple phase
transitions, due to the complex mineralogical
composition of the lithosphere. The dynamic re-
sponse of the lithosphere due to numerous phase
transitions depends on both the scale and the
depth of the tectonic process. It is obvious that
during continental stretching involving large vertical movement in the lithosphere, phase transitions with strong density effects will play an important role in the tectonic evolution.
The most widely used model for the subsidence of sedimentary basins is the pure shear
model for passive rifting 111. One of the problems
0012-821X/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved
SSDI 0012-821X(94)00074-9
96
Yu-Yu.
Podladchikov et al. /Earth and Planetary Science Letters 124 (1994) 95-103
with this model is that the crustal stretching is
much less than that predicted by thermal subsidence [2,3,4]. This is a direct consequence of the
fact that stretching is the only cause of subsidence in this model. The second problem with
this model is related to the often observed late
acceleration of the subsidence rate (i.e., deviation
from t-0.5 behaviour) which requires some type
of non-thermal mechanism [5,6,7].
Lithospheric phase transitions have long been
proposed as a possible contributor in the formation of sedimentary basins [4-6,8-201. These authors did not take stretching into account, assurning the phase transition as the only cause of
non-thermal subsidence. As a result, they only
considered phase transitions with extremely high
density effects. The most well known in this respect is the basalt-eclogite phase transition, which
is the one (and perhaps the only one) phase
transition in the lithosphere having a density effect of up to lo%, which makes these studies
highly hypothetical because of the absence of
convincing seismic and petrological evidence (except possibly in the case of a subducting slab),
suggesting the presence of thick layers of eclogites in the lithosphere [21,22]. First estimates of
the depth of the basalt-eclogite phase transition
have been made by linear extrapolation of hightemperature experimental data to lower crustal
conditions [21,23]. The results of Ito and Kennedy
were distinctly different from those of Ringwood
and Green, which were the subject of a wellknown discussion [24,25]. However, the validity of
this extrapolation is not supported by any theoretical model and seems to be in disagreement
with recent experimental data, which suggest a
non-linear character for the corresponding phase
boundary curves and a greater depth of the
basalt-eclogite phase transition [26,27]. Theoretical thermodynamic models explain the discrepancy in the early experimental result by the difference in the chemical composition of the rocks
studied in the experiments, but these models
themselves suffer from a significant discrepancy,
in the prediction of phase boundary positions at
conditions of low temperature and pressure
[27,28]. This is partly because of the fact that the
thermodynamic models are developed by the fit-
ting of high-temperature experimental data and
the lower temperature predictions are outside
their calibration range [28].
An additional problem is that, due to strong
temperature dependence of the transformation
rate, the transition does not take place at normal
crustal conditions [29,30,13,15,17, and references
therein]. Namiki and Solomon [30] came to the
conclusion that the basalt-eclogite phase transition is not in equilibrium at the base of the
Venusian crust beneath the highly elevated
mountain belts despite the very high surface temperature on Venus (750 K).
Here we propose a new model which combines
both stretching and phase transitions occurring
together in the lithosphere. Due the non-linear
interaction of the two mechanisms of subsidence
in our model, a substantial amount of thermal
subsidence can be obtained as a result of the
interplay between a relatively small amount of
extension and a weak lithospheric phase transition (i.e., the spinel to garnet lherzolite phase
transition with a density contrast of 3% and a
depth of 60-90 krn).
2. Model description
It is certainly a very difficult task to take into
account all the possible phase transitions occurring in the lithosphere for every particular tectonic situation and bulk composition of the rocks.
However, most of the lithospheric phase transitions with strong density effects are usually located at the 50-100 km depth and have a similar
small positive Clapeyron slope [28,31]. According
to seismic and petrological models of the lithosphere [32-341, the garnet-spinel transition has
the most profound density effect (about 3%) on
mantle rocks with ultramafic (Iherzolitic) bulk
compositions, compositions which can be assumed for depths between 50 and 100 km. The
spinel-garnet transition has been observed in the
laboratory at upper mantle temperature and
pressure 135-381, and xenoliths of both facies are
common [39], so it seems likely that this reaction
does occur in the uppermost mantle [34]. Fortunately, the relatively high temperature in the up-
Yu.Yu. Podladchikou et aL /Earth and Planetary Science Letters 124 (19941 95-103
BASIN SUBSIDENCE
\ 1
Fig. 1. Schematic diagram of pure shear model lithospheric extension with a phase transition.
perrnost mantle (the conditions are similar to
those of the experiments and reactions rates are
high), the relatively dry conditions, and the simpler mineralogical composition of ultramafic rocks
compared to basic rocks makes the phase dia-
-
gram predictions much more reliable [40]. Observations of increasing seismicvelocity in the 50-100
km depth range have been made by a number of
workers. Such observations have been made for
different geographic localities and distinct tec-
GEOT H E W
CLAPEYRON LINE (P-T PHASE BOUNDARY)
p g ~ ~ d g ~ ~ : ~ ; g gP~0~ST
, ?-R~ >I F
~ 'I:
A)
B
Fig. 2. Geometrical relationship between the Clapeyron lines and the geotherm for two different cases: (A) Positive Clapeyron
slope with 0 < y' < 1. (B) Positive and negative Clapeyron slopes with y' > 1 or -inf < y' < 0. fi = stretching factor; z,,,, and
z,,, = thickness of the crust and lithosphere; ,z, = depth of phase transition; p,,,, and pscdim= densities of crust and sediment;
I = inflection point of the transient geotherm; TI = temperature at the base of the lithosphere zlith.The column in the middle
shows the density distribution in the lithosphere and the shifts in the phase boundary during the stretching. Note that the direction
is the dimensionless Clapeyron
of the surface movement is opposite to the movement of the phase boundary. y' = yT1/(plithlg~Sth)
slope.
98
Yu.Yu. Podladchikou et al. /Earth and Plan!etary Science Letters 124 (1994) 95-103
tonic settings, suggesting that increasing velocity
in this depth range may occur globally (see [34]
for review). Hales [41] has attributed this discontinuity to the spinel-garnet transition. Revenaugh and Jordan [34] have developed a new
technique to image the seismic discontinuities
and to examine the nature of mantle layering,
and have confirmed the persistent character of
the discontinuity at a mean apparent depth of
about 60 km. This they designated the H
(Hales)-discontinuity. The widespread geographical distribution of the H-horizon and the lack of a
tectonic correlation to the apparent depth variation of this horizon lends, according to Revenaugh and Jordan [34], further credence to the
spinel-garnet phase transition hypothesis. These
authors have discussed an alternative hypothesis
that attributes the observed increase in compressionaI wave speed to a corresponding increase in
the intensity of preferred orientation of olivine,
and, finally, they concluded that " . . .the H discontinuity is best described as the spinel-garnet
facies boundary characterized by a small effective
Clapeyron slope." The spinel-garnet transition
actually consists of a sequence of phase transformations involving fields of coexisting phases on
the P-T diagram and their solid solutions. The
exact positions of the phase boundaries are poorly
constrained because of their extreme sensitivity
to the bulk composition and the difficulties in
both experimental and theoretical studies of multicomponent systems. Thus, in this paper, we will
assume a linear superposition of tectonic responses for multiple phase transitions occurring
at approximately the same depth and treat them
all as a single transition with some average property.
We therefore considered the effect of a single
phase transition on the formation of a sedimentary basin. We employ the classical pure shear
stretching model [1] as a basis, dividing the lithosphere at the depth of a phase transition z g ,
into layers with density plith, and p,,,,,. The rest
of the notation and the values are almost the
same as in the, classical model [I] (see Figs. 1 and
2).
We will now justify our arguments by some
simple analytical consideration. For very slow
rates of extension the geotherm barely changes
during rifting, because the amount of advected
heat is small compared with the conductive heat.
Therefore the phase boundary deflection will be
very small. However, for rifts with a relatively
high rate of extension, the geometrical relationship between the Clapeyron line (the phase
boundary in the P-T diagram) and the perturbed
geotherm will strongly influence the subsidence
history. This is the situation for most of the
existing basins where the instantaneous rifting
model [I] is a good approximation [42]. In this
case, the point of intersection between the
geotherm and the Clapeyron line changes with
time (Fig. 2). Thus, for a Clapeyron line lying in
the angled sector (bounded by the dashed horiin Fig. 2A and the initial
zontal line ,,z,
geotherm) the phase transition boundary moves
downwards during rifting. The shift in the phase
boundary position increases the amount of light
material (p,,,,), which causes either an uplift of
the surface or a decrease in the initial subsidence, depending on the parameters of the phase
transition.
For Clapeyron slopes which are less steep than
the geotherm and for all negative Clapeyron
slopes (Fig. 2B) the phase boundary moves up
during the rifting process. In this case the shift in
the phase boundary increases the initial subsidence.
Thus the dimensionless parameter y', which is
the Clapeyron slope ( y ) normalized to the initial
geothermal gradient (7' = yTl/(Plithlgzlifh)),determines the direction of the phase boundary
movement during rifting. The condition for the
Fig. 2A case (downward movement of the phase
boundary) is 0 < y' < 1. Other values for y' define the Fig. 2B case, which deals with the upward movement of the phase boundary. Because
strong volumetric effects among the phase transitions with negative Clapeyron slopes (y' < 0) or
with Clapeyron slopes steeper than the geotherm
(Y' > I) are not common (e.g., study of orthoclinopyroxene transition [43]), we have restricted
ourselves here to the case where phase transitions have small positive Clapeyron slopes (0 < y'
< 1).
During post-extensional thermal subsidence,
Yu.Yu. Podladchikou et al. /Earth and Planetary Science Letters 124 (1994) 95-103
the phase boundary moves in the opposite direction, and finally the geotherm and phase boundary return to the initial position. Therefore the
total tectonic subsidence is not affected by the
phase transition.
In order to assess quantitatively the effect of
the phase transition, we need to estimate the
maximum undulation of the phase boundary
Azph!. This value can be found from geometrical
relationships between a Clapeyron line and the
geotherms (initial and perturbed after instantaneous stretching). There are two cases of the
intersection between the Clapeyron line and a
perturbed geotherm separated by the configuration when the deflection point I in Fig. 2A belongs to the Clapeyron line.
The stretching factor for this configuration is
dence compared with the effect due to thermal
expansion. The other parameter H gives the ratio
of the density effect due to a single phase transition to the density effect caused by thermal expansion,
Comparing the column weights above the level
of isostaic compensation before stretching, after
stretching and after thermal relaxation yields the
following expressions for initial subsidence Sinit
and thermal post-rift subsidence Sthe,,,, [c.f. I]:
aTl plithIzlith
Sinit
=
P lithl( l - a T )~ - Psedim
1
'C
= 7'
Azp11t
+ ( 1 - yi ) * zpht/zlith
(1)
Y 1 ( P- 1)
= Zpht
* (1 - P
* Y j
(2)
For extension in which /3 > P, the intersection
of the Clapeyron line with the-flat part of the
geotherm
remains at the same depth and this
yields the following relationship:
Azp,lt =zPllt
X - ) Zlithc(
αρ
T Z
~ l i t h l l( -
w
8th1 1T~lith
$+h
lith1
For the small amount of extension ( p < P C )
the change in the phase boundary depth is given
by
*zpllt
99
m
(F-0.5)-H-
A zPht
'lith
St hermu1
=
a T 1 ~ l i t h l~ l i t h
~ l i t h l (l
- a T 1 ) - psedim
* Y' * ( z j i t l l / z p h t - 1)
There are three processes affecting the density
distribution in our model: (i) thinning of the
crust, (ii) thermal expansion of the lithosphere,
and (iii) density change due to phase transitions.
Therefore, for convenience of analysis, we will
introduce two ratios:
Setting Sinitto zero gives the criterion for
initial uplift (see Fig. 3):
and
The dimensionless parameter F quantifies the
contribution of thinning of the crust to the subsi-
We note that for the case of the initial uplift
the density of the sediments pSedirnshould be set
to zero in the expression for initial subsidence.
XL.Hd.Podladchiko~?et al. /Earth and Planetary Science Letters 124 (1994)95-103
0.5 + H-
pht
Fig. 3. F-P diagram showing the fields of parameters for initial uplift and subsidence. Expressions for parameter F at three
important points (/3 = 1, p, and infinite limit) are given in the plot.
Because of relaxation of the phase transition
boundary to the initial position during the post-rift
thermal subsidence, a different amount of
stretching (P,) is required to produce the same
amount of thermal subsidence, as in the classical
model without phase transitions (Az,,, = 0). We
can compare p, to the McKenzie stretching (P,)
by the following equations:
1 ---
-PM PB
* Y' * ( P B - 1)
-7'
*B
~ )
Zpht
*-
'lith
for PB
and
The comparison between PB in our model and
PM in the McKenzie model for different values of
H is shown in Fig. 4. This figure shows that a
given value p, corresponds to a smaller value p,
for all cases with H > 0.5 and with y' = 0.4 (Fig.
4).
Fig. 4. Relationship between the standard stretching model
of the phase transition
model. This comparison is made on the basis of the same
amount of total subsidence. H = dimensionless parameter
which measures the influence of the phase transition. H =
0.3-0.7 corresponds to the phase transition parameters for
the spinel-garnet transition in peridotite.
(BM) and the stretching factor (P,)
3. Discussion and conclusions
A regional domal uplift preceding rifting is a
common feature in the formation of intercontinental extensional basins [44-471. The simple
stretching model requires a very thin crust to
Yu.Yu. ~odladchikovet al. /Earth and Planetary Science Letters 124 (1994) 95-103
reproduce this effect. However, many rifts occur
on continents where the crust is thicker than 30
krn. This situation does not allow uplift in the
simple model. Another important problem in sedimentary basin analysis is that relatively small
amounts of crustal thinning and extension are
observed in many basins [4,48]. It is difficult for a
simple stretching model to explain the high
amount of subsidence in these basins. Both of
these observations have been explained by differential stretching of the crust and mantle [2,3].
However, the mechanism of differential stretching within the framework of passive rifting is not
so clear, because there are problems with space
and mass conservation. The differential stretching could be caused by the active upwelling of hot
mantle material [49]. This, in fact, means the
substitution of a passive model by an active rifting
model [50-521. However, according to Turcotte
and Emerman [51], it might take as much as
50-75 m.y. to thin the continental lithosphere to
the base of the crust by mantle plume impingement. Similarly, Mareschal [44] concluded that
the most reliable mechanism of uplift preceding
rifting is the ascent of an asthenospheric diapir,
but Mareschal needed to lower the lithospheric
viscosity to lo2' Pa s to satisfy the timing problem. Therefore, the above observations cannot be
accounted for completely by the existing passive
stretching models. Mechanisms of active rifting,
in turn, involve a much higher degree of complexity and a large number of poorly constrained
controlling parameters, such as the rheological
properties of the lithosphere, and too long a
duration for the process.
The model presented here can explain in a
simple way both the initial uplift and the small
amount of extension, taking into account a phase
transition with a moderate volumetric effect and
a small positive Clapeyron slope. The effect of
the phase transition is controlled by the following
three dimensionless parameters: (i) the Clapeyron slope normalized to the geothermal gradient
(f), (ii) the ratio of the depth of the phase
transition to the thickness of the lithosphere, and
(ii) the parameter H , which is a ratio of density
effect due to phase transition to the change in
density due to thermal expansion. The influence
101
of the phase transition on the subsidence history
becomes stronger with increasing values of each
of these parameters. These parameters for the
garnet-spinel transition yield the following values: y' = 0.2-0.4, H = 0.3-0.7 depending on the
M 2 0 3content in the peridotite, and a zpht/zlith
value of, say, about 0.5-0.8 (the data from [33]
were used). From Fig. 4 we see that these values
give a substantial decrease in the amount of
stretching estimated on the basis of thermal subsidence, compared with the classical model.
For this set of phase transition parameters and
a standard set of other parameters initial uplift is
feasible if ,,,z,
< z,/5
and ,f3 = P C = 1.1-1.2,
whereas for the McKenzie model the condition
would be,,,z,
<zlith/7 for the same set of parameters. Therefore our model will predict synrift
uplift after a small amount of extension for a
continental crust with a thickness of 30 krn and a
lithosphere with a thickness of 150 km. For a
greater amount of extension ( p > p*, where p* is
a critical stretching factor, p* = PC),synrift uplift
may change to synrift subsidence (see Fig. 3),
which seems to be in agreement with the typical
evolution of intercontinental rifting. Doming usually precedes rifting, and therefore we can identify it with the first phase of homogeneous regional stretching with p < p,. The second phase
of stretching (according to the traditional interpretation, this is the beginning of stretching) may
be related to the localization of extension and
formation of rift valleys. The rift valleys subside
because of much greater values of the local /3
factor ( p > P C ) compared with adjusted areas,
which can still be uplifted.
In summary, our model shows that inclusion of
the phase transition effect for existing stretching
models of sedimentary basins can give an extra
significant parameter controlling the subsidence
and the entire extensional tectonics related to
such basins.
Acknowledgements
We are grateful for discussion with B.J. Wood
and S.S. Sobolev. The constructive comments
from an anonymous reviewer were greatly appre-
102
Yu.Yu. Podladchikov et a!. /Earth and Planetary Science Letters 124 (1994) 95-103
ciated too. Paul J. Johnston kindly- improved the
English. This research was supported by the Department of Energy.
*
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