Crustal temperatures along the Central Segment of the European Geotraverse

Tectonophysrcs, Elsevier

241

195 (1991) 241-251

Science Publishers

B.V., Amsterdam

Crustal temperatures along the Central Segment of the European Geotraverse

european

V. Cermiik a, L. Bodri b, R. Schulz ’ and B. Tanner d LIGeophysrcs Insrrtute, Czechoslooak Academy ofScrences, CS-14131 Prague, Czechoslounkra h Geophysrcs Research Group. L. Eijtviis Unrversrty. H-1083 Budapest, Hunga? r Ntedersiichsrsches Landesamt fir Bodenforschung, D-3000 Hannover, FRG d Geophysrcs Instuute. Unrversriy of Keel, D-2300 Keel 1, FRG (Received

March

16, 1990; revised version accepted

geotraverse

June 22, 1990)

ABSTRACT i‘ermlk. V.. Bodn, L., Schulz, R. and Tanner, B., 1991. Crustal temperatures along the Central Segment of the European Geotraverse. In: R. Freeman, M. Huch and St. Mueller (Editors), The European Geotraverse, Part 7. Tectonoph_wcs, 195: 241-251. By mcluding the data on crustal structure, the temperature distribution was calculated for a srzeable part of the Central Segment of the European Geotraverse. A two-dimensional steady-state equation of heat conduction in an inhomogeneous medium was solved by means of the fmrte difference method, and several shghtly different approaches are compared and discussed. The data compiled on the surface heat flow together with the data from the vertical distribution of thermal conductivity and from the heat production along the EGT served to test the computation techniques and assess the resultant temperature field. It is shown that quite flat isotherms could be expected along the Central Segment with values of 800°-900°C, which are typical at 40 km deep.

The solution is assumed to satisfy the following boundary conditions: (1) T(x, z = 0) = To(x),corresponding to the

Introduction The EGT Central Segment (total length of 825 km) runs from the southern rim of the Molasse

surface temperature, which, for simplicity. was taken as 0 o C. (2) dT/dx=Oatx=Oandatx=L; Listhe length of the profile (symmetry of the temperature field at vertical boundaries). (3) Neither the temperature nor the heat flow

Basin (shotpoint D, near Chur) to the Baltic Sea (shotpoint K, near Kiel). The crustal temperatures were calculated for the southern, 500 km long, part which was used for a preliminary interpretation between shotpoints D and J (see Fig. 2); this section passes through the Alpine Molasse Basin

is known at the base of the model, and this presents a certain difficulty. Either the conditions

and Variscan units of the Swevian Jura, the South German Basin, the Mid-German Crystalline Rise, the Hessian Depression and the Leine Graben. To describe the temperature distribution in the

at depth must be estimated from other data or the problem is ill-posed and requires first the solution of the inverse problem, in which the observed

crust and the upper mantle down to a depth of about 40-50 km a two-dimensional steady-state

surface heat flow Q(x, z = 0) = Q, evaluate the heat flow at depth.

is used to

heat conduction equation was solved: a/9x( /&IT/ax) + a/&( kW/az)

=.4(x,

z)

Crustal structure and heat flow data

where k (x, z) is thermal conductivity and A( x, z) heat production; T is temperature and x, z are coordinates. The successive overrelaxation method of the finite difference technique was applied. 0040-1951/91/$03.50

0 1991 - Elsevier Science

Publishers

In order to be able to extrapolate the temperature field to a greater depth, we require a certain model for the crustal structure. This model is B.V.

247

necessary bution

for the assessment

of the thermal

duction. resents

The surface

of the vertical

conductivity

heat flow density,

the major constraint

distri-

and heat prothen, rep-

for such an extrapola-

tion.

holes and also to assess the outflow of heat from depth, we corrected the measured heat flow data for the effect of long-term

data together

with similar

tion

surrounding

countries

from

interpreted

all

in terms

the corresponding

Heat flow density

(Fig. 2) (Hurtig To calculate ature gradient mine

must

conductivity

the value of heat flow, the tempermeasured

in a borehole

be multiplied

by the

or in a deep

mean

thermal

of the rocks from the same location.

Values of heat flow density known for western Germany are shown in Fig. 1. As most of these

palaeo-climatic

The individual

There

heat flow pattern

German

mW

rnA2 (north

a few heat

Basin,

then and

was proposed

flow data

with values

of Hamburg)

(east of Hannover). pattern

were structure

et al., 1991).

are only

North

of the crustal

changes. informa-

vary

in the from

to 90 mW

50 m -’

In order to draw the heat flow

we took advantage

of our knowledge

of

---_-_---_-__ ---_ _-_-_-_ ----_-_ --__ -_-_-_-_ VF

values were determined in fairly shallow boreholes (50-300 m), all the data were corrected for surface topography. The accuracy of the individual measurements is of the order of 10%. To be able to compare

the results

from shallow

and deep bore-

temperatures in a number of deep boreholes (> 3000 m) drilled in this area (Haenel and Staroste, 1988).

northern

Few heat

flow data

and central

are available

parts of the Central

in the

German

Uplands (Rhenohercynian and Saxothuringian), where values vary from 65 to 85 mW m --*. The

(A)

(8)

-a

yc

28

Fig. 1. Heat flow data (mW m-* ) measured in western Germany. (A) Measured (uncorrected) palaeoclimatic effects.

data. (B) Data corrected

for

CRUSTAL

heat

TEMPERATURES

flow increases

ALONG

THE

to the south

mW m - ’ in the Black Forest higher

heat

flow

CENTRAL

is also

SEGMENT

and

OF THE

reaches

90

(Moldanubian).

typical

of the

EUROPEAN

system. Based on a detail analysis of conductive and convective heat transfer (Clauser and Vil-

A

Alpine

linger,

1990) and taking into account

Molasse Basin (70-95 mW me2), where most measurements were made in the lakes (Finckh.

determination

1976). The Upper

Rhine

is more likely

by a pronounced

heat

mW m-l),

Graben

(over

this high heat flow being mainly

by the convective

effects

Schmidt

is characterized

flow anomaly

100

in the

and Schulz,

granitic

the heat flow

basement

(Schell-

1990) a value of 80 mW m-’

to characterize

the basal

heat flow

here.

caused

To define the surface conditions

of a deep groundwater

8

243

GEOTRAVERSE

Central

IO

Segment

for the temperature

along the EGT calculations,

12

Fig. 2. Heat flow pattern m western Germany and adjacent areas (after Hurtlg et al., 1991) together with the posltlon of the Central Segment of the European Geotraverse and shotpomts D to K. Sites where heat flow density was measured are shown by dots.

744

the

heat

following window

flow pattern

in a 100 km wide

the EGT line and smoothed technique

(window

Techniques of temperature modelling

strip

by a sliding The two different

size 25 x 100 km) was

approaches

used.

are demonstrated

Crustal structure

a direct

problem,

lishment

of a petrological

as methods

below,

Ml and M2. Tanner which

The crustal model used for the temperature calculation was based on the preliminary interpre-

values of geothermal

tation

flow to be assessed

of the seismic refraction

points

D and

J (Aichroth,

data between pers.

the individual

shot-

commun.).

required model.

parameters

crustal

layers,

mation

on the mantle

seismic model appears in Fig. 3. The crust-mantle boundary rises from a depth of 34 km near shot-

surface

heat flow was presumed

of the profile

is shown

point D to 29 km beneath the Suevian Jura: further to the north the crustal thickness is practically

constant,

at

29 f 1 km.

The

cover is 4-5 km thick in the south,

sedimentary 2-3 km along

the major part of the profile, and increases again to 5-6 km in the north below the North German Lowland. A quite specific feature of the whole investigated part of the EGT Central Segment is a pronounced low-velocity zone (up - 5.5-6.0 km s - ’ ) ranging in thickness from 3 to more than 5 kilometres which characterizes the middle part of the crust in the depth range 7-20 km. Towards the

(1989) has solved first the estabthe characteristic to be ascribed Cermak

to heat and

when no cl-pnorr mfor-

in Fig. 2 and the

location

to here

and the mantle

independently.

Bodri solved the problem

The

that were adopted

and are referred

heat flow was available.

The

to be the sum of

two components: Q, = Q, + QM. where Q, was the crustal contribution by heat sources within the crust, and QM was the mantle (Moho) heat flow. By repeated calculation of the surface heat flow corresponding to the model Q, starting with an arbitrary value of QM and successively correcting the calculated QM- value using the difference Q,Q,, the conditions on the lower boundary could be set. Re!UltS Method MI

Alps the character of the lower crust changes: the average velocity here is low, at only about 6.2 km

In addition to the above seismic crustal model, Tanner used petrological investigations on xeno-

s-‘,

liths (Mengel, 1990) to assess the heat production at depth for the Northern Hessian depression, and

which is in distinct

6.8-7.2 km s-’ Prodehl, 1989).

contrast

to the values

more to the north

(Aichroth

of and

also the date of Sachs (1988) for the southern

ALPINE MOLASSE

South

I-J

LEINE SUEVIAN IuI)A I.llo GEAMAN RISE BASIN SOUTH GEAf-lAN BASIN HESSEN DEPRESSION

100

200 DISTANCE,

Fig. 3. Simplified

preliminary

2D seismic velocity distribution

300

430

part

GRABEN

500 North

km

along the EGT Central Segment after Aicbrotb

commun.).

and Prodehl. (pers.

CRUSTAL

TEMPERATURES

ALONG

THE

CENTRAL

SEGMENT

OF THE

EUROPEAN

DISTANCE,

5

245

GEOTRAVERSE

km

N

250 a

500

I II

E Ir:

I t% 501

V

-

s

E

F

Fig. 4. Fwe-layer

of the studied

EGT

section.

was

(Fig.

4) to calculate

proposed

temperature

field. Layer

crustal

H

model used for direct solution

A five-layer

I corresponds

G

model crustal

a constant the entire

to Meso-

production

the

I

by Tanner

Lhot p0in.r

(see text).

mantle heat flow of 50 mW mP2 along section studied. In addition the heat distribution

within

the

individual

zoic and Cenozoic sediments, its thickness increases towards the Alpine Molasse Basin in the

crustal simple

south and towards the North German Basin in the north. A velocity isoline of 5.4 km s-l marks the

in the whole corresponding

bottom of this layer. The composition of layers II and III is highly problematic and has not yet been

layer, and (c) exponentially decreasing heat production within each layer with specific. values of

satisfactorily defined. Layer II, here marked as an upper crustal sialic layer, corresponds to seismic velocities increasing from 5.4 to 6.3 km S-I and is underlain by a low-velocity zone (layer III). This latter zone corresponds to the mid-crustal metamorphic layer and is characterized by up = 5.3-6.3 km s-‘. A mafic granulite layer (IV) follows,

the logarithmic decrement. The results of temperature modellmg are illustrated in Fig. 5. There are no considerable

which has velocities of 6.3 < up < 7.3 km s-’ and which reaches down to the Moho. The upper mantle

(layer

V) is supposed

to have peridotite

composition. The following value of the thermal conductivity (W rn-’ K-l), specific heat (J gg’ K-‘) and heat production (pW mP3) within the individual layers were used for the temperature modelling: layer I: 2.3, 1.0, 0.8; layer II: 2.6, 0.85, 1.61; layer III: 2.7, 0.8, 0.85; layer IV: 3.6, 1.0, 0.2; and layer V: 3.8, 1.0, 0.015. These data are based on the information assembled by numerous authors in LandoltBornstein (1982) and on personal from Haak and Mengel.

communications

In order to calculate the crustal temperatures several models were tested to show the likely differences obtained from different approaches. To estimate the mantle heat flow, two possibilities were considered: (1) assessment of the heat flow from depth by applying the 1D calculations from Lachenbruch’s (1968,197O) model of a continental crust from known surface heat flow, and (2) use of

layers was considered in different ways: (a) exponentially decreasing heat production

differences individual

crust, (b) constant heat production to the values above within each

in the shape of the isolines among the models. Model 5A gave the highest

values of over 1000” C at 50 km deep (about 700°C for the Moho temperature). The minimum temperature gradient in the near-surface layer is 32 mK m-‘; the maximum value is 38 mK m-‘. Deeper in the crust this range decreases to 24-30 mK m-‘. Model 5B is considered the most reliable, the temperature gradient ranging from 31 to 37 mK mP1 near the surface and from 23 to 30 mK rn-’ deeper in the crust. Moho temperatures are

10-20”

C lower

compared

with

model

Model 5C gives the lowest with a difference of about

crustal 50°C

mantle

boundary

to the other

Method

M2

compared

5A.

temperatures, at the crust/ models.

The results of the seismic modelling were used by Cermak and Bodri to define individual crustal layers of specific seismic velocities. The experimental relationship (Rybach and Buntebarth, 1984) between seismic velocity up and heat production A was then employed: In A = 13.7 - 2.17 up (A in PW m-3, ur, in km ss’) to describe the heat production distribution along the studied

I i-

a LLI

n

DISTANCE,

km

Fig. 5. Results of temperature modelling by direct solution. (A) Moho heat flow calculated from a ID model, heat production exponentially decreasing in the crust, A, = 2.5 PW rne3, D = 10 km (B) Constant Moho heat flow of 50 mW rn-’ and constant heat production in each crustal layer. (C) Constant Moho heat flow and exponentially decreasing heat production in each layer.

CRUSTAL

TEMPERATURES

EGT

segment.

priori

petrological

conductivity

ALONG

THE

In contrast model

CENTRAL

SEGMENT

OF THE

to method

MI, no a-

was necessary.

Thermal

was taken as temperature

dependent,

EUROPEAN

where T(z ) and P( z ) are temperature and pressure conditions at the depth for which the conversion is used and u = -6.802

k = k,(l + CT))‘. k, being the thermal conductivity in surface conditions and C the experimen-

b=

-1.686~10~”

s-’

and

tal parameter.

lated

The relationship lished

between

empirically

processed

and

laboratory

are, regardless

data

and

certainly

reflects

only

Fountain

statistically samples

subject

that

to limita-

The use of the u,-A

means

rela-

a degree of speculation

the general

and A distributions critical comments

A was estabon

on rock

of their number,

tion of representability. tionship

up and

is based

tendency

of the up

in the continental crust. Some on its validity were raised by

(1986) and were followed

by discussions

241

GEOTRAVERSE

km

d = 25 MPa

X

s-’

lo-’

K-‘,

km s-’

Kp2.

c=O.135

are the coefficients

for a large set of crustal

km calcu-

and upper

mantle

rocks. The conversion very problematic) several

factors:

technique cannot in the uppermost high and highly

derivative

of seismic

pressures,

the existence

tures

allowing

water

velocity

be used (or is crust due to

variable at

of rmcrocracks

penetration

pressure

relatively and

and

low frac-

subsequent

redistribution of radioelements, and also often an extremely complicated geological structure to-

of Rybach and Buntebarth (1987) and Fountain (1987). The nature of the up-A relationship has not been explained satisfactorily yet and there may be large deviations when the relationship is

gether with a highly variable field of seismic velocities. Therefore, the “UTK layer” (upper ten kilometres) was treated separately and the conversion technique was only used below 10 km (Cermak. 1989).

applied to randomly selected groups of rocks (e.g. see Kern and Siegesmund, 1989). With careful subdivision or re-arrangement of the experimental material, however, the reported disagreement can

In the UTK layer knowledge of the distribution of heat production was based on the formal combination of two empirical findings: (i) the concept of heat flow provinces (linear relationship between

be smoothed (Cermak et al., 1990a). As no direct information usually exists to describe the radioac-

surface heat flow and near-surface heat production) described by Lachenbruch (1968) and Roy et

tivity

al. (1968). and (ii) the 40&60% partition crustal contribution and mantle heat

of the deeper

parts

of the crust,

the ~lr-A

relationship (Rybach and Buntebarth, 1984) may be used as it provides the only opportunity for improving our knowledge in this Laboratory determinations of ity used to establish the u,-A carried out (T - 20 o C, P - 100

respect. the seismic velocrelationship were MPa). Before the

or-A conversion technique can be applied on the in-situ ~‘r observations, the temperature and pressure effects on seismic velocity must be assessed. For this purpose Rybach and Buntebarth (1984) introduced a correction factor. Here, to assess the corresponding correction as a function of depth the pressure (P) and temperature (T) dependences of wave velocity were considered by an integral approach, based on the P and T dependencies of the derivatives: dv,/d P = f(P),dv,/dT =f( T) (Cermak et al., 1991). The correction function C( Z) was proposed, as follows:

C(z)=h[20-T(z)] +c{ln[lOO+d]

++[400-T’(Z)] -ln[P(z)

+d]}

between flow, re-

vealed by Pollack and Chapman (1977) Two simple relationships for the surface heat production A, can be thus obtained: (a) A, = 0.4Q,/D and (b) A, = 0.4Q,/(i - e-’ )D respectively. Here Q(, is the observed surface heat flow and D is the logarithmic presumed,

decrement (= 10 km). It is further that the heat production within the

UTK layer decreases exponentially (Lachenbruch. 1968). Version (a) of heat production within the UTK layer involves radioactivity in the lower crust and thus corresponds to a higher Moho heat flow (by 6-10 mW me2) and higher crustal temperatures (by 50-80°C) compared to version (b) and was preferred by Cermak and Bodri (1986) as being more realistic. Certain problems are connected with the existence of low-velocity zones within the crust. As the nature of these zones has not been satistfactorily explained, it is a question of how to interpret the experimental relationship between seismic

velocity

and heat productlon

here. Two extreme

cases were discussed by Cermak (1989): (1) either to accept that the lower seismic velocity corresponds

to increased

Rybach

and Buntebarth’s

interpolate velocity

heat

the heat

production, formula

~~~~~~

i.e. to use

as it is, or (2) to

production

within

zone from the data above

this case two-dimensional

f ;

the low-

and below.

spline interpolation

In was

used.

m TEMPERATURE .‘C

am

0

-

I

ICC

0

&

ail

m

&I

km

DISTANCE, km

Fig. 7. Comparison to several additional

of the crustal temperatures corresponding models.

near-surface

radloactivity

interpolated

heat

Model

in the

production

Models lb and 2b correspond radioactivity

m

2a distribution

wIthin

the

low-velocity

to distribution

within

the low-velcuxty

zone.

(b) of near-surface

in the UTK layer and a different

up- A conversion

(a) of

UTK layer (see text) and

treatment

zone similar

of the to that

used in models 1 a and lb.

SEISMIC VELOCITY, km I-’

As mentioned 0

above, the thermal

were taken in the form k = k,(l the following numerical values:

3E ?Pa

conductivities + CT)-‘,

with

3

0

upper

crust

C=O.OOl THERMAL CONDUCTIVITY,

W m-‘K-’ 2

25

3

35

(up ~6.8

km

s-l):

k, = 3 W m-’

K-’

and

K-’

lower crust (6.8 c up I 7.9 km s-l):

k, = 2.0 W rn-’

K-’

and

C-OK-' upper

mantle

(u,, > 7.9 km s-‘)

k. = 2.5 and

C = -0.OOQ25

K-’

The resulting temperature field to&&her with heat the distributions of the thermal conductivity, production and also the comparison of the : observed and calculated heat flows, the Moho heat fg.

6.

Model

Results of temperature modelling by the inverse method. la corresponds

the near-surface

to the application

radioactivity

within

of distribution

the UTK

and gives a higher Moho heat fiow. Within zone, Rybach

and Buntebarth’s

layer (see text) the low-velocity

u,- A conversion

as It IS, I.e. lower velocity corresponds

(a) of

was applied

to higher radioactivtty.

flow and crustal contribution to the surface heat flow are shown in Fig. 6. To test the effect of (i) higher heat production in the near-surface layer of 10 km (lower Moho heat flow) and (ii) the different approach to the nature of the low-velocity

CRUSTAL

TEMPERATURES

THERMAL

ALONG

CONDUCTIVITY,

THE

CENTRAL

SEGMENT

OF THE

ms’Kd

W

EUROPEAN

upper

0

249

GEOTRAVERSE

mantle

case vaiues

is demonstrated similar

to those

layer V in her model

20

10

.“C

2

25

3

35

for

Ml (see above} were used.

2

The results

obtained

vealed relatively

using

flat crustal

ally higher temperatures al

DISTANCE.

Fig. 8. Deep temperatures lower

by Tanner

Conclusions TFMPFRATLJRE

with

in Fig. 8; in this used

km

corresponding

model

la,

but with

crust

and

upper

hqh

thermal

mantle

to a model conductlvitles

to resemble

the data

in the used by

Tanner.

fields thermal

compared (Fig. 7). conductivity in the

SEISMIC

‘+.-i-+4

0002 ALPINE

which correspond

to the surface heat flow pattern. calculated

at 40 km deep reach

o C in the south (surface

mW rn-*) compared with mW md2) in the north. disagreement between the difference between Moho

heat flow Q - 95

650-750

o C (Q - 65-70

There is no s.ubstantial two methods used: the temperatures calculated

Due to parameters

M2 (Figs.

the uncertainties in the individual entering the calculation procedure,

such as surface

heat

flow, thermal

conductivity,

km,s-’

VELOCITY,

1t- +-- .~4

002

02

MOLASSE

1 BASlN

I

GERMAN

0002 002 SUEVIAN

a2

0002 002 RfSE

-2

I

JORA

’ t-e

adorn MID

in the south,

by method Ml (Fig. 5) and by method 6-8) are within the range 100-200 o C.

zone on the calculated crustal temperatures, several additional models were proposed and their corresponding temperature The effect of higher

were found

re-

and gener-

The temperatures 800-950

identical

our calculations isotherms.

02

SOUTH

02

GERMAN

1 BASIN

0002 002 MID

1

HESSEN

DEPRESSION

HEAT

GENERATlON,

Fig. 9. Heat pr~uction-seismic

0002 002

velocity-depth

l_ElNE

GRABEN

JJW. rnh3 profiles

along the EGT Central

Segment.

GERMAN

02

1

RISE

-I

750

TABLE Heat

1

flow characteristics

values correspond UTK m

1

layer

of 1D heat production

to dtstribution

(see text). All heat

models.

(a) of heat production flows data

All

m the

are gwen I” mW

Cermak,

Heat flow

Heat flow

Moho

heat

from UTK

from below

heat

flow

layer

UTK

flow

97

24.5

46

26.5

Shot-

Surface

point

and Eastern

V. and Bodn,

lithosphere Central

-

D

flow m Central 195-215

L., 1986. Temperature

and Eastern

mal Modelling

Europe.

Cermak,

V.. Bodn.

Relationship tions:

L.. Rybach.

between

comparison

83

21

22.8

39.2

22.5

23.4

43.1

G

83

21

21.3

40.7

productton

H

79

20

19.0

40.0

dence. In: V. Cermak

I

72

18.2

18.5

35.3

and Lithosphere

J

70

17.7

22.6

29.6

Earth

Planet.

Cermak,

Clauser,

strated

and especially heat production, as well as the uncertainty in the reported data on the crustal structure and seismic velocities, no fixed error bars of calculated temperatures can be given. Only the comparison of various approaches to calculate the temperature-depth distribution can give an insight in to the relibility of each such a technique, and the above range of 10&200°C corresponds of the temperature

L and Rybach,

heat

Dissert

heat production A( I) profiles (Fig. 9). Regardless of the considerable scatter and the existence of the low-velocity zone in the crust which complicates the use of the conversion technique, this conversion enabled a detailed calculation of the Moho heat flow and of the heat contribution of the individual crustal layers (Table 1). The Moho heat flow along the Central Segment of the EGT varies from about 30 mW m-* to over 40 mW m-* and the crustal contribution to the surface heat flow due to radiogenic heat sources is 40-60 mW m-‘.

Fountain,

seismics. Data

In:

Extended

Compilation

and

abstracts, Integrated

Sixth

EGT

Interpreta-

tion. Einsiedeln. Cemrak,

V., 1989. Crustal

D.M.,

and mantle

heat

produc-

heat

(Editorb),

depen-

Heat Flow

Berlin, pp. 23-69. of conductive

in a sedimentary Geophys.

basin

and

demon-

J., 100: 393-414. in Randalpenseen.

1986. Is there a relationship for crustal

between

seismic

rocks? Earth Planet.

Sci. Lett., 79: 145-150. Fountam, and

D.M., heat

1987. The relation

production-reply.

between

Earth

seismic

Planet.

velocity

Sci. Lett.,

83:

178-180. Haenel,

R. and Staroste,

mal Resources Swttzerland. Hurtig,

Kern,

E. (Editors).

in the European Schaefer,

E.. Cetmak,

V., Haenel.

Lachenbruch,

and

Geophys.

Res.. 75: 3219-3300.

Mengel,

Rybach,

Hessian

Rybach,

temperature

Physical

heat

and heat proflow relation.

Properties

xenoliths

J.

of

Rocks.

Springer,

Berlin,

from Tertiary

Depression:

Conttib.

and

Mmeral.

Chapman,

Petrol.,

D.S.,

volcanics

Petrological

of

and chem-

104: 8-26.

1977. Mantle

heat

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