Experimental geodynamical models relating to continental drift and orogenesis

T~~tonophysics,

19 (1973)

0 Elsevier Scientific

EXPERIMENTAL CONTINENTAL H4NS

RAMBERG

105-132

Publishing

Company,

Amsterdam

GEODYNAMICAL DRIFT

and HAKAN

~ Printed

MODELS

in The Netherlands

RELATING

SJGSTRiiM

University of Uppsala, Uppsala (Sweden) and University of Connecticut, University of Uppsala, Uppsala (Sweden) (Accepted

for publication

TO

AND OROGENESIS

February

Storrs, Conn. (U.S.A.)

9, 1973)

ABSTRACT Ramberg, H. and Sjostrom, H., 1973. Experimental geodynamical models relating to continental drift and orogenesis. In: E. Irving (Editor), Mechanisms of Plate Tectonics. Tectonophysics, 19(2): 105-132. After introductory comments on scale-model theory, descriptions and discussions of experimental models of continental drift and orogenesis are presented. The driving mechanism of the models is the spontaneous overturn in layered systems with gravitationally unstable density stratification. The pattern of the overturn movement is similar to thermal convection currents. A model Pangaea breaks in tension above the upwelling branches of the overturn cells in the model mantle, and the fragments are set adrift by the horizontal limbs of the current. Though buckling occurs along the leading edges of the wandering continental fragments, this fold structure is not of the kind encountered in natural orogens. The latter kind of structures - including basement upheaval, batholith intrusion, nappe formation etc. - is generated in models with no net horizontal shortening across the orogen.

“Though the primary direction of the force which thus elevated them must have been from below upwards, yet it has been so combined with the gravity and resistance of the mass to which it was applied, as to create a lateral and oblique thrust, and to produce those contortions of the strata, which, when on the great scale, are among the most strikingand instructive phenomena of geology. ” John Playfair: Illustration of the Huttonian Theory of the Earth, 1802.

THE EXPERIMENTAL

METHOD

The effect of the gravity force relative to the pressure force on the motion of rocks and mantle materials increases with increasing mass of the moving and deforming parts. Likewise gravity as an active force in geodynamical

processes becomes increasingly

effective rel-

ative to the viscous resistance and the strength of the materials as the mass of the system increases. These relationships are explicitly shown by the following two force ratios (Kline, 1965), which are applicable to models in which gravity plays a significant role:

(1)

106

H.RAMBERGANDH.SJijSTRijM

and:

Fg_P12g ---_ F,

(2)

w

Each of these force ratios has to be equal when taken at corresponding dynamically

points in several

similar systems in which neither of the three forces: the gravity force, the pres-

sure force and the viscous force are negligible. In the above expressions p is density, 1 a defined linear dimension

in the system, g acceleration

and v velocity of motion.

due to gravity, p pressure, p viscosity

Fg, F, and Fv stand for the gravity force, the pressure force and

the viscous force (Kline, 1965), respectively. Another condition of course that the systems compared are geometrically similar. For systems consisting of materials with equal corresponding

for dynamic similarity is densities we see that the

gravity force increases with the geometric dimensions all other things being equal. For regional and global-scale geologic structures such as erogenic belts and continents or oceans 1 is of the order 107-lOa cm, while in a convenient laboratory model I is more likely to be of the order 10 cm. The density of most rocks varies between 2.5 and 3.3 g/cm”. Model materials of the kind generally used have densities between 1 and 2 g/cm3. g is the same in the upper part of the earth’s mantle and in the crust as in a model resting on the laboratory table, viz. 981 cm/set’ . We have thus reasonable numbers to put in the nominator

of eq. 1, The denominator

p needs perhaps special consideration.

much the pressure itself which is important

It is not so

in a dynamic sense, but rather pressure differ-

ences, &. But if the ratio pig/p is to be the same in a natural structure and in a dynamically similar model at corresponding points then indeed one can show that the ratio pIglAp is also the same in model and nature when considered

at two corresponding

points between

which the pressure difference is Ap. Furthermore a pressure difference in a system generally corresponds to shear stresses (unless the pressure difference happens to correspond to hydrostatic

equilibrium).

For dynamic similarity to prevail it can be shown that these shear

stresses ri must be related in the model and in nature as are the quantity

pig in the two sys-

tems. Hence the ratio: Pk -

(3)

'i must also be the same when compared at corresponding points in a natural structure and in a dynamically similar model. Equality of the force ratio must also be fulfilled if ri is replaced by the shear strength, s, of the materials. Rocks in nature, e.g., in the state of regional metamorphism, are believed to deform at stresses much less than their strength as measured in the laboratory. The latter is of the order 1000 bar for silicate rocks (Clark, 1966). We do not believe we are underestimating the yield strength of many silicate rocks undergoing metamorphism if we put it at say 100 bar (= 9.81 * lo7 dyn/cm2) or even 10 bar. Hence for global-scale dynamic systems whose linear dimension is of the order lOa cm (= 1000 km) and density 3 g/cm3 the ratio:

EXPERIMENTAL

GEODYNAMICAL

. -Pk is of the order s

For a gravity-driven

107

MODELS

3 * lo8 * 981 9.81 . 1o7 = 3 * lo3 dynamically

similar model with p = 2g/cm3 and I= 10 cm the yield

strength, s, of the proper model material is then determined 2 * 10. 9gl=

--___

3 .

by putting:

1o3

s

The dynamically

correct strength of the model material is then:

s = 6.54 dyn/cm2,

or 6.54 - 10e6 bar

This is the strength of a material so weak that it will yield under its own weight even in pieces less than 1 mm across. It is obviously impossible to build anything but the very simplest models of this kind of materials because a model complex enough to represent even a rather plain geologic structure will simply collapse under its own weight before the construction

is finished.

We reach a similar practical obstacle when considering model materials must show. To determine

the viscosity which properly scaled

the viscosity conditions

the force ratio above

(eq.2) is useful. For the global-scale structure we take p, I andg as above. A viscosity of the order 10” poises is not perhaps unrealistic as a sort of average for the lower crust and the upper mantle though we shall not forget that much lower effective viscosities have been determined of some rocks in the laboratory,p of the order as low as 10’4-1015 poises are for example recorded for limestone and rock salt (Clark, 1966). For global-scale dynamic processes such as continental drift velocities of the order 1 cm/year (a 3 - lo-’ cm/set) seem realistic. Inserted in eq. 2 these values give the ratio between the gravity force and the viscous force in the natural system: p12g_ 3 * 1016 * 981 --/.U 10Z2 -3. 10 _s = 9.81 * 10“ For the model we select p = 2g/cm3, I = 10 cm as above, and of course g = 981. We wish that the model develops with a reasonable spead under the force of gravity, v may for example be of the order 1 cm/day which is approximately

10V4 cmlsec. The scale-wise correct vis-

cosity of the model material follows then from the force ratio: p12g_ 2 * 102 * 981= 9.81 . /J * 1o-4 W

v-

IO4

* lo8 = 2. lo4 poises Hence: p = 19.62 9 8l . 1o4 This is the viscosity of a very thick oil or a soft asphalt. It is clearly not only unconvenient but often physically impossible to use this kind of materials to prepare models of complex global structures consisting of many kinds of rocks in intricate juxtaposition. To overcome the experimental obstacles caused by the small strength and low viscosity

108

H.RAMBERGANDH.SJbSTRiiM

of the materials as required for models exposed to gravity as the only body force, we run our models in a high-capacity 1967, 1971; Stephansson,

centrifuge (for description

negative of the centripetal-acceleration the acceleration

of the apparatus see Ramberg,

1972). The reaction against the centripetal

acceleration

(i.e., the

vector) plays the same role in the models as does

due to gravity in nature. In the centrifuged

models the two above-men-

tioned force ratios take the forms pla/p and pZ’a/pv where a is the centripetal

acceleration

affecting the model while it is whirled in the machine. At dynamic similarity between model and nature the conditions:

4lGL =__md-PITl 4TlaITl 4lG4l 4nclaIn snl

s”

41v*

4nvm

must be fulfilled. Here subscript ‘n’ refers to the natural geologic structure,

‘m’ to the mod-

el. Since the acceleration a, in our machine is up to 4OOOgn it follows that the strength, sm, and the viscosity, pm, of the model materials can be up to 4000 times larger than these properties of the materials in an otherwise identical model not run in the centrifuge. This circumstance enables one to study scale models of intricate geologic structure not susceptible to experimental tests by other means. It is of particular value that the method permits us to study model structures different

containing

any number of unlike rocks or earth materials with

densities, viscosities or strengths. Since there is practically

no sagging of the rather

strong materials during the construction of the initial structure of the models, the initial pattern - which of course has to be potentially unstable in a body-force field - can be made as complicated as we wish in order to conform to the natural situation. The dynamic evolution of the model is confined to the period of centrifugation. Thus the finite structure can be scrutinized to any desired degree after the run. It is fortunate that we can disregard the inertial forces in flow processes involving crystalline rocks and mantle materials. Because of the high effective viscosity of the plastically flowing rocks and their slow motions, the inertial forces are negligible as demonstrated by the small value of Reynold’s number. Reynold’s number is a force ratio much used in ordinary model studies of fluid flow. It relates the inertial force to the viscous force (Kline, 1965):

Inserting

the values for v, I, p and /J as used above for the global processes we obtain:

This is a negligibly small value of Reynold’s number. When inertia becomes significant in fluid flow the smooth laminar flow changes to irregular turbulent flow. For flow of fluids through tubes it has been shown experimentally that turbulence does not occur when Re < 1000 (Prandtl, 1934, p.34) even if large disturbances occur in the fluid prior to en-

EXPERIMENTALG~ODYNAMICALMODELS

109

tering the tube. The disturbances

the

are damped in the tube if Re G 1000, and ultimately

flow becomes laminar. Even though flow of rocks and mantle materials does not take the shape of tubes (except in the trunks of diapirs), there is no chance that turbulence

can occur at a Reynold’s

number of the order lo-‘*! As long as the Reynold’s number is much less than the critical value for the transition: l~l~nar

how-turbulent

onstrating

flow both in the natural system and in the model - thereby dem-

negligible inertial force relative to the viscous force - it is not necessary that the

Reynold’s number be the same for the two systems to be dynamically To get a rough check on the Reynold’s number in our centrifuged the values for Y?I, p and y as used above for the models.This

This is about 10 orders of magnitude

similar. models we employ

gives:

below the critical Reynold’s value. Hence, even though

Re is very different in the models and in the natural structures both values are so small that inertia can safely be disregarded,

and there is consequently

no need to attempt

to obtain

matching Re-values in model and “prototype”. THEMODELS

Introduction Since the senior writer started to use the centrifuge method some 12 years ago in Chicago the evolution of a large number of geologic structures has been studied in the Uppsala laboratory (Ramberg, 1963, 1967, 1971, 1972a; Stephansson, 1971, 1972; Berner et al., 1972; Hall and Sjostrom, unpublished works). The present report is, however, confined drift. We shall focus the attention

particularly

to models related to the theory of continents on two phenomena

believed by many earth

scientists to be closely related to the wandering of continents, viz.: (1) thermal convection or other density-overturn processes in the mantle; and (2) the evolution of erogenic belts, The convective overturn in the mantle is probably the most seriously considered driving mechanism supposed to keep continents moving. Fur~ermore, the plate-tectonics idea holds that erogenic belts are intimately connected with our wandering continents: the erogenic fold belts rise in front of the leading edge of the continental blocks much like the bow-wave of, say, a blunt-bowed giant landing craft. Our exper~ents show rather convincin~y that a density overturn in a gravitation~ly unstable mantle may well create lateral tension in the solid crust sufficient to cause a splitting above the upwelling branch and a drifting apart of the fragments. In the same experiments a bow-wave of folded surficial layers also often forms along the leading edge of the spreading fra~ents. However, this fold structure is but super~ci~y comparable with the structure encountered in natural erogenic belts.

110

H. RAMBERG

AND H. SJhTRijM

On the other hand, the latter structure with its characteristic intricate pattern of nappes, granitoid batholiths, folds and faults etc. is strikingly simulated in experimental models which are not necessarily

connected

with continental

drift or with lateral compression

across the erogenic belt. Some of these models will be discussed below.

Mantle diapirism The experimental

models have been constructed

based on the hypothesis

either in the mantle or in the sub-crustal low-velocity continents

adrift. We note in this connection

layer is the mechanism

that the movement

that diapirism which sets

pattern characteristic

for

diapirism is very similar to the pattern characterizing thermal convection, though diapirism is not necessarily connected with a super-adiabatic thermal gradient. Moreover, in diapirism - contrary to the situation in thermal convection - the flow comes to a stop as soon as the initially unstable density stratification has been overturned to the gravitationally stable arrangement.

Rise of the low-velocity layer A particularly simple model stems from the assumption that the low-velocity layer, which according to many seismologists (e.g., Gutenberg, 1959; Press, 1970; Anderson and Sammis, 1970), now seems to be a reality, is not only more mobile (lower viscosity) than the overlying mantle, but also less dense. On this assumption the low-velocity layer tends to rise in the form of anticlines and domes or diapirs which spread underneath the crust thereby forcing the latter to move horizontally. A difficulty with this model is, however, that the dominant wavelength of the rising turbations - and consequently the spacing between the diapirs - is generally too small fit global-scale structures. The dominant wavelength of an unstable system of this kind pends upon the thicknesses of the various layers, their relative viscosities (provided the terials behave as Newtonian ry of gravitationally

materials) and their densities. (The general fluid-dynamic

perto dema-

theo-

unstable systems has been developed by Lord Rayleigh (1900), Taylor

(19.50), Chandrasekhar

(1955)

Hide (1955)

Biot (196.5), Ode’(1966),

Ramberg (1967,

1968a and b, 1972a and b) and others,) Under otherwise identical conditions wavelength increases with in.creasing thickness of the buoyant with increasing thickness of the overburden.

the dominant

layer and, within limits, also

In most systems the wavelength also becomes

larger when the viscosity ratio between the overburden

and the buoyant

layer increases.

The low-velocity layer appears to be about 100 km thick (Press, 1970; Anderson and Sammis, 1970), existing at a depth of some SO- 180 km. In a numerical analysis we assume a crust 20 km thick with density 2.80 g/cm3 and viscosity 10z3 poises, resting on a layer 60 km thick, with density 3.50 g/cm3 and viscosity 10z3 poises below which a 100 km thick low-velocity layer exists with density 3.35 g/cm3 and viscosity 102’ poises. The substratum has a density 3.60 g/cm3 and a viscosity 1O22 poises. To complete the model the surface is supposed submerged below an ocean with density 1 g/cm” and negligible viscos-

0.2 31.4 628 km -0.11699 -0.009/0.224/1/0.00018 2.077 - 10-‘s yf cm&c

2 - lo6 cm 10z3 poises 2.8 g/cm3 0.5/2l6/1~/~ 0/1000/1000/1/100 l/2.8/3.5/3.35/3.6 -1.7756 - 1614/sec

._. ._--_-.-.-~

2 - lo6 cm 10z3 poises 2.8 g/cm3 OS/2161 lo/” o/106/106/1/105 l/2.8/3.5/3.35/3.6 -1.7756 * 10-14/sec

Model 2

__.

~-~~-

2.106cm 1O23 poises 2.8 g/cm3 o.~/2iloll~l~ 0/1000/1000/1/100 l/2.8/3.5/3.35/3.6 -1.7765 * 10-14/sec

Model 3

---.

2 - lo6 cm 1O23poises 2.8 g/cm3 0/2/10/10/~ 0/1000/1000/1/100 O/2.8/3.5/3.35/3.6 -2.7468 * lo-r4/sec

Model 4

- -- .---------..--

0.045 0.121 0.125 $,,lhz 139.6 52 50 %?r 2790 km 1040 km 1000 km Kr -0.11832 -0.210541 -0.13526 Yl/YZ/Y3/y4 -0.0106/0.241/1/0.00003 0.011/0.176/1/0.007 0.0078/0.174/1/0.007 vi* = kr9rYi 1.985 * lo-r5 Yj cm/set 3.738 * 10-r’ J’j cm/see 3.715 - lo-i5 yrcm/sec - ..__--..-. .-___ -.._-______. -.. ...~ * Vigives the velocity or rise of the amplitude in cm/set at interface i when the amplitude Yj is given in cm. This is only valid when neither of the four amplitudes is larger than 10% of the dominant wavelength, A,.

42 = 2nhz/k,,,

output data

qr = 'h-p2WW/ez

di’Z/P3/&‘4/PS

fl1/~2//‘3/c(4/&

Irz ~~/h~/h3,~~,hs

hz

Input data

Model 1

Theoretical models of the rise of a buoyant low-velocity layer

TABLE I

.

t

E;

112

H. RAMBERG AND

Sea

h,= 5km

PI -0

p, =1.0g/cm3

Crust

h,= 20 km

g2 =102$oises

p2 = 2.8 g/cm3

Monlle

hj=60

~3z1023poiscs

p3=3.5

)L& rlO**poises

pr -3.35

~s=1022poises

p5=3.6g/cm3

tow velocity layer

Mantle

h,=lOO

hg= m

km

km

H. SJiiSTRiiM

g/cm3

g /cm3

Fig. 1. Idealized layered arrangement in the earth’s crust and the uppermost part of the mantle.

ity (relative to that of the crustal layers). From top to bottom ocean, are numbered from 1 to 5 in Fig.1. As shown in Table I this model has a dominant

the layers, including

the

wavelength equal to 628 km. This will

also be the spacing between the ridges or diapirs which rise spont~eously

from the low-

velocity, low-density layer provided that the various layers in the model are homogeneous and uniform in thickness. If the Mid-Atlantic Ridge is in fact caused by an anticline spontaneously rising from the low-velocity layer the dominant wavelength of this unstable system must be larger than some 3000 km, otherwise several parallel anticlines or oceanic ridges should form in the Atlantic whose average width is about 6000 km. With a dominant wavelength 3000 km or more the Mid-Atlantic Ridge could coincide with the crest of a rising anticlinal diapir whereas the two neighbor anticlines on either side of the central ridge would be underneath the continents and therefore either suppressed or not readily detectable. If the viscosity ratio between the overburden and the low-velocity layer is greater than lo3 -,which, however, seems unrealistic - the dominant wavelength will be larger, see Table I, model 2. This is a general rule for systems of this kind as demonstrated

by numer-

ous c~culations and ex~rimenta1 tests (Ramberg, 1968 a, b; Berner, 1972; Steph~sson, 1972). A thicker overburden and/or a thicker low-velocity layer will also give larger wavelength at the same viscosity and density conditions. So, for example, if the layer just above the low-velocity layer is 100 km thick rather than 60 the wavelength increases to about 1000 km as recorded in Table I, models 3 and 4. In this table h is thickness, /1 viscosity, p density, h, dominant wavelength and K 1 the important eigenvalue of the system which determines both the dominant wavelength and the velocity of rise vi of the ~plitudes~i.

EXPERIMENTAL GEODYNAMICAL MODELS Air

P, =O

PI =0

hl

113

pi= 3.39 /cm3

Uppermantle

h, = 1OOOkm g2= 10”

poises

pi= 4.2glcm3 Low-density

Lower

layer h, =lOOkm

mantle

h‘ .=

~3=10’6,101g,1022poises

fib= 10ZZpaises

p3 :3.9g/cm3

pi=4.2glcm3

PI/=5.5gkm3 fig.2. Low-density layer located at 1000 km depth in the mantle.

Rise of a deeply buried layer Numerical calculations For given thickness

of a buoyant

layer, and given density and viscosity contrasts

maxi-

mal dominant wavelength is obtained if the thickness of the overburden equals or exceeds a certain limit. Beyond that limit further increase of the overburden thickness does not affect the wavelength.

On the basis of this general rule we have studied numerically

namic behavior of a buoyant

layer located at 1000 km depth in a hypothetic,

the dy-

homogeneous

mantle, Fig.2. In all models the mantle both above and below the low-density layer consists of a material with viscosity 10” poises and a density which because of compressibility changes from 3.3 g/cm3 at the top of the upper mantle to 4.2 glcm3 at the contact with the buoyant layer, and from 4.2 g/cm” at the lower boundary of the buoyant layer to 5.5 g/cm3 at the bottom of the lower mantle. (For simplicity, however, the lower mantle is actually regarded as an infinite half space.) The low-density

layer has a density* 3.9 g/cm” in all versions of the model, while three

different viscosities of the layer are tested, viz. /AU,’ = lo’*, 1019 and 1016 poises, and a large number of thicknesses, varying from 100 km to 1 km. Details are discussed in Ramberg (.1972 a, b) so let it suffice here to give the dominant wavelengths for the thickness 100 km and the three different viscosities, Table II. The calculated ratio between the amplitudes, yi, of the waves at the different interfaces is also recorded, so is the velocity of growth, vi, of the amplitudes. The dominant wavelength is now considerably larger than for the low-velocity layer in *

When protrusions rise from the low-velocity layer decompression is supposed to keep the density of the protrusions 0.3 g/cm” less than that of the surroundings at all levels during the rise.

data

in cm/set at interface wavelength, km.

3.1 2.03 2030 km -0.00398 0.0067/l/0.752 6.442 - 1 O-l4 yi cm/set

Ollllll O/3.3-+4.2/3.9/4.2-5.5 -1.6186 - 10-“/see

vi gives the velocity or rise of the amplitude amplitudes is larger than 10% of the dominant

l

data

deep in the mantle

lOa cm 10” poises 334.2 g/cm3 “/IO/l/”

Model 5

data for the rise of a layer buried

cO~-pz)ghzl2lrz

Output

qt=

l’l/PZ/P3/P4

Pl/b’2/#3/P4

AtfAzlWr4

P2

P2

h2

Input

Theoretical

TABLE II

i when the amplitude

-

0.63 9.968 9968 km -0.493 0.0995/1/0.0059 7.979 * 10-t2 yi cm/set

IO8 cm 10” poises 3.34.2 g/cm3 “/10/l/” o/106/1/106 O/3.3+4.2/3.9/4.2-5.5 -1.6186 - IO-“/see

Model 7

yj is given in cm. This is anly valid when neither

2.2 2.85 2850 km -0.026202 0.04089/1/0.180712 4.24 1 * 1O-*3 Yi cm/set

lo8 cm 10z2 poises 3.3-4.2 &m3 m/loll/” 0/1000/1/1000 O/3.3+4.2/3.9/4.2-5.5 -1.6186 - lo-“/see

Model 6

of the three

L

E:XPERIMENTAL

GEODYNAMICAL

115

MODELS

the upper part of the mantle (Table I). For a viscosity ratio /J~//.I~ = lo3 or larger the wavelength is sufficient

to cause disturbances

over extensive regions on the earth’s surface.

Note that for unit viscosity ratio - i.e., equal viscosity for all three members of the sysof the waves at the bottom

tem - the amplitude,y,, 75% of the amplitude

literally sucked up into the core of the rising anticlines by the experiments,

of the buoyant

layer is no less than

of the waves on the top. This means that the heavy substratum

is

and diapirs. This is well sustained

Fig.3 and 4.

Experimental tests of a deeply buried layer The theoretical prediction of a large wavelength/thickness ratio and a pronounced sucking-up of the heavy substratum is verified in experimental tests such as those recorded in Fig.3 and 4. The tests, ihrhich were only semi-quantitative, were run in the centrifuge in 10 cm diameter trunnion cups. Most other models described in this paper are run in 20 cm diameter cups. Prior to centrifugation

the model in Fig.3 was similar to the structure

that the substratum was not infinitely thick. However, in the experimental stratum was about 25 times thicker than the buoyant layer. The overburden

and the substratum

in Fig.2 except model the sub-

consisted of the same kind of painter’s putty with

density 1.85 g/cm3. The putty has a very low yield point, but its effective viscosity varies with the stress applied so it is impossible to give a reliable value for the viscosity under the condition of the test. In Fig.3 the buoyant stratum is 2 mm thick, has a density 1.14 g/cm3 and consists of a silicone putty with a viscosity about lo6 poises. A small initiating anticline was made in the center of the buoyant

sheet.

Fig.3. Diapiric anticline of a thin silicone-putty layer with density 1.14 g/cm3 that has risen through an overburden of painter’s putty with density 1.85 g/cm3. The substratum consists of the same kind of painter’s putty. Model run in centrifuge at 1000 g, the centrifugal force pointing downward in model.

H. RAMBERG

AND H. SJ&STRtiM

Fig.4. Model similar to that shown in Fig.3 except that the black and grey layered overburden and the substratum consist of silicone putty which has a little higher density than the buoyant layer. The latter is the thin light grey mantle around the diapir. Note the sucked-up substratum in the core of the diapir and the strong deformation in the overburden. Run in centrifuge at 1000 g for 5 min.

After run in the centrifuge at IOOOg for a few minutes the thin buoyant in the form of a funnel-shaped body as shown in the cross-section, Fig.3. The predicted sucking-up

of the substratum

of the fact that the substratum

is splendidly

layer had risen

displayed in the test. In spite

has the same density as the overburden

and thus is not buoy-

ant, it fills the core of the funnel-shaped diapir and is brought up almost to the surface. This large upheaval - relative to the geometric dimensions of the model - is caused solely by the buoyant force associated with the thin low-density layer. Incidentally, we feel that this rather surprising ability of diapirs to bring heavy mantle materials up to the surface should be closely considered in discussions of the emplacement of, e.g., ultrabasics in orogens. Another well-displayed

feature is the lateral spreading of the hat of the diapir; we shall

see in other models that this spreading is important

as a propellant

for lateral movements

in the crust. That the wavelength/thickness ratio is large is also sustained by the test inasmuch as only one diapir developed from the thin layer. If the dominant wavelength/thickness ratio for the system is in fact small, one would expect several anticlines and/or diapirs to rise from the buoyant sheet. True, a small central anticline was made on the sheet prior to the run in the centrifuge in order to localize the rise in the center of the model rather than

117

EXPERIMENTAL GEODYNAMICAL MODELS

Fig.5. Deformation structure formed in a two-layer model after run in centrifuge at acceleration increasing from 800 g to 2000 g through 5 min. Black silicone-putty overburden has a density 1.36 g/cm3, light buoyant silicone-putty layer a density 1.13 g/cm3.

along the edges. According

to experience

from other models, however, such an anticline

on-

ly locates a rise at a given place, but it does generally not prevent the layer to rise also at other points, provided the dominant of the buoyant

wavelength

sheet. If the dominant

of the system is not greater than the width

wavelength in our system was in fact appreciably

less than the width of the model, several diapiric protrusions

would form such as in models

whose wavelength/thickness ratio is small, see Fig.5. Another model which supports qualitatively the theoretically predicted long wavelength and the sucking-up of the heavy substratum is shown in Fig.4. The initial structure was essentially the same as in the model shown in Fig.2 except that the overburden and the substratum now consist of silicone putty with density 1.38 g/cm”. To show the deformation the overburden

was made of alternating

dark and light sheets which originally were paral-

lel to the equipotential surface in the centrifuge. (The unsymmetry due to an edge effect from the drag along the sides of the trunnion

in the final pattern is cup.) The thin buoyant

sheet - which now forms the light-colored thin mantle around the diapir - was initially 2 mm thick and its density 1.14 g/cm3. All materials show a viscosity of the order lo6 poises. After run in the centrifuge for a few minutes at 1OOOg a central diapir pierced the surface, and a cross-section through the center of the model gave the pattern shown in Fig.4. In all its essential features the structure is similar to the one discussed above. The filling of the core of the diapir with the sucked-up substratum, the spreading of the hat, the corresponding lateral spreading of the overburden indicated by the formation particular

above the diapir and the long wavelength

of only one diapiric rise are all characteristic

as

features of this

kind of models.

Note that the theory predicts that the dominant of the substratum

wavelength decreases and the upheavel

in the core of the diapir becomes less striking if one makes the substratum

either more stiff or more dense than the overburden.

These effects have been considered

in detail by Ramberg (1972a). Models simulating con tinen tal drift In the models above a strong lateral spreading of the overburden above the hat of the diapirs is inferred from the intense vertical compression in this region. This is particularly well demonstrated in Fig.4 where the strain is visualized by the deformation of the layered overburden. A question relevant to continental drift is, however, whether a relatively stiff crustal layer in models would break in tension above the diapir and become displaced laterally in a manner simulating our wandering continents. To study this question we have

118

H. RAMBERG

AND H. SJijSTRiiM

Fig.6. Top view and profile of model after run in centrifuge at 2000 g. Dotted body in profile is siliconeputty diapir profile cut normal to elongate diapir. For description of initial structure see Fig.9 and 10. (From Ramberg, 197 1.)

tested several diapir-type

models with surface layers of various brittle or viscoelastic ma-

terials as earth-crust imitations. In Fig.6, 7 and 8 three models are shown from above and in cross-section after run in the centrifuge. All three models show essentially the same feature, viz. the spreading and/ or splitting of a surficial crust above a mushrooming diapir of an originally deep-seated, low-density mass. Fig.9 shows the surface of the models with their unbroken Pangaea con-

EXPERIMENTAL GEODYNAMICAL MODELS

119

Fig.7. Top view and profile of model after run in centrifuge for 75 set at 13OOg, 107 set at 2OOOg, 63 set at 3000 g and 23 set at 1500 g. Mushroom-shaped diapir outlined by ink in profile which is cut normal to elongate diapir. For description of initial structure see Fig.9 and 10. (From Ramberg, 1971.)

Went prior to the run in the centrifuge, and Fig.10 is a cross-section tures of one of the models which initially were quite alike.

of the initial struc-

The essential difference between models CD 1 and CD 2 on the one hand and CD 4 on the other is that the continental plate is quite brittle in CD 4 where it consists of a compressed powder of paraffin wax mixed with a little oil. In models CD 1 and CD 2 the continental plate consists of compressed colophony powder mixed with oil. This has rheological properties similar to stitching wax and is quite ductile under low strain rate. There are also significant differences between models CD 1 and CD 2 in the sense that the silicone-putty layer immediately subjacent to the continental plate has a density 1.45 g/cm” in CD I but only 1.28 g/cm” in CD 2, whereas the density of the buoyant mass is 1.28 g/cm” in CD 1 and 1.55 g/cm3 in CD 2. For this reason the diapir rises closer to the

H. RAMBERC

AND H. SJOSTROM

Fig.8. Top view and in&ned profile of model atier run for 35 see at 1000 g, 120 set at 2100 g, 22 set at 2500 g and 60 set at 3000 g. For description of initial structure see Fig.9 and 10. (From Ramberg, 1971.)

E:XPERlMENTAL

GEODYNAMICAL

Fig.9. Top view of model

MODELS

similar to CD I, CD 2, CD 4 and CD 7 prior to run

121

in centrifuge. (From

Ramberg, 1971.) surface in CD 1 and penetrates the continental plate which is pushed completely the region occupied by the wide hat of the diapir.

out from

In model CD 2 the buoyant material does not pierce the surface - except along the middle of the diapir - and the continental plate has responded partly by plastic flow, partly by cataclasis to the lateral tension created by the subjacent spreading diapir. In model CD 4 the continental

plate has behaved almost completely

as a brittle and rig-

id substance, weak enough to rupture under the tensile stress created by the spreading diapir, but strong enough to transmit stresses necessary to buckle the thin surficial layer of plasticene

along the leading edges of the crustal fragments.

Fig.lO. Initial cross-section of model CD 2 (Fig.7). CD I,CD 4 and CD 7 were quite similar prior to the dynamic rearrangement in the centrifuge. Only left half of the symmetrical models shown. I = silicone putty with fine tungspar and magnetite powder, p = 1.55 g/cm3 (1.28 g/cm3 in CD I,1.46 g/cm3 in CD 4);2= silicone putty with tungspar powder, p = 1.28 g/cm3 (1.45 g/cm3 in CD I);3 = black modelling clay, p = 1.68 g/cm3; 4 = white modelling clay, p = 1.78 g/cm3; 5 = green painter’s putty, p = 1.85 g/cm3; 6 = grey painter’s putty, p = 1.85 g/cm3; 7 - yellow painter’s putty, p = 1.85 g/cm3 ; 8 = mixture of collophony powder and oil in CD I and CD 2, paraffin wax and oil in CD 4.

122

H. RAMBERG

Vertical

Eroggwotion

VC

Altered

p

-104

+ ++ l Borement

Mont18

llt~lt

Fig.1 1. Profile across the Mid-Atlantic Talwani et al., 1965.)

////

Oceanic

AND H. SJijSTRdM

Layer

Month

Ridge according

to gravimetric

and seismic observations.

(From

This model shows close similarities with the structure believed to exist underneath Mid-Atlantic Ridge as illustrated in a profile by Talwani, Fig. 11. [f one wishes to demonstrate the concept of “continents in collision”

the

one simply con-

struct an initial model with rheological and geometrical (layer thicknesses) characteristics such that two (or more) parallel ridges or diapirs will rise when exposed to the centrifugal field. This was done in model CD 7 in which the initial Pangaea broke in several fragments above two diapirs and the fragments between the two diapirs “collided” force to cause considerable

deformation

with sufficient

along the contact, Fig. 12.

Models simulating erogenic belts The European Alps, the Scandinavian Caledonides, the Appalachians in America and other orogens exhibit convincing field evidence of large horizontal relative movements of the rock masses. At some places rocks are displaced horizontally over their substratum for distances of the order 100 km. There are also abundant signs of lateral compression in the form of buckle folds in stratified rock complexes. To many the obvious conclusion from such findings is that an orogen represents a large lateral shortening across the belt from the one edge to the other. This is the “giant vise” hypothesis of orogenesis. This idea of overall shortening

has for a long time been a prevailing basic assumption

the geologists’ models of orogenesis, an assumption iom for many theoreticians

concerned

in

which has reached the status of an ax-

with continental

drift and plate tectonics.

However, our model studies warn that erogenic belts should not unconditionally be taken as evidence of crustal shortening. A remarkable result of the experimental work is that structures

strikingly

similar to the very erogenic structures

which are regarded as

proof of overall lateral compression form in fact in the models without a net shortening across the orogens. Moreover, these model structures form spontaneously from a gravitationally unstable mass distribution of a kind which, we believe, may well have existed in “geosynclines” and along continental edges from where orogens rise. The chief field observations taken as indicative of an overall lateral shortening across erogenic belts are in part the large recumbent folds (nappes) and thrust sheets of rock masses which override their substratum of both younger and older rocks, in part the abun-

EXPERIMENTAL GEODYNAMICAL MODELS

123

Fig.12. Top view and inclined cross-section of model with brittle crust split and spread above two diapirs risen during centrifugation. Initial structure quite similar to that shown in Fig.10 except that the buoyant layer in CD 7 was made of four silicone sheets with somewhat different color in order to show the internal flow pattern formed during the run. Note “continent collision” between crust fragments located between the two diapirs.

dant buckle-folded

strata with steep axial plane. For observations

and reasoning behind the

large-scale horizontal movement hypothesis see, e.g., Rodgers (1970) for the Appalachians, and Kautsky (1953) and Magnusson et al. (1962) for the Scandinavian Caledonides. The idea that a thrust sheet is evidence of shortening across an orogen appears to rest on the assumption that the sheet which overrides one edge of the orogen is rigidly connected with the craton (whether the latter be oceanic or continental) on the opposite side of the fold belt. This, of course, need not be so, and the present authors know of no place where

124

H. RAMBERG AND H. SJoSTRijM

such a situation

is sustained by recorded field observations.

nides, for example, there is convincing Sweden has moved southeastward icant relative movement Caledonides

For the Scandinavian

Caledo-

evidence that the frontal part of the thrust sheets in

over the old Baltic Shield, but there is no sign of signif-

between the sheets and their substratum

in Norway (see e.g., Nicholson

and Rutland,

in the interior

of the

1969).

There is no physical objection against a process which permits the front of a sheet to move laterally relative to its substratum at the edge of the orogen while in the interior of the orogen the same sheet remains fixed in relation to the substratum even if the latter has not been shortened. In other words, the movement is in the form of vertical flattening and compensating lateral spreading of the thrust sheet, much like the movement in a giant ice cap. It is also possible that the sheet simply glides downhill from above elevated basement culminations in the central parts of the orogen. A spreading sheet of sufficient thickness may even move up the slope of its substratum provided that the surface of the sheet slopes in the direction of movement. These kinds of movements

are demonstrated

in many of our models as examplified

in Fig. 13, 14 and 15.

These are gravity driven, or at least gravity controlled, tectonic processes as visualized in one version or another by Haarmann (1930), Van Bemmelen (1933, 1960), Ramberg (1945, 1963, 1971), Beloussov (1961) and others. A condition which strongly supports the spreading and/or gravity slide hypothesis the Caledonian

thrust sheets in Norway and Sweden is that the individual

toward the interior of the Caledonides 1969). The thinning The picture geanticline sheets does tion which

in Norway (Nicholson

and Rutland,

for

sheets thin out 1969; Zachrisson,

is not due to erosion, and it is not believed to be primary sedimentary.

fits well the hypothesis of spreading from a center above the rising basement along the coast of Norway. Obviously, the general westward thinning of the not speak for a forceful thrust from the west. This would give a stress distribucompresses the thrust sheets laterally more in the west than in the east (because

of the resistance along the thrust plane), and consequently

should make the sheets thicker

toward the west. That recumbent

fold-type nappes, such as the well known Pennine nappes in the Alps

and the less known Iltay nappe in Scotland (Craig, 1965) be taken as proof of lateral shortening is also contradicted by the experiments. In the tests Pennine-type nappes form readily when giant upheavels of low-density gneiss-granitic basement approach the surface and there spread laterally to form huge folds with quasi-horizontal axial plane and inverted Fig.1 3. Section through model of orogen run for 8 min. at acceleration increasing from 1300 g to 2200 g. Initial layered structure shown in Fig.17. The final structure shows domes and nappes of grey, white and black silicone having risen through putty overburden (inclined hatching) and thin “sedimentary” layers of modelling clay and silicone putty under cover of soft wax. (From Ramberg, 1967.) Fig. 14. Section through model initially quite similar to S I14 in Fig. 13; see, however, Fig.1 7. Run for 15 min. at 2400 g - 2900 g. (From Ramberg, 1967.) Fig.15. Section through orogen-imitation model Ny 9. Run for 290 set at 2200 g, 10 set at 2600g and 632 set at 3000 g. Initial structure shown in Fig. 18.

EXPERIMENTALGEODYNAMICALMODELS

125

126

H. RAMBERG AND H. SJGSTRCrM

Fig. 16. Section through orogen-imitation in Fig. 18.

model Ny 7. Run for 95 set at 2000 g. Initial structure shown

stratification in their lower limb. Examples are presented in Fig.13, 14 and 15. See also Fig. 16- 18. In these experiments there is no shortening of the distance from one craton to the other. Sometimes

the model nappes even exhibit a so-called imbricate structure

in many orogens. This structure

is well developed in model

thin surficial sheets of white and black plasticene fold came “rolling”

which is typical

Dv 7, Fig.19, 20 and 21. Here

broke to small flakes when the recumbent

over its lower limb. The broken flakes became partly stacked on top

of one another in the process, much like the imbricate

structure

one encounters

along the

edge of orogens.

s 114

5116

Fig.1 7. Cross-sections of initial structures of model S 114 and S 116 Fig.13 and 14. Only left half of symmetrical models shown. I = soft oil-wax mixture, p = 0.9 g/cm3; 2 = white silicone putty, p = 1.14 g/cm3; 3 = grey silicone putty, powder mixture, p = 1.25 g/cm3; 4 = green painter’s putty, p = 1.87 g/cm3; 5 = black silicone-magnetite p = 1.35 g/cm3; 6 = silicone putty with thin layers of modelling clay; 7 = painter’s putty, p = 1.87 gjcm3.

EXPERIMENTAL

GEODYNAMICAL

MODELS

Fig.18. Cross-sections of initial structures symmetrical models shown.

of models Ny 7 and Ny 9, Fig.15

127

and 16. Only left half of

1 = grey painter’s putty, p = 1.85 g/cm 3 , 2 = black modelling clay, p = 1.68 g/cm3 ; 3 = silicone putty with tungspar powder, p = 1.28 g/cm3; 4 = white modelling clay, p = 1.78 g/cm3; 5 = green painter’s putty, p = 1.85 g/cm3; 6 = red modelling clay, p = 1.71 g/cm 3., 7 = yellow painter’s putty, p = 1.85 p/cm3; 8 = silicone putty with magnetite and tungspar powder, p = 1.58 g/cm3 in model Ny 7, 1.33 g/cm3 in Ny 9.

Fig.1 9. Cross-section of centrifuged model showing spreading surficial nappe or thrust sheet with well developed imbricate structure along sole. Nappe is spreading lobe of silicone-putty diapir which has risen from underneath a layered overburden of painter’s putty and modelling clay. Arrows indicate flow directions. Small dome on bottom a little to the right of center consists of stiffer silicone which has risen more slowly. See also Fig.20 and 21.

AND H. SJijSTRijM

Fig.20. Enlarged spreading nappe

part of Fig.19, model Dv 7, showing details of imbricate structure along sole of (dotted). Surficial thin sheet of dark modelling clay outlined in ink.

For the understanding of natural imbricate structures along the sole of nappes some details in Fig.20 and 21 are illuminating. The recumbent fold nappe has moved over a surficial multilayer consisting of three thin sheets of competent plasticene embedded in incompetent silicone, the whole complex resting on the “craton”. We think that it is tectonically significant that the three sheets have responded very differently when being overridden by the nappe. The uppermost

black sheet, which is directly subjacent

to the spreading

nappe, has broken to small equalsize planar flakes, the one stacked on top of the other. The white plasticene sheet occurring a little below the contact has also broken but some of the flakes have the form of an isoclinal syncline tipped over in the direction of the nappe propagation. None of the flakes form an anticlinal

pattern.

The lowermost

sheet has not broken at all but has been thrown into a continuous

black plasticene

series of gentle folds

with uniform wavelength.

Fig.21. Part of cross-section of model Dv 7 taken some distance this section the small dome shown in Fig. 19 and 20 has pierced diapir. Note the tilted small syncline of the white modelling-clay

away from profile in Fig. 19 and 20. In the nappe of the early-formed spreading sheet underneath the nappe.

EXPERIMENTAL

GEODYNAMICAL

MODELS

129

As evident from the structure just in front of the nose of the nappe the plasticene sheets became buckle-folded

in the zone of compression

along the leading edge of the nappe. When

the nappe passed over the folds they were tilted and tightly compressed until all hinges broke in the uppermost

sheet and all anticlinal

hinges but only some synclinal hinges broke

in the middle sheet. The gently folded lower-most

sheet remained unbroken.

know, of course, if the model simulates the evolution

of imbricate

orogens, but we are impressed by the geometric similarity that the dynamic similarity

structures

We do not in natural

of the results, and we feel also

- i.e., the nature of the forces and the movements

involved -

between the model and an “average” natural orogen is quite satisfactory. What then about the abundant buckle folds with steep axial plane present in most orogens, they certainly must mean lateral shortening? Of course they do, but not necessarily a net shortening

in the sense that the two cratons adjacent to the fold belt have come

closer together. For one thing the lateral compression gions may well be compensated

by lateral extension

proven by bucklefolds

in some re-

- e.g., above domes, batholiths

and

basement upheavals ~ in other regions within the same orogen such as found in many of the experimental models, see e.g., Fig.22. In addition, folded stratified rocks are conspicuous in the field, while horizontal stretching of strata is a phenomenon easily overlooked because it does not ordinarily change the pattern of the initial horizontal layering. Only when boudinage and pinch-and-swell structures are produced is the stretching readily recognized. The impression of shortening in fold belts is therefore likely to be exaggerated. Our experiments have, however, made us aware of another much less obvious circumstance which must be considered before using buckle folds as evidence of overall shortening. The centrifuged models emphasize a fact which, incidentally, could also have been predicted theoretically, namely that a continuous series of buckle folds, each representing true lateral shortening, extending from one edge of the erogenic belt to the other can form without narrowing the space between the two adjacent cratons. In other words, there may be true local shortening everywhere in the orogen, and an integration of the strain across the whole width of the fold belt may give a large apparent shortening, tween the two edges has not shrunk.

yet the distance be-

F‘ig.22. Dome in buoyant silicone-putty layer with thin sheet of modelling clay which has been buckled by the horizontal flow toward the base of the rising dome. The overburden of painter’s putty has been removed and the model cut both horizontally and vertically to show the buckling of the embedded “competent” sheet. (From Ramberg, 1967.)

H. RAMBERG

Fig.23. burden

Schematic profile of a series of diapirs with buckled internal structure which has been buckled in the synclines between the diapirs.

This apparent paradoxical

structure

AND H. SJijSTRijM

intruded

develops when the basement

in layered

over-

rises in the form of one

or more rows of diapirs in the orogen. Then the surficial strata of sediments and lavas become squeezed and buckled in the narrowing synclines between the diapirs at the same time as buckles form in a layered gneissic basement when it flows plastically toward the roots of the rising diapirs. The upward flow in the core of the upheavels only accentuate the folding. The situation is schematically illustrated in Fig.23. Experimental models containing this kind of structures are numerous in our collection in Uppsala. If erosion had uncovered the structure down to the marked level in Fig.23 a continuous series of buckle folds would have been exposed, some in the sedimentary-volcanic

geosyn-

clinal column others in the diapiring portions of the basement. It would have been excusable to reach the erroneous conclusion that the whole fold belt had been “squeezed between the jaw of a giant vise” such as emphatically advocated by Rodgers (1970) for the Appalachians. Write Rodgers (p.224): . . . for me the vise is not a metaphor but a fairly exact model. Thus the evidence of intense shortening

perpendicular

to the length of the chain,

not only in the folded marginal belts but also in the central core belt, is too clear for me to doubt.

. .”

The evidence of “intense

shortening”

used in the Appalachians

is the same as applied

in other orogens, namely folds and thrust sheets of a kind geometrically

similar to those

produced in the experimented models, but there without overall shortening. On the other hand the orogen-imitation models do of course not exclude the possibility of shortening

across the belts, but they do show that most of the structures

belts can form without

a net shortening

and thus indicate that a narrowing

in erogenic

of the space oc-

cupied by orogens must be proven by other means such as, e.g., paleomagnetic

studies of

the cratons adjacent to the fold belts. We feel it appropriate to conclude this account by emphasizing the view on the Alps expressed by Van Bemmelen based upon his extensive field work. Van Bemmelen (1960): “In contrast to the current opinion that the Alps are the result of crustal shortening in the mobile Tethys belt, the author’s field studies in recent years have led to the conclusion that this shortening is not needed to explain the structural overlap of the East Alpine and Pennine nappes . . .“.

EXPERIMENTAL GEODYNAMICAL MODELS

131

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Beloussov, V.V., 1961. The origin of folding in the earth’s crust. J. Geophys. Res., 66: 2241-2260. Berner, H., 1972. Experimental Studies of Diapirisi,s Applicable to the Earth. Thesis, to be published. Berner, H., Ramberg, H. and Stephansson, O., 1972. Diapirism in theory and experiment. Tectonophysits, 14: 197-218. Biot, M.A., 1965. Mechanics of incremental deformation. Wiley, New York, N.Y., 504 pp. Chandrasekhar, S., 1955. The character of the equilibrium of an incompressible heavy viscous fluid of variable density. Proc. Camb. Philos. Sot., 51: 162-178. Chandrasekhar, S., 1961. Hydrodynamic and hydromagnetic stability. Oxf. Univ. Press, London, 653 pp. Clark Jr., S.P. (Editor), 1966. Handbook ofPhysical Constants. Geol. Sot. Am. Mem., 97: l-586. Craig, G.Y. (Editor), 1965. The Geology of Scotland. Oliver and Boyd, Edinburgh, 556 pp. Gutenberg, B., 1959. The asthenosphere low-velocity layer. Ann. Geofis., 12: 439-452. Haarmann, E., 1930. “Die Oszillationstheorie”. Enke, Stuttgart, 260 pp. Hide, R., 1955. The character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Camb. Philos. Sot., 51: 119-201. Johnson, M.R.W., 1960. The structural history of the Moine thrust zone at Loch Carron, West Ross. Trans. R. Sot. Edinb., 64 (7): 139-168.

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Ramberg, H., 1972b. Theoretical models of density stratification

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Stephansson,

0. and Berner,

H., 1971. The finite-element

method

in tectonic

AND H. SJGSTRGM

processes.

P&s.

Earrh

Planet. Inter., 4: 301-321 Strand, T. and Kulling, O., 1972. Scandinavian Caledonides. Wiley-Interscience, New York, N.Y., 302 pp. Talwani, M., Le Pichon, X. and Ewing, M., 1965. Crustal structure of mid-oceanic ridges. J. Geophys.

Res., 70: 341-352. Taylor, G., 1950. The instability of liquid surfaces when accelerated in direction perpendicular to their planes, I. Proc. R. Sot. Land., Ser. A, 201: 192-196. Van Bemmelen, R.W., 1933. The undation theory and the development of the earth’s crust. Int. Geol. Congr. Rend., 16 (2): 965-981. Van Bemmelen, R.W., 1960. New view on the Alpine orogenesis. Inr. Geol. Congr., 21st, Copenhagen, 1960. Rept. Session Norden. 18: 999116. Zachrisson, E., 1969. Caledonian Geology of Northern JPmtland-Southern Vasterbotten. Sver. Geol.

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