The Vredefort structure: estimates of energy for some internal sources and processes

153

Tectonophysics, 171 (1990) 153-167

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

The Vredefort structure: estimates of energy for some internal sources and processes BRIAN BAYLY Department of Geology, Rensselaer Polytechnic Institute, Troy, NY 12180 (U.S.A.)

(Revised version accepted March 28,1989)

Abstxaet Bayiy, B., 1990. The Vredefort structure: estimates of energy for some internal sources and processes. In: L.O. Nicolaysen and W.U. Reimold (Editors), Cryptoexplosions and Catastrophes in the Geological Record, with a Special Focus on the Vredefort Structure. Tectoncrphysics, 171: 153-167. The conspicuous features of the Vredefort structure are the concentric arrangement of gneissose core, steeply dipping metasediments and metavolcanics and a peripheral rim syncline; the alkali intrusive suite and its metamorphic aureole; the indicators of fracturing and high pressure (shatter cones, coesite and stishovite, and microscopic deformation textures); and the predominance of CO2 over H,O in fluid inclusions in the gneissose core. The cause of the Vredefort structure lies in either external or internal agencies; possible internal agencies and sources of energy are discussed here. In reviewing possib~ties, a ~ntinuum is recognized between two extremes: at one extreme the major sources of energy are taken to be the density inversion (met~d~ents overlying granitic gneiss) and the alkali intrusions, whereas at the other extreme the major source of energy is taken to have a deep-seated and explosive character, most of the energy being liberated in one or two short, but very great, bursts. Between the extremes lie scenarios in which violent ener@ releases form substantial, but not overwhelming ~nt~butions to the total. Attention is focused initially on the less explosive end of the range: the hypothesis explored is that the gneiss rose because of buoyancy, while being disturbed and accelerated by the alkali intrusions. The aspect selected for emphasis is the energy budget; quantities of energy are estimated as follows: (1) Gravitational energy available from the density inversion, -102’ J, (2) thermal energy associated with the alkali intrusions-10zl J, and (3) energy consumed in forming shatter cones-10” J. (By comparison, for Mount St. Helens in April-May 1980 the estimates are: thermal energy associated with magma-10 l8 J, and energy released in four major seismic events-10’s J.) In addition to the energy budget, aspects requiring attention are the apparent compressive stress intensities (8-10 GPa to form stishovite) and the form and dist~bution of the shatter cones. Possibilities are (1) for stishovite, that sufficient compressive stress developed locally at asperities on fracture surfaces, and (2) for the cones, that they formed by quasi-static Mom-Coulomb fracture in radially sy~et~~l local stress fields produced by seismic pulses of magmatic origin imposed on rocks already prestressed during gravity doming. With regard to the role of compressed volatiles, they may have been important in affecting fracture behavior, preserving stishovite by quenching and promoting development of certain microdeformations at low stress levels. Their relative importance as a source of energy, in comparison with the other sources mentioned, is not brought out by the calculations. Nothing in the above is intended to exclude other possible reconstructions from consideration, the method of multiple working hypotheses being upheld.

Inception A purpose of the 1987 symposium on Cryptoexplosions and Catastrophes was to attract 0040-1951/90/$03.50

0 1990 Eisevier Science Publishers B.V.

the attention of people from diverse backgrounds to the Vredefort structure. Coming from the outside puts a beginner in a precarious position. Workers from many universities, especially the

154

University of the Witwatersrand and Potchefstroom University, have made extensive studies of the rocks discussed. The following remarks are made in a spirit of cooperation and inquiry. It is hoped that defects due to lack of thorough acquaintance with the Vredefort region and its problems will be viewed leniently and corrected gently. The salient features of the study area have been outlined by Nicolaysen (1987): “The Vredefort structure is a deeply eroded cryptoexplosion structure in which a domical mass of basement granitegneiss has been sharply uplifted-by at least 30 km in the centre of the structure. The basement uplift is surrounded by a “collar” of uplifted strata which lie unconformably on the basement... In plan, the uplift is strikingly polygonal. The strata are overturned in the NW sector, but lie with moderate dips on the basement in the S and SSE sectors. Manton showed that Vredefort manifests a feature present in many cryptoexplosion structures: the integrated perimeter is greater than the mean outline for a particular unit. There has evidently been inward movement of such units.... The Vredefort dome has a clearly defined metamorphic aureole, with the collar strata converted to hornfelses of varying metamorphic grade. The aureole is widest and most pronounced in the northwest sector, where hornfelses of the highest grade surround distinctive alkalic igneous intrusives. The metamorphic isograds are non-parallel to the bedding of the collar strata, and the eccentric nature of the metamorphic aureole is marked.... Vredefort has attracted wide attention in the past two decades for a very unusual category of deformationthe “shock deformation” observed in the collar strata. The deformation features include cataclasis in thin section, presence of coesite and stishovite (the high pressure SiO, polymorphs), formation of mylonites and pseudotachylites, planar micro-deformations in quartz and the widespread occurrence of shatter-cones.” Hypotheses for the origin of the structure by internal processes form a continuum between two extremes: HZ. The structure is similar to other domes or doubly plunging anticlines, and formed at a slow

8. BAY LY

rate comparable with other tectonic updoming processes (order of magnitude, mm/yr); sudden bursts of energy release were a very small part of the total energy budget. H2. The structure formed in one, or at most two, catastrophic events comparable to the Krakatoa eruption or the even greater Toba event. Almost all of the energy budget was expended in one or two short large bursts. In Hl a conspicuous difficulty is to explain the shock-deformation features, and in H2 the main difficulty is to explain the geometry of the collar and its continuity- although the collar rocks are rich in joints and faults on every scale, they are not jumbled, and stratigraphic units are still confined within mappable stratigraphic boundaries. Between the extremes of Hl and H2 lies a range of possibilities in which it is supposed that the collar reached its present geometry sufficiently slowly for some bending, but stress magnitudes were high, close to the rupture point of the rocks. At the same time the ascent of the central gneiss was more rapid and erratic than in most diapirs or salt domes, with frequent earthquakes and gas bursts. Such shocks were recurrent through the long history of updoming; considerable energy was expended in the shocks, but considerable energy was also expended in slow deformation. Having recognized hypotheses Hl and H2 and a range of intermediates, we wish to narrow the field to something more specific. In this connection, we note the Schurwedraii alkali intrusive suite which was emplaced at about the time when the uptilting occurred (Bischoff, 1982), and also the fact that all fluid inclusions so far analyzed from the central gneiss seem to be almost totally water-free and CO,-rich (Schreyer and Medenbath, 1981). These two facts, both probably related to mantle involvement in the evolution of the Vredefort structure, suggest that when the central gneiss was ascending it was unusually hot, but anhydrous. Such an ascent would be more erratic than a water-mediated movement, with a likelihood of shear melting (Orowan, 1960, p. 341; McKenzie and Brune, 1972, p_ 68): In Orowan’s words, “the avalanche-like increase of the shear rate... may then develop heat faster than it is conducted away, and finally almost sudden shear melting and faulting may take place.” This conjec-

PROCESS

ENERGY.

VREDEFORT

ture is supported pseudotachylite,

by the widespread and

thus it seems

events could be explained Similarly,

155

STRUCTURE

aspects

occurrence unlikely

of that

of the collar

to be shown on many maps and sections and

slightly

circumferential misaligned,

example,

segments impact

as shown by Manton

Vredefort

strata

as strata are faulted

the misalignment

than that at well-displayed are much

(considering apirs,

by Hl.

of the geometry

suggest that events cannot be explained by H2 either: The collar rocks have sufficient continuity and, although

cone axes and with the actual

is less

structures.

For

(1965, fig. 16) the

less disarranged

than

that

planar

faults

emerges

that

but the energy

estimates

aspects

existence

most

rule)? No account ent

ordinary

around

and joints is fully

di-

are the

satisfactory,

help to bring

of the enigma

of cones

gravity-driven

together

the differin concrete

form. Aside from the matter sufficient that

of finding

quantity of energy,

certain

features

brief, high-stress

seem

pulses.

a source for a

there is also the fact to require

energy

in

This may be true for the

those at Gosses Bluff (Milton et al., 1972, fig. 3). Detailed mapping shows the collar to be rich in

cones, and is almost certainly true for the coesite and stishovite reported by Martini (1978). How-

faults-the uplifting may have been more by close faulting than by true bending; but nonetheless, its

ever, in order

geometry

suggests

some cohesiveness

and orderly

behavior. Application of hypotheses at the extreme explosive end (H2) of the range seems likely to be difficult

owing to the high degree of order in

the geometry of the collar. There remains the intermediate hypothesis, that updoming was gravity-driven and fairly slow and yet was sufficiently vigorous and erratic to produce the deformation features. To explore the plausibility of this, attention is focused on quantities of energy: can we estimate the quantities of energy involved in each of the subprocesses, and when that is done, do the estimates form an internally consistent set? In terms of energy con-

to keep the focus on quantities

energy, the topic of intensity for later inquiry. There

is, of course,

deformation

features

this possibility, neutral.

“Supposing

no bolide

of stress is delayed

the

possibility

are bolide-related.

the present

The question

studied

that

discussion

is wholly

could be stated thus:

is involved,

how might

A second

possibility

is that a pocket

or stream

of compressed volatiles brought significant energy to Vredefort from a source deeper in the earth, at a depth of 90 km or more. It will be suggested that, in terms of energy quantities, it is not neces-

include

stishovite,

much

energy

might

be available

(in

broadly dispersed form) on the basis of the density inversion (metasediments overlying gneiss)? (2) How much volcanic energy might be available (in a more central localized form) from alkali magmatism? (3) How much energy seems to have been absorbed in forming cones? (4) If the localized magmatic energy source is favored, are there processes to convert sufficient energy first to mechanical disturbance at the central site and then to seismic waves to produce the cones? (5) If the distributed favored, is it compatible

gravitational source is with the orientations of

we

account for the updoming and the shatter cones?” The pros and cons of bolide hypotheses are argued in other contributions in this volume.

sary to call on such a source; but in accounting the deformation features and preservation

the following:

the

Regarding

sumed the shatter cones require more attention than the other deformation features. Questions (1) How

of

portant With

compressed

volatiles

for of

may have an im-

role. bolides

and

mantle-derived

mind, we should review the purpose

volatiles

in

of the follow-

ing remarks. The purpose is not to advocate any particular hypothesis; instead, the purpose is to make more specific one particular group of ideas. The approach preferred is the method of multiple working hypotheses, each hypothesis being explored and expressed, where it is weak as well as where it is strong, through trial values and estimates of orders of magnitude. The reader is asked to view the estimates that follow as contributions to a cooperative inquiry and not as advocacy for any particular view of cryptoexplosion hypotheses.

B. BAYLY

156

The process begins very slowly, passes through a peak in the rate of dissipation of energy, and

Energy associated with a diapir The development

of a diapir

driven

sity inversion

has been

thoroughly

with models

by Ramberg

(1981).

pose is to derive energy

liberated

portion

an order

by a den-

documented Here,

the pur-

of magnitude

for the

in the process.

As an example,

a

of crust 30 km thick and 80 km in diame-

ter is considered.

The geometry

would in detail be rather purpose

of estimating

assume

that it passes

of its evolution

complicated

quantities

the five stages

in

Fig. 1A. The process of diapirism ultimately replaces stage (a) with stage (e). The difference in relative density between the material that sinks and the less dense material that rises might be, for example, 2.76-2.68 = 0.08, or 80 kg/m3. released is then: (80) x (volume

of material

x (vertical

distance

of gravity) = 80 kg/m3

The

down

again

energy

that moves)

Fig. 1A). We focus burst

of energy

X (g)

attention

released,

X 5.10’3 m3 x 20 km x 9.8 N/kg

stages;

but

on this,

the

the main

and approximate

of energy released

stage (a) to stage (e) is based and final configurations,

it also

in passing

edge of stresses, strains,

from

only on the initial

and involves

no knowl-

ascent rates etc., but a few

more details can be sketched in. Between stage (a} and stage (c) the diameter of the ascending mass changes from 80 to 54 km (shortening strain = 0.33) and its thickness changes from 10 to 22 km (vertical elongation strain = 1.2). In Appendix 1 it is estimated that if density contrast were the only driving agent on a gneissose diapir of comparable local stress differences amax - amin to magnitudes of the order of 10 or

20 MPa. If we assume

a viscosity

and ask for how long a stress magnitude estimated lows:

or 102’ J

final

by 102i J.

dimensions, might climb

moved by center

in the

dissipation between stages (b) and (d) is threequarters of the total (see center of gravity heights,

The estimate

but, for the

of energy, we can

through

slows

would need strains, orders

for the gneiss,

difference

of this

to act to produce the of magnitude are as fol-

Assumed viscosity of gneiss:

f5iii3 5km

225km

15 km

7.5 km

25 km

10” Pa-s > 1020 Pa-s, Radial strain rate: lo-l5 s-1 ( lo-t4 s-t, Time scale for diapirism: 10 Ma, 1 Ma, Ascent rate for gneiss: 10 mm/yr, 1 mm/yr,

10t9 Pa-s 1o-‘3 s-1 0.1 Ma 100 mm/yr

All these are average, or typical the relationship

based

on

for a homogeneous, uniformly straining cylinder, where ca, en, ut, and N are radial strain rate, radial compressive stress, axial compressive stress

desipatlon rate

a-

values

11 -Tb

t.

t2

C

d

-e

Fig. 1. A. Five stages in the evolution of a diapir. Top row, somewhat idealized. Botton row, highly idealized. The numbers (km) are the heights of the center of gravity of the rising mass (stippled) above the base of the cylindrical envelope shown. B. Idealized curves for change of strain rate, stress and energy dissipation rate with time. See text for details.

and viscosity, respectively. Actual magnitudes would vary greatly from point to point and over time. The values are quoted simply to indicate orders of magnitude, and to enable readers to form their own opinions as to whether the processes at Vredefort could have taken place in a comparable manner.

PROCESS

ENERGY,

VREDEFORT

(Ramberg’s

far more careful

103) gives an ascent

157

STRUCTURE

analysis

rate of 1 mm/yr

for a dome

of viscosity 10 i9 Pa-s in surroundings slower rate than that indicated above.

of viscosity 10” Pa-s-a However,

in Ramberg’s

is smaller

and the ascent rate quoted

in the evolution

well before

so the suggestions

totally

different map

Chamberlain

line

New England,

lo4

J/m3,

the

based

of isograds,

By a and

2 mm/yr

In a rather different geoEngland and Holland ascent rates

consider-

A significant fort structure intrusive

event in the history was the emplacement

suite. Outcrop

being

length bodies

of the alkali

of the alkali suite extends

for only 5 km, but metamorphic to the intrusion

of the Vrede-

effects attributed

are disproportionately

wide for a

For purposes of calculato a cube of 10 km edge

is assumed; corresponding of other postulated dimensions

results for could obvi-

ously be obtained by the same method. The heat associated with a magmatic is of three types: tion (molten by exsolution

(1) Heat liberated

intrusion

by solidifica-

rock + crystals), (2) heat absorbed (fluids such as water and CO, that

lo4 J/m3 for a shear stress at 17 MPa and lo6 J/m3 for shear stress at 170 MPa. A simple argu-

dissolve

ment in Appendix 1 suggests that for the average shear stress throughout the deforming region, 17

exsolved phase), and (3) heat of cooling crystallizing, the igneous rock is normally

MPa is the correct order of magnitude. On the other hand, if the fluid pressure is anywhere low enough to give 200 MPa of effective compressive

hundreds

of degrees

displaced, it cools).

and delivers

stress, local shear stresses as high as 170 MPa could be present (Byerlee, 1978). In a somewhat different context, Bumham (1985) concludes that the value sought must necessarily be less than 10’ (The energy stored in change of volume is than the energy of distortion, but very little volume-strain energy can be released by of the type considered here.)

From

the dimensions

by

made.

Energy associated with magma&m

body of this dimension. tion, a body equivalent

value of 3.104 MPa for the shear modulus of the rocks involved (Birch, 1966, pp. 169 and 170). Then, the distortional strain energy stored varies of the shear stress present,

the assumptions

values

in

as

gneiss domes in

buoyancy-driven

varying

Clearly,

of

dissipated

on the

Allen

or elastic strains at any moment during the diapirism. To make an estimate, we can use a typical

J/m3. larger of the events

total

movement.

are compatible.

on

is of the order

or less than this could be obtained

of 40 mm/yr.) Before going further it is interesting to inquire how much energy might be stored in recoverable

with the square

contains

at any moment

that,

the diapiric

domes which again are smaller than

(1979) have discussed

the rock stored

most will

supposes

ably greater

rate for certain

the Vredefort structure. metrical configuration,

average, energy

of fracturing, If one

is for a stage

(1988) have suggested

the emplacement

be on this point.

the peak rate is re-

of argument

separation

of rock are on the point not

10” J, or low4 J of the total energy

case the dome considered

ached, observed

(1981, p.

of the ring structure,

it

appears that about 2.10i3 m3 of rock are strongly deformed. If all of this rock were strained to the point of fracturing simultaneously, the total energy stored before fracturing could approach 1019 J. However, this state is not likely to develop in nature; at any moment, even if some portions

in the melt, but are not accommodated

the crystals

that form from it, appear

hotter

than

in

as a separate (after some

the host rock it

heat to its surroundings

as

As emphasized long ago by Graton (1945) for example, item (2) is strongly dependent on the pressure at which the fluids exsolve: as they ultimately escape to atmospheric pressure they are a powerful refrigerant, but as long as the fluids remain at pressures of 100 MPa or more, effect (2) is small in comparison with (1) and (3) (Bumham et al., 1969; Burnham of solidification and

and Davis, 1971). For heat specific heat typical values

are 250 kJ/kg and 1.3 kJ/kg- o C, respectively, so that if magma solidifies and then cools through, e.g. 200 o C, the energy delivered = 250 + 200 (1.3) = 510 kJ/kg. For 1000 km3, the energy delivered = 102’ J, the same order of magnitude as for the diapiric process.

B. BAYLY

158

We see at once a difference between thermal and deformational events: Roughly equal quantities of energy can be involved, but in deformation the energy is dispersed far more widely; magmatic activity can deliver comparable amounts of energy in less space and possibly in shorter times (in our example, in about one-hundredth of the space, and regarding time the late stages of cooling are very slow, but half the excess heat of the magmatic body could be lost in 100,000 yrs, or less if associated fluids carried away part of the heat (Larsen, 1945; Jaeger, 1961)).

Energy associated with shatter cones The cones at Vredefort have been described by Hargraves (1961), Manton (1965), Simpson (1981) and Albat (1988), and exploration continues. An ideal shatter cone is a conical surface of weakness, on which striations fan out from the apex. In the field, it is rare that a complete cone is exposed, but many surfaces from a few centimeters to a meter in dimension are seen that can be imagined as parts of cones. Where a few square meters of outcrop display sufficient partial cones, many striations can be measured and their attitudes combined ste~o~ap~cally. In favorable circumstances the result defines a complete imaginary cone that is a sum or generalization of all the partial cones. Manton gives axial directions for 48 such cones, and apical angles for 23 of these, ranging from 90 * to 122”. Quartzite most readily forms outcrops and most cone segments seen are in this rock type, but cones have also been reported in shale and epidiorite, in the central Archean core and in rocks of the alkali intrusive suite. An attempt to estimate the energy absorbed in forming cones follows. The orientation of the cones, as now seen and as they might have been when first formed, is discussed in a later section. Consider a partial cone with area 100 cm2, and suppose that in forming the striated cone surface, a shear stress af IO MPa operated by travelling through 0.1 mm. The energy expended in forming one partial cone would be (lo7 Pa). (10m2. 10m4

m3) = 10 J. * Aside from outlying examples, most of the reported cones lie within a field area of about 400 km’. However, this must be taken as representative of a volume of rock: perhaps 10 km of rock in the third dimension contains or contained cones, part of the 10 km now extending downward beneath the outcrops and part having been already eroded away from above them. The volume thus pictured is 4000 km3. To form just one partial cone per cubic meter throughout this volume would consume 4.1013 J. The true abundance of partial cones is very difficult to assess. Where well developed their intensity is equivalent to perhaps lo4 segments/ m3, each segment having an area of 100 cm’ as postulated (Nicolaysen, pers. commun., 1988). On the other hand, many square meters of outcrop show no cones at all. Suppose each pocket rich in cone segments is separated from the next pocket by a barren zone. If the barren zone is ten times as wide as the rich pocket, then on a volume basis the average concentration for the region is onethousandth of the concentration in the rich pocket, or ten segments/m3. Then, the estimate of total energy absorbed becomes 4. 1014 J. This is less than one millionth of the thermal energy or gravitational energy estimated, and so we come to the following questions: In magmatic activity, how much thermal energy is converted first to mechanical disturbance at the source, then to radiated energy of seismic waves, and thence into actual formation of rock flour on cone surfaces? Or, in diapiric activity, how much of the low-intensity gravitational energy available can be concentrated in order that it is released in short, sharp, local-

One can check the estimate as follows.

Shear-melted

cones

(Gay

kJ,kg

for heat liberated

reverse:

of 10 J/100

cm’ of cone surface

glass has been reported

et al., 1978) and the factor

10 J of energy

as magma

from some

used above

solidifies

of 510

can be used in

can heat and melt 20 mg of granitic

rock if the rock is already

hot. It needs to be 200°K

or less

from its melting point when the 10 3 of energy are released. it is more than 200 o K below its melting with not cause melting.

This is sufficient

pm thick over 7 cm’ of surface. be heated, However, report

and less than the orders

cited.

to form a skin 10

In reality,

20 mg would

of magnitude

If

point, 10 J of energy more rock would

be actually

are compatible

melted. with

the

PROCESS

ENERGY,

VREDEFORT

ized, cone-forming bursts? If, at each step of the magmatic sequence, one-thousandth of the energy is converted to the next required form, we achieve a value below the quantity estimated for shattercone production: lO*l J of thermal energy, 1018 J of mechanical disturbance at the source, and lOI J of seismic wave energy released, from which perhaps 10 I2 J could be absorbed in forming shatter cones. On the other hand, if this sequence is merely the trigger, and acts to release gravitational energy that has been temporarily stored in elastic strains, we find more than enough energy on hand. Even at lo4 cone segments/m3, at 10 J/segment we need only lo5 J/m3, whereas the elastic energy of deformation that can be stored in a sandstone or shale before rupture can be locally lo6 J/m3, as mentioned above. The comparisons just made complete the first trial survey of quantities of energy. The conclusion-that a magmatic energy source might contribute to cone formation but more as a trigger than as the main source-is obviously very tentative. To explore the validity, one can turn firstly to laboratory studies and secondly to observed behavior at magmatic sites; of the latter, Mount St. Helens is a particularly well documented example. Comparison

with other indicators

Laboratory studies have been made of the stress magnitudes required to produce planar microdeformations in quartz and to produce coesite and stishovite. Planar microdeformations

159

STRUCTURE

in quartz

Shatter-coned rock from Vredefort contains abundant planar microdeformations and lamellae in quartz (Carter, 1965, 1968; Lilly, 1981; Reimold, 1987). It was suggested above that the stress magnitude involved in forming a shatter cone was of the order of 10 MPa; the cone is presumably covered by a thin film of rock flour and this stress magnitude is compatible with estimates of the stress that produces rock flour in earthquakes and on glacial striated surfaces. In contrast, experiments in which quartz lamellae have been formed have involved shear stress magnitudes at least 100

times larger (H&z, 1968), and shatter cone material from Vredefort contains abundant lamellae (Carter, 1965, 1968; Lilly, 1981). The difference raises intricate questions about water content and temperature, about the extrapolation from laboratory tests to natural conditions, and about exactly how short and sharp a natural compression wave might be. These are substantial questions, but they are of a somewhat different type from the energyrelated questions that form the main focus of the present paper. Just one link will be noted here between questions of deformation on a microscale and the more coarse-scale geological processes under review, namely, the “carbon dioxide hypothesis”. As mentioned in the introduction, one can speculate that the alkali intrusives and the Vredefort dome in general were CO,-rich and water-poor. The effect of water in affecting the mechanical behavior of quartz is well known, but the mechanical effect of perhaps 300 or 600 MPa pressure of CO, is less well known. In attempts to reconcile the stresses required for deformation microstructures with the stresses generated by eruptive processes, it is possible that the pressure and carbonic character of the volatile fraction have a role. Summarizing, the deformation features are intriguing and important, but at present do not provide firm information about conditions; instead, they draw attention to inte~elations~ps about which more info~ation is desirable. Occurrence of coesite and stishouite

In comparing hypothetical geologic processes with conditions for formation of coesite and stishovite, a first step is to consider local concentrations of stress. A fractured rock at a depth of 30 km might be subjected to a nominal 1 GPa lithostatic pressure. If, upon being disturbed, the fracture changed to a geomet~ where there was only 0.1 m2 of rock contact/m’ of fracture, the compressive stress could rise locally to magnitudes of the order of 10 GPa (depending on the behavior of the fracture-filling material present over the remaining 0.9 m* of fracture area) (stishovite requires 8-10 GPa to form (Holm et al., 1967)). The fact that stishovite formed at Vredefort and,

B. BAYLY

160

equally

important,

the fact that it survived

converting

back to quartz

facts must

be woven

events

at Vredefort,

directly

For example,

mentioned related

in connection to a stress

MPa or perhaps

the entire

although

on the energy

discussion.

is si~fi~ant,

into

and these sequence do not

currently

of bear

under

the 10 MPa shear stress with cone formation

difference

a little

they

estimates

al. give body-wave

without

(a,,-~,~,)

is

of 20

more, and is an average

over 100 cm2 or a comparable

area. The connec-

as follows: May

April

magnitudes 7, magnitude

12, 4.8 and

triggered

May

thus appears

slightly

4.9; April

18, 4.7 (the

the north-slope

cursors).

mb for four events

collapse

and

less energetic

These authors

16, 4.9;

last, than

give a surface-wave

which

eruption, its premagni-

tude M, of 5.2 for the May 18 event. The Gutenberg-Richter in joules,

(1956) relationship

energy estimate

for the energy

= 4.8 + 1.5 MS, then

log,,E

E

gives

an

of 10 ‘2.6 J . The total for four such

shear stress and

events would be over 1013 J. Endo et al. (1981) use

a possible 10 GPa of locally concentrated compressive stress is only indirect, and estimating one figure is scarcely of use in estimating the other.

local magnitudes, and describe the May 18 event as the “largest magnitude earthquake, 5.1”. Despite discrepancies, however, their preliminary calculations agree well with those of Kanamori et al., indicating a lower limit of 1.8 * 1013 J for the

tion between

10 MPa of averaged

Energy release at Mt. St. Heelens

entire April-May The events of April and May 1980 are of interest because they permit a quantitative comparison of the thermal energy inside a volcano with the seismic energy released. The thermal energy estimate is 10’” J and the seismic energy estimate is 1Or3 J. As usual, the uncert~nty in the estimates is considerable, but they do, in some sense, support

swarm.

We have now to speculate

about

a quantity

of

magma 1000 times larger and a quantity of energy absorbed in forming shatter cones that was estimated

in the range

10’4-10’5

J. The mechanism

by which a pocket of magma inside the earth releases energy in seismic waves is not at all well understood,

but it seems likely that a larger pocket

could produce a somewhat larger single event, while almost certainly a larger pocket would have

the suggestion made earlier that the alkali magmatism at Schurwedraii could produce the shatter cones only under rather extreme and improbable circumstances. The basis for the thermal estimate just given is

a longer emplacement history, so that presumably it could give rise to a Longer series of seismic events. Let us imagine individual events at 1Oz4 J

as follows: After the north-slope collapse at Mt.St. Helens a discharge of ash continued for 9 h (Christiansen and Peterson, 1981); the equivalent

each, more than ten times as violent as at Mt. St. Helens, and let us imagine 1000 of them instead of four. Alternatively, ten events at lO“j J each

volume

When a magma saturated with volatiles at high pressure is “uncorked”, the ratio (rock mass dis-

{seismic magnitude Iw, = 7.5) would give the same total, 10” J. Out of such a total, possibly lOI J could be available for absorption in producing

charged

shatter

of solid

rock was estimated

as ash)/(mass

remaining)

at 0.2 km3.

might

lie be-

tween l/2 and l/20. Taking l/5 as a convenient trial value gives 1 km3 as the volume of parent solidifying magma. This is l/1000 of the estimated volume of the alkali intrusives (which were assumed to approximate

at Vredefort a cube with

an edge 10 km long). Thus the Mt. St. Helens magma would carry 1Ol8 J of excess thermal energy according to the pattern of calculation given above. The estimate of seismic energy released at Mt. St. Helens is based on the work of Endo et al. (1981) and Kanamori et al. (1984). Kanamori et

cones.

The conclusion from these considerations that they do not force us to dismiss outright

is the

possibility of magmatic action being the sole source for the energy that was absorbed in forming the shatter

cones,

but

the possibility

of magmatism

being the sole source does seem marginal. Furthermore, as a general rule granitic plutons are not surrounded by shatter conesthe relations~ps at Vredefort are exceptional rather than typical. Hence we return to the idea that was introduced earlier (at the end of the section “Energy associated with shatter cones”) that the cones result

PROCESS

from

ENERGY,

a combination

conjunction produced readily

161

STRUCTURE

of processes.

of diapiric

If it was

and magmatic

these

and

the absence

and plutons reasons

the “conjunction

ther:

As well as their

shatter

cones

space

that

arrangement hypothesis

what

hypothesis” energy

from

somewhat

is compared

might a little

requirements,

have a geometrical is

are more

of cones

with

be furthe

arrangement

systematic,

and

host-rock

bedding,

the restored

very well organized

inward

On the other and

Mayer

hand,

(1989)

in this

where

conjugate

bisecting

set.

by Albat

(1) or (3). In certain

cones,

joint

sets are present

Albat

found

the obtuse angle between

(2)

outcrops

that

as

the line

conjugate

joints

was roughly

parallel

intersection

angle and the apical angle of the cone

were roughly

the conjunction

radial

an observation

planar

well as shatter

cone axes form a

pointing

fits less well with process

and favors process

is more easily explained.

we consider

called

a

stresses that

the cones, the energy quantities handled

other diapirs For

VREDEFORT

equal,

to the cone axis, and the joint i.e. the cones

nested

neatly

into the obtuse angle between the planes. Suppose the direction of the cone axis is the direction of

in the next section.

Shatter cone orientation

least compressive stress. Then, conjugate planes could result from compression increasing by

As noted for forming

unequal amounts

in the preceding paragraphs, energy shatter cones might arise in one of

three ways: (1) Purely locally, by release of elastic that were imposed on the cone-containing during

strains rock

sion increased equally along all directions normal to the axis, without any direction being predominant. These two stress conditions are closely related,

uptilting.

(2) Purely centrally, by magmatic events and radial seismic transmission. The energy would come from outside contains the cones.

the axis, whereas

the cubic

meter

of rock that

and lead toward

and conjugate

joints

the idea that

are genetically

the cones

similar,

one

arising where the stress field has a radial symmetry and the other where it is not so highly symmetrical.

(3) By a central shock triggering locally stored elastic strain energy. In (1) the orientation

along two directions normal to a cone could result if compres-

of the cones

release

of

should

be

A means Albat

related to the local deformation, in (2) it should be related to the position of the central source, and in (3) one might expect a rather complicated set of cone segment orientations. Following initial work by Hargraves (1961), the most extensive study of cone orientations is that

and

of reconciling Mayer’s

Manton’s

(1989)

work

observation

can

with be

found if we explore the idea that bedding was already tilted at the time the cones formed. Conjectures of this type have already been put forward by Brink and Knight (1961), Ramsay (1961), Manton

(1965,

p. 1046) and

Nicolaysen

(1972).

Here we emphasize the facts in Manton’s fig. 17, that cone axes make angles between 2” and 32”

of Manton (1965). Observations by Simpson (1981) do not conform with the generalizations proposed

with the bedding, and consider a segment of collar-forming sediments as shown in Fig. 2. Figure

by Manton. Observations by Albat (1988) conform with Manton’s generalizations if one makes

2A shows the segment (stippled) region (dotted outline) through

an ad hoc assumption faulting affected most

material process,

that 18” of rotation by of the outcrops studied;

possibly Albat’s and Manton’s observations can be reconciled without this assumption, but the point requires further study. A prominent aspect of Manton’s observations rather favors process (2). As shown in his fig 17, if a method is used for restoring outcrops to a set of hypothetical positions they occupied before uptilting, and cone axes are restored along with the

from beneath the sediment

and the circular which buoyant

the sediments rises. By this slab is flexed upward and

simultaneously dragged inward. involves shortening tangentially,

The inward drag while the uptilt-

ing involves bed-parallel shearing, with a shortening direction that plunges radially inward and downward into the slab, and an elongation direction that projects radially inward and upward out of the slab. If it projects upward at between 2O and 32” with respect to bedding, then at a loca-

9. BAYLY

162

enlarging on this conjecture are given in Appendix 2. The suggestions just made have much in common with those of Nicolaysen (1972) who also envisages the cones forming at a stage when bedding was steeply inclined. A difference is that in Nicolaysen’s hypothesis, the cones form as the material escapes from strong lateral confinement, and form in a stress regime where the maximum compressive stress is approximately vertical. As discussed here, in contrast, the cones form while the lateral or radial compression exceeds the axial compression.

elongation

Summary and conclusions Fig. 2. The stress state produced diapir

by inward

cover

drag.

being dragged

in metasediments

A. A sector

inward

as the diapir

radial

symmetry. radial than

are equal

C. The orientation

symmetry

elongation

shortening were

direction

bedding,

and

cone

shortening

in amount,

giving

of the cone that could

sufficiently

a

rises. B. The stress

state in that part of the sector where tangential inclined

around

of the metasedimentary and radial

result if

closely

approached.

(The

axis would

dip more

steeply

but it is not suggested

that they would

neces-

sarily be vertical.)

tion where the two shortening effects are equally strong, conditions would be suitable for a cone, while at a location where the two shortening effects were unequal, a conjugate fracture pair could appear. (Strain in the uptilted sediments is discussed in more detail in Appendix 1.) The suggestions just made have partial success in accounting for the orientations reported; but by emphasizing normal tectonic processes they fail to explain why Vredefort is rich in cones while most domes are not. Using normal tectonic concepts, one may only explain the radial stress symmetry needed for a cone as a coincidence. In contrast, when a plane or spherical compression wave advances through homogeneous material, radial symmetry of all the transient local stress states is expected. For this reason, the idea comes up again: Could the phenomena be due to some combination of elastic waves from a central source passing through material that is already predisposed to failing, on account of containing stresses and stored elastic energy of tectonic origin? Details

(1) Energy for creating the collar of upturned sediments may have been available from density inversion; neither a bolide nor an explosion is required to account for the collar. (2) The coincidence in space of the alkali intrusions occurring within the collar may be due to the intrusions having initiated the updoming (by increasing the mobility of the rocks they intruded). Even though much energy was purely gravitational in source, its release may have been triggered and localized by the intrusions. (3) There is room for a range of possible opinions about the relative importance of volcanism and the density inversion as sources of energy. Thermal energy associated with magmatism could have been as little as one-fifth of the energy derived from gravitational sinking and doming, or could have exceeded the ~a~tational energy by a factor of five or more. it is difficult to put an upper limit on the amount of energy that might have been transported through the Vredefort region by escape of volatiles from the mantle. (4) The shatter cones-their presence, internal structures and preferred orientations-can be explained (though not readily) by a hypothesis involving the conjunction of volcanic and gravitydriven effects; such a hypothesis involves assuming special conditions and favorable circumstances, and is considered weak rather than strong. If the abundance of planar fractures relative to cones were better known, the matter could perhaps be resolved.

PRGCESS

ENERGY,

VREDEFORT

163

STRUCTURE

(5) The mechanism that created the cones remains in doubt. It appears that the region formerly contained far more than sufficient energy-but mainly in dispersed, low-intensity forms. By contrast, there is evidence to suggest that the cones were formed by high stress intensities (presumably in short, sharp pulses). It is not known whether this evidence and the low regional stress-intensity level can be reconciled. (6) The pseudotachylite veins, the bronzite granophyre and the very water-poor, CO&h fluid inclusions analyzed from the granite gneiss all hint at an environment poor in water and rich in some type of carbonic volatile. Such an environment would be wholly consistent with observations on other alkali intrusive suites worldwide, and with the idea of a mantle source. (7) The physical behavior of slightly porous rocks whose pores are charged with a carbonic fluid at a pressure close to the overburden pressure is not well known. Impacts and man-made explosions have not yet yielded information on the stress magnitudes required to produce deformation features in rocks in this state-stresses which may be smaller than for rocks subject to low pore fluid pressure. (8) The presence of stishovite at Vredefort implies both high local pressure and efficient quenching. Sufficient pressure to form stishovite may be commonplace in deep-seated fractures: the rarity of stishovite may be due more to the rarity of efficient quenching than to rarity of the required stress level. An episode of rapid escape of a volatile phase through a fracture at a depth of lo-30 km could provide high transient stress concentrations at asperities and also part of the required quenching action. (9) Two sources undoubtedly provided energy at Vredefort, the density inversion and the alkali intrusions; the energy available was of the order of 102r J from each. Energy considerations do not require us to postulate abnormal quantities of compressed volatiles as a third source, but if we attempt to account for the deformation features by internal processes, postulating compressed volatiles seems to help toward plausible mechanisms for creating the features. It is once again emphasized that other hypothe-

ses are by no means discounted. The purpose has been to add detail within one field of possibilities while rern~~ng neutral overall, and to emphasize quantities of energy as a means of study. It is hoped that readers will be prompted to modify all of the above, in favor of more robust versions of their own. Acknowledgements

It is a pleasure to acknowledge the support and interest of Louis Nicolaysen and the Organizing Committee of the Workshop. Neville Carter, Louis Nicolaysen and a third reviewer made very helpful comments on the text. A travel grant from the Organizing Com~ttee made participation possible. Appendix 1

Estimates

ofstress and

strain in the diapir

We use the dimensions and sequence of geometrical states from Fig. I, and make the following rough estimates or assumptions: (1) The total energy dissipation is divided into two-thirds in the rising gneiss and one-third in the descending surroundings. (2) Each half of the process, stage (a)-(c) and (c)-(e) (Fig. lB), dissipates the same energy (i.e. in the gneiss, in each half of the process, one-third of the total energy). (3) Of this (one-third x total), one-quarter is used during the slow change (a)-(b) and tree-quarters during the more rapid change (b)-(c) (i.e. the change (b)-(c) in the gneiss dissipates one-quarter of 102r J). Let the strain rate reach half its peak value at time t, and, after passing the peak, return to half its peak value again at time t,; let the stress do the same. Then, the dissipation rate reaches onequarter of its peak value at time t,, and must follow a change with time of the type shown. Inspecting the first half, we find that if the area between t, and t, is divided into three equal areas (ii), (iii) and (iv), the long lead-in period (shaded in Fig. 1B) can be taken as a fourth similar area, so that time t, corresponds to geometrical stage

B. BAYLY

164

(b). The volume dissipation

is 5 - 1013 m3 and the

of gneiss

during the change (b)-(c)

J, so the average dissipation/m3 There are some additional

is (l/4)

* 102’

is 5 . lo6 J/m3. approximations:

Halfway between t, and t, strain rate = 0.8 X peak rate, stress difference dissipation

= 0.8 x peak stress difference,

rate = 0.64 x peak dissipation

= average dissipation

rate

rate

over t, - t,

5 * lo6

= 7

J/m’+

where T = t, - t, seconds. With the factor 0.64 removed (peak stress difference) x (peak strain rate) = 8.106/T J/m3-s. We next examine strain

magnitudes.

Passing

from stage (a) to stage (c), radial shortening strain = 26/80 = 0.33 and vertical elongation strain = 1.20. In terms

of stretch,

these are equivalent

to

0.67 radial stretch and 2.2 vertical stretch, which for convenience we may consider as built up from four consecutive stretches of 0.9 and 1.2 each [(O.9)4 = 0.67; (1.2)4 = 2.21. In terms of strain, these equal 0.1 radial shortening strain and 0.2 vertical elongation. These four strain increments develop in successively shorter periods of time, found by dividing the area under the first the strain rate curve into four equal parts. approximation the last of these occupies, ample, 0.3T at strain rates of 0.1/(0.31”) and 0.2/(0.3T) vertical. At this stage, the strain rate is very close to the peak strain that peak stress difference equals: (8 . 106/T /(0.67/T

half of As an for exradial average rate, so

s-l

vertical

Fig. Al. Deformation of layered material overlying a diapir. A. Tbe element considered, in its original configuration and a later configuration. B. Examples of dimensions (km). C. An orthogonal grid on an idealized diapir neck. D. A typical profile for an overlying layer that is pierced by a rising dome.

Strain in the overlying sediments Using the idea presented deformation of a tapering,

strain rate)

= 12 * lo6 Pa = 12 MPa. This result can be checked by the following argument: The shear stress on the vertical sides of the cylinder at stage (c) can only be less than (buoyancy of cylinder)/(area of vertical surface) = (80 kg/m3) (5 . 1013 m3) (9.8 N/kg)/(2ss 27 km)(22 km) = 11 MPa (because the upward motion of the cylinder is hindered by stress on its circular top and base as well as by drag on its vertical sides). The order of magnitude confirms the conclusion already reached.

in Fig. 2, we consider long, thin radial ele-

ment of sediment as shown in Fig. Al. We give attention to a circle of initial radius 27 km (this figure is chosen merely to agree with Fig. 1) and assume that it maintains this radius while rising through 10 km. Then, the 90” arc shown would have a length

of 16 km and the outer end of this

arc, now 37 km from the center of the circle, initially have been 27 + 16 = 43 km from

would the

J/m3-s)

D

C

center

length during

(approximately, bending).

ignoring

change

of

If a circle of radius 43 km

shrinks to radius 37 km, the tangential or circumferential strain is 0.14. This strain is a lower limit for the actual strain due to inward radial drag; more strain will accumulate if the tapering element continues to move on through the 90” arc shown, and in some sections the Vredefort collar in fact dips inward at 45* (i.e. has turned through 135 o rather than 90 “). However, the displacements that gave the extra 45O of overturning are not sufficiently well understood to permit a revised strain estimate. Around some domes, lines (e.g. the dotted lines

PROCESS

ENERGY,

VREDEFORT

165

STRUCTURE

in Fig. Al C) are considerably

elongated

circumferential

lines are shortening,

of the mantle

of the dome

while the

and portions

are moved

through

709-710) theory.

while Gash Milton

not

as in Fig. Al

all features

strain

D. In such a situation,

the above

of 0.14 would not underestimate

the true

It was suggested layer-parallel shortening

erroneous”

avoided

(1977,

at the outset:

in connection

shearing

could

as the inward

with Fig. 2 that generate

drag.

The

as much amount

of

explanations

necessarily

that

shatter that

have been

formed

a glass object The

and

Two

called

shatter

that every feature “shattered”

shatters-on with

possibility

high

considered

here

cone is produced

is of the order of 1 s. This is of course

through

by a pressure

that cones and

called

a time

extremely

could

if a layer were bent

are

a

in the sense

layer-parallel shearing required would be about 18”, or a shear strain of 0.3. Such an amount easily develop

if

errors

by the same mechanism,

cone necessarily

milliseconds tions.

are at best incomplete, p. 703).

(1) We avoid assuming

(2) we avoid assuming

by very much.

an alternative

“ theoretical

that have been advanced

great vertical distances. On the other hand, a true diapir pierces its mantle rather than ballooning it, estimate

(1971) offers

suggests:

scale of accelerais that

a

pulse whose period “instanta-

20 o or 30 o before fracturing (but of course could not develop as a homogeneous strain if the entire

neous” on geological time scales, but is slow in comparison with a true shock event; it is on the

deformation were by cataclastic processes). If tangential shortening of 0.14 due to inward motion and shortening at 45O to bedding due to

same time scale as human breathing, and the response within a cubic meter of rock is quasistatic. Inertia is involved only in the onward trans-

layer-parallel shearing were combined to give radially symmetrical shortening as in Fig. 2B, the

mission

associated

movement of one part relative to another ciently slow for inertia to be ignored.

to bedding.

finite

elongation

However,

would

still be at 45’

cone axes make angles from

of the pressure

ters farther

on; within

pulse to more rock kilomethe cubic meter considered, is suffi-

32” down to 2” with bedding (Manton, 1965, fig. 17). It is possible that the layer-parallel tension

We begin by considering a cylindrical specimen in an idealized, slowly changing,

that arises in the outer when superimposed on

axial stress state. Let the longitudinal and radial compressive stresses be u,_ and uR respectively;

part of a curved layer, the effects already dis-

rock uni-

cussed, could account for the observed inclinations being less than 45 O. Regarding layer-parallel elongations and shortenings due to bending, these are likely to have been smaller. For an arc of radius 10 km and a

then, when ur exceeds un, an ideal fracture would be conical with an acute apex and when uR exceeds (I~, an ideal fracture would be conical with an obtuse apex. (If the cylinder axis were vertical, these would correspond to normal and reverse

bend through 90”, as shown in Fig. Al, a layer 500 m from a neutral surface suffers only 0.05 of

faulting

linear strain. Or, in non-typical locations where the radius of curvature is only 1 km (Fletcher and

fort in mind, we note that the cones there are obtuse (Manton, 1965, table 2; Albat, 1988, fig. 4),

Reimold, 1987) a layer 50 m from a neutral surface would suffer the same amount. The abun-

and we attend

dance of bedding-plane weaknesses and other fractures suggests that, in fact, layer-parallel strains would have been less than these hypothetical amounts. Appendix 2 Shatter cone mechanisms An unpublished 1964 thesis contains a theory for shatter cones (summarized in Milton, 1977, p.

respectively,

try rather

than

but with cylindrical

on planar

mainly

surfaces.)

to that

With

condition,

symmeVrede-

despite

the fact that elsewhere some cones are reported to be acute. When a plane compressional wave advances along some direction through an outcrop, the direction of advance corresponds to the longitudinal

axis L above,

and moments

when

u,_ ex-

ceeds (In are normally followed by moments when aR exceeds ui,. It is suggested that it is during the latter period that cones will form if they form at all. The reason for the change in relative magnitudes of ur, and uR is that, not uncommonly, an

B. BAYLY

166

advancing compressional pulse is followed by a dilational pulse. We assume a uniform plane wave (or spherical wave from a distant source so that in the outcrop-sized region of interest, it approximates a plane wave): Then, displacements and strains are non-zero along L, but are zero along R. In this geometry, zfR= ui, v/(1 - V) where P is Poisson’s ratio, so that ffn might be typically 0.4a,. Let the ambient stress state before arrival of the pulses be a lithostatic compression P, and let the extreme values of et_ first in compression and then in dilation be GE and -UC. Then during compression, total stresses become P f G: and P + 0.402, and during dilation they become P - t$ and P - 0.40:. Of the latter pair, the net radial effect P - 0.40; is a larger compression than the net longitudinal effect P - (7:. Or, if the ambient stress state before arrival of the pulses was nonhydrostatic, it would be necassary to distinguish different pm-pulse magnitudes P, and P,,and to evaluate P, - uf and P, - 0.4~:. Conical fractures would be most likely where P, - uf was positive but small. (Equations for et and eIR are given, for example, by Acheubach f1975, eqns, 4.34 and 4.35). Examples of curves showing how uL and cra remain in proportion while changing from compression to tension are given by Rinehart jI960, figs. 7. 1fF and 7.13F).) In considering the rather elementary ideas offered, we note that the malpnitudes of the different stress components would normally not be suitable for fracturing. At, for example, 10 km deep, P, and P, would be - 300 Mfa while S_T:would probably be less than IO MPa at I km from the source of disturbance and less than 0.1 MPa at 10 km away. It seems that the cubic meter of rock considered would first need to have a considerable fluid pressure, to bring the effective stresses P -p (fluid) down to tens rather than hundreds of mega-Pascals. Additionally, it might require a pre-existing difference P, - P, already almost sufficiently large to produce failure. It would only be under these unusually favorable circumstances that typical values of GE could trigger fractures. On the other hand, as Rinehart (1968, p. 42) points out: “,,. a rock mass, with its inherent heterogeneities in physical properties, is an ideal spawning ground for secondary wavelets which

are capable of generating highly localized, potentially destructive, stress concentrations.” Even if typical values of 0: are too weak to trigger fracturing, it is possible that the localized concentrations that Rinehart mentions would be sufficiently strong. As elsewhere in this ~ont~bution, the preceding hypothesis is not especially favored over other hypotheses. We attempt only to answer this question: If one attempts to form a hypothesis of this general type, how far can one proceed into details, and what numerical values give the best prospects of success? A certain amount of detail and quantification must be obtained before one hypothesis can be effectively evaluated against another. References Acbenbach, J.D., I975 Wave prop~ation in elastic sofids. North-Holland Publ., Amsterdam, 425 pp. Albat, H.M., 1988. Shatter cone/bedding interrelationship in the Vredefort Structure: evidence for meteorite impact? Trans. Geol. Sot. S. Ah., 91: 106-113. Albat, H.M. and Mayer, J.J., 1989. Megascopic planar shock fractures in the Vredefort Structure: a potential time marker? Tectonophysics, 162: 265-276. Allen, T. and Chamberlain, C.P., 1988. The thermal consequences of gneiss dome formation. Eos, Trans. Am. Geophys. Union, 69: 509. Birch, F., 1966. Compressibihty; elastic constants. In: S.P. Clark, Jr. (Editor), Handbook of Physicai Constants. Geol. Sot. Am. Mem., 97: 97-173, Bischoff, A.A., 1982. Thermal metamorphism in the Vredefort Dome. Trans. Geol. Sot. S. Afr., 85: 43-57, Brink, A.B.A. and Knight, K.A., 1961. Discussion on “Shatter cones in the rocks of the Vredefort ring”. Trans. Geol. Sot. S. Afr., 64: 157-158. Bumham, C.W., 1985. Energy reiease in subvolcanic environments: implications for breccia formation. Econ. Geol., 80: x515-1522. Bumham, C.W. and Davis, N.F., 1971. The role of Ha0 in silicate melts 1. P-V-T relations in the system NaAISi, Os-Ha0 fo 10 kilobars and lOOO*C. Am. J. Sci., 270: 54-79. Bumham, C.W., HoBoway, J.R. and Davis, N.F., 1969. Thermodynamic properties af water to 1000°C and 10,000 bars. Geol. Sot. Am. Spec. Pap., 132. Byerlee, J., 1978. Friction of rocks. Pure Appl. Geophys., 116: 615-426. Carter, N.L., 1965. Basal quartz deformation lamellae, a criterion for recognition of impactites. Am. J. Sci., 263: 786-806 Carter, N.L., 1968. Dynamic deformation of quartz. In: B.M. French and N.M. Short (Editors), Shock Metamorphism of Natural Materials. Mono Book, Baltimore, pp. 453-474.

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