Tectonophysics,
78 (1981)
Elsevier Scientific
Publishing
385-402 Company,
VARIATION IN AMPHIBOLE DEFORMATION
385 Amsterdam
-Printed
AND PLAGIOCLASE
in The Netherlands
COMPOSITION
WITH
K.H. BRODIE Department
(Received
of Geology,
January
Imperial
College,
London
SW7 2BP (Great
Britain)
26, 1981)
ABSTRACT Brodie, K.H., 1981. Variation in amphibole and plagioclase composition tion. In: G.S. Lister, H.-J. Behr, K. Weber and H.J. Zwart (Editors), Deformation on Rocks. Tectonophysics, 78: 385-402.
with deformaThe Effect of
Investigation of the mineral chemistry of a shear zone in an amphibolite facies metagabbro has shown that the composition of the amphibole and plagioclase varies with deformation. Chemical analyses of the rocks indicate that the shear zone approximates an isochemical system. The amphibole varies progressively from an initial magnesio-hornblende to a ferroan pargasitic hornblende in the shear zone, alkalies, Ti and Fe’+/Fe’+ + Mg increasing, while the plagioclase becomes more anorthitic, varying from labradorite to bytownite. These changes in composition of amphibole and plagioclase from metabasic rocks are normally associated with increasing temperature in prograde regional metamorphic terrains; such chemical variations observed in localized shear zones would suggest that shearing stress in regional metamorphism may play an important role in producing 1 the documented discrepancies in amphibole chemistry between different metamorphic belts.
INTRODUCTION
Attention has recently been paid to the role of deformation in metamorphism and its effect on mineral and rock chemistry. In particular the effect of localised shearing, which produces narrow mylonitic zones within initially homogeneous rocks, on the rock chemistry has been considered (Boyle, 1961; Beach, 1973, 1976; Kerrich et al., 1977). These investigations have mainly considered changes in rock chemistry together with variations in mineral assemblage into the shear zones. Most examples have involved open systems where a fluid has been introduced leading to the formation of an hydrated, .apparently retrograde, mineral assemblage. The main effect of the deformation has been to reduce grain size, increasing the grain boundary area available for reaction and diffusion and allowing the influx of a fluid phase. Kerrich et al. (1977) studied two shear zones, one of greenschist and the other of amphibolite grade, formed in metabasalt and adamellite, respectively. 0040-1951/81/0000-0000/$02.50
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Their results supported the conclusion that lower grade shear zones involve chemical and volume variation and that diffusional mass transfer is the dominant deformation mechanism, while at higher grades deformation occurs under nearly isochemical and isovolumetric conditions over the scale considered, dislocation creep being dominant. Little attention has been paid to the effect of deformation on mineral chemistry. It has been shown that the mineral chemistry may change in shear zones (Beach, 1973; Borges and White, 1980; Brodie, 1980) but that this is partly due to the changing chemical environment produced by the introduced fluid phase rather than directly to the deformation (Brodie, 1979, 1980). Ideally an isochemical shear zone in a homogeneous rock is required to gain any information about the effect of deformation on mineral chemistry. Other problems associated with using shear zones to determine the effect of deformation on mineral composition include the possibility of heterogeneity in the initial composition of the rock (shear zones may form preferentially along zones of varying composition) and the generally complex assemblage of mineral phases present which may make interpretation of any observed compositional variations difficult. This paper summarizes the initial results of a study of a shear zone formed in an amphibolite facies metagabbro. The problems outlined above appear to be minimized. The observed progressive change in mineral composition into the shear zone and between relict and recrystallized grains within one slide argues against any initial chemical inhomogeneity in the rock, while the simple, two-phase mineral assemblage makes interpretation less complicated. The analyses indicate that H,O content is approximately constant across the zone, which, together with the absence of a secondary hydrated assemblage, indicates that there was no large influx of fluids into the system. Mass balance calculations indicate that the concentrations of major and minor elements do not change appreciably across the zone. SAMPLES
STUDIED
The samples studied are from the Valle d’Ossola (Tote Valley) region of the Ivrea-Verbano Zone in Northern Italy. This zone consists predominantly of steeply dipping mafic, ultramafic and pelitic metamorphic rocks and is truncated in the north by a fault zone, the Insubric Line, which separates it from Alpine metamorphic rocks. In the centre of the zone, along the Tote Valley, a general increase in metamorphic grade (from amphibolite to granulite facies) is observed from SE to NW. This has been attributed to increasing pressure and temperature along an ambient geothermal gradient (Berckhemer et al., 1968; Giese, 1968), or alternatively to intrusion of mafic magmas into a series of steeply dipping pelitic rocks that were undergoing amphibolite facies metamorphism (Schmid and Wood, 1976). The shear zone investigated is from an amphibolite facies metagabbro near Anzola which is comprised dominantly of amphibole and plagioclase. Garnet
381
is developed in some parts of the metagabbro. The zone is approximately five metres wide and trends nearly vertically along 005” discordant to the weak foliation in the host metagabbro. The age of the shear zone is not known, but it may be associated with movement on the major fault, the Insubric Line, further to the west. PETROLOGY
The unmylonitized rock is a coarse grained amphibolite facies metagabbro (Plate 1A) that contains an essentially two phase assemblage of hornblende (average grain size -2 mm) and plagioclase (-1 mm) with minor opaques (Fe-Ti oxides and Fe sulphides). Some of the hornblendes contain narrow, dark-brown lamellae that appear to be spinel; their small size precludes a definite identification. In the shear zone there is a progressive reduction of grain size due to recrystallization of the hornblende and the plagioclase, producing a finegrained (0.05-0.08 mm) mylonite in the centre of the zone. This consists of porphyroclasts of hornblende, and more rarely plagioclase, in a matrix of recrystallized hornblende and plagioclase. The grain size of the matrix varies depending on the proportion of plagioclase to amphibole, being finer in the plagioclase-rich regions (Plate 1B). Some of the hornblende porphyroclasts show slight changes in pleochroism towards their margins, becoming browner in colour; this is very irregularly developed. Minor opaque phases, mainly FeTi oxides containing small amounts of Mn, are present. There is an apparent modal increase in the abundance of amphibole into the shear zone, although the very fine grain size of the recrystallized plagioclase makes modal determinations difficult. This could, in part, reflect an initial modal heterogeneity. It is common in the area studied to find shear zones in metagabbros forming preferentially along amphibole-rich layers. MINERAL
CHEMISTRY
The compositions of the amphiboles and the plagioclases were determined using a Cambridge Instrument Mark 5 electron microprobe fitted with a Link Systems energy-dispersive analyser. Standard deviations for the analyses were obtained from ten replicate analyses on individual grains and the values are listed in Table I. The errors are small for most elements, but are more significant for Si (this will obviously introduce errors into calculations of tetrahedral Al in the amphiboles), Ferric iron values in the amphiboles were determined following the method outlined by Papike et al. (1974). Analyses were carried out on three samples that are considered to be representative of unmylonitized, partly mylonitized, and completely mylonitized metagabbro. These are: Al: relatively undeformed metagabbro from the edge of the shear zone; A6: partly recrystallized metagabbro, 0.2 m into the shear zone;
388
Plate 1. Optical micrographs. A. Sample Al, the unmylonitized metagabbro containing euhedral hornblende and twinnned plagioclase. B. Sample A8, the mylonitized metagabbro from the centre of the shear zone. Note the reduced grain size in the plagioclase-rich bands. (Crossed nicols).
389 TABLE
I
Standard
deviations
Oxide
5.12 + 0.18 -
NaaO
28.28 54.57 -
Al203
SiO2 Fe0 CaO MnO TiOz
+ 0.29 + 0.38
-
Total
TABLE
_+0.16 + 0.18 + 0.26 + 0.51 + 0.18 + 0.08 + 0.14 f 0.09 f 0.14
97.30
99.30
II
Averaged
amphibole
SiO2 TiOz A1203
*
Formulae Si AP Ti Fe’+ Fe3+ Mn Mg Ca Na Na* K
1.68 11.88 10.40 44.57 14.46 0.85 11.41 0.27 1.78
0.19 f 0.04 11.14 f 0.21 -
K20
Aiv
Amphibole
Feldspar
MgC
FezOJ Fe0 MnO MgC CaO NaaO KzC Total
(wt. % oxides)
analyses
Al
A6 relict
A6 recryst
A8 relict
A8 recryst
44.54 1.87 10.63 2.86 11.75 0.20 11.86 11.53 1.77 0.88 97.89
43.21 1.93 12.01 0.77 13.22 0.15 11.32 11.65 2.25 0.97 97.48
42.34 2.15 12.47 0.52 13.70 0.13 10.92 11.73 2.21 1.12 97.28
42.78 1.94 12.03 2.03 12.43 0.17 11.28 11.66 1.96 1.06 97.33
42.15 2.18 12.60 0.77 13.59 0.06 10.80 11.72 2.00 1.24 97.12
(23 oxygens) 6.557 1.443 0.401 0.207 1.447 0.317 0.026 2.602 1.819 0.181 0.325 0.165
* Recalculated
from
total FeO.
6.422 1.578 0.524 0.216 1.643 0.086 0.018 2.507 1.855 0.145 0.505 0.183
6.331 1.669 0.528 0.242 1.713 0.059 0.017 2.434 1.879 0.121 0.519 0.214
6.370 1.630 0.480 0.217 1.547 0.228 0.022 2.504 1.860 0.140 0.427 0.201
6.314 1.686 0.539 0.245 1.702 0.087 0.008 2.411 1.881 0.119 0.464 0.237
TABLE
III
Averaged
feldspar
SiO2 A2O3
CaO Na20 KzO Total Formulae Si Al Na Ca K MolSb i
analyses Al
A6 relict
A6 recryst
A8 relict
A8 recryst
A8 edge
54.16 28.86 11.74 4.84 0.17 99.77
51.89 30.25 12.99 4.15 0.07 99.35
49.00 32.42 15.59 2.75 0.00 99.76
50.80 30.83 14.38 3.39 0.11 99.51
48.70 31.74 15.67 2.62 0.09 98.82
53.15 28.50 11.72 4.77 0.10 98.24
9.475 6.511 1.469 2.541 0.015 36.5 63.1 0.4
8.975 7.001 0.977 3.060 0.000 24.2 75.8
9.295 6.651 1.203 2.819 0.026 29.7 69.6 0.7
9.014 6.926 0.941 3.107 0.013 23.2 76.5 0.3
9.778 6.181 1.702 2.310 0.024 42.2 57.2 0.6
(32 oxygens) 9.806 6.160 1.700 2.277 0.039 Ab 42.3 An 56.7 Or 1.0
0.0
AS: fine grained mylonite, 0.35 m from the margins of the shear zone. Averaged analyses of relict and recrystallized amphiboles and plagioclases from each sample are listed in Table II and Table III respectively. The individual analyses are plotted on Figs. 1 to 4 and are briefly discussed below. Some of the scatter on these diagrams is due to the fact that no distinction is made between analyses from the centres and the edges of porphyroclast grains within any one sample. Amphibole
The unmylonitized amphibole is a magnesio-hornblende with (Na + K)* < 0.50, which becomes progressively more pargasitic into the shear zone, with an increase in (Na + K)A, together with decreasing Mg/Mg + Fe2+ (Fig. 1) and increasing A1”‘/A1”’ + Fe3+ (Fig. 2). Ti”’ also increases (Fig. 3) while Ca remains approximately constant. These changes are observed in the relict porphyroclasts but are more pronounced in the recrystallized grains which have a ferroan pargasitic hornblende composition. Some of the porphyroclasts show a slight variation in composition from centre to edge but this is rather irregular and depends to some extent upon the orientation of the grain. Plagioclase
Initially the plagioclase is labradoritic in composition (An5& but becomes more anorthitic in the shear zone (Fig. 4). The changes are again more pro-
391
PARGASITIC
PARGASITE
HORNBLENDE
[Na+ M
[
<0,50 eso-Hornblende
.v 1
.
C
Mg(
:DENI‘ E
1.60
EDENITIC HORNBLENDE
Mg+Fe2+
FERROAN PARGASITE FERROAN PARGASITIC HORNBLENDE
El5
no
F:ERRC E DENIT
-ERRO-EDENITIC HORNBLENDE
5
h+KlA,@50
,
IO
Si Ti c 0.50
6.25
Fe3+G AI”’
showing the change Fig. 1. Variation of Mg/Mg + Fe’+ with Si content of the amphiboles from a magnesio-hornblende to a ferroan pargasitic hornblende into the shear zone. Nomenclature after Leake (1978).
nounced in recrystallized grains, which have compositions up to AnT6 (bytownite). The plagioclase porphyroclasts show abrupt marginal increases in Na that are presumably due to late alteration along grain boundaries (see Table III). Electron microscopy shows micaceous material to be present along some grain boundaries (see later). This is similar to the effect of late alteration observed by. Borges and White (1980) and consequently all analyses were taken from the centres of the grains. Since the alteration has the reverse effect on the chemistry to that due to the deformation, it should not con-
392
Fig. 2. Variation as in Fig. 1.
of (Na + K)* with AlV’/_@ + Fe3+ content
of the amphiboles.
Symbols
. .
I
016
. 0 55
O-60
065 Mg/
Fig. 3. Variation
1.
070
Mg+Fe*+
of Mg/Mg + Fe’+ with TiV’ content
of the amphiboles.
Symbols
as in Fig.
393
Fig. 4. Variation in anorthite content of the feldspars into the shear zone. Weathering may be responsible for some of the spread in the analyses. Symbols as in Fig. 1.
fuse the observed variations although it may produce some scatter in the results. ELECTRON
MICROSCOPY
Preliminary investigation of the dislocation microstructure of the plagioclase and amphibole has been carried out. The amphibole from the unmylonitized sample (Al) contains semicoherent exsolution lamellae parallel to (100) with dislocations along the boundaries of the lamellae accommodating the misfit between the crystal structures (Plate 2A). In addition low densities of free dislocations are present generally with associated stacking faults; the separation between the partial dislocations is relatively small. The plagioclase in the unmylonitized sample shows regular twin lamellae parallel to the (010) and (001) planes and show evidence of irregular, antiphase domain texture (Plate 2B). The dislocation density is very low. Compared to the unmylonitized samples, the amphiboles within the shear zone contain a higher density of free dislocations and the separation of the partial dislocations appears to be larger. Subgrain boundaries and dislocation arrays are formed (Plate 2C). Recrystallized grains contain lower densities of free dislocations but some subgrain boundaries are present indicating that the recrystallization is probably syntectonic. The recrystallized plagioclase con-
Plate 2. Electron micrographs of hornblende and plagioclase. A. Amphibole from sample Al (unmylonitized) showing the planar
exsolution
lamellae,
parallel to a*, bounded by dislocations. The density of free dislocations is low and they are generally split into partials separated by stacking faults. B. Plagioclase (labradorite) from sample Al showing the antiphase domain texture, producing splitting of the spots on the diffraction pattern.
C. Amphibole from sample A8 (mylonite) containing a regular network of dislocation walls producing a subgrain structure, intersected by cleavage traces in places. D. Plagioclase (bytownite) from sample A8 showing fracturing along (001) and (010) cleavage planes and parallel twin lamellae, containing fine tweed-like exsolution. Note the dislocation wall.
396
tains twin lamellae and fine, tweed-like lamellar intergrowths (Plate 2D) similar to the Huttenlocher intergrowths described in the literature (Yund et al., 1975) from plagioclase of composition between An70_90. The relict plagioclase contains high densities of tangled, free dislocations and some dislocation walls. Alteration to a micaceous phase is observed in places, particularly at grain boundaries and fractures along cleavage traces parallel to {OlO) and (001). ROCK
CHEMISTRY
Major element analyses of the three samples Al, A6 and A8, determined by X-ray fluorescence analysis, are listed in Table IV. Fe was determined as total Fe,O,. Density values determined on the rock powders using a standard density bottle technique are also shown. The density appears to remain nearly constant across the shear zone. There does not appear to have been any significant fluid influx into the shear zone consistent with optical microscope observations described earlier. The slightly higher Hz0 content in the unmylonitized sample is probably due to the unavoidable presence of some weathered feldspar. Mass balance Mass balance calculations following the method (1967) indicate that the shear zone is approximately
TABLE Whole
SiOs TiOz A1203 Fe203
MnO MgO CaO NazO KzO PZOS H20L.O.I. Total Density
outlined by Gresens isochemical with the
IV rock analyses Al
A6
A8
46.01 1.23 15.35 12.37 0.20 8.84 11.15 1.88 0.54 0.13 0.31 1.25 99.26
43.60 1.88 14.40 14.70 0.25 9.56 11.23 1.36 0.77 0.35 0.12 1.00 99.22
42.97 1.98 14.49 14.89 0.25 9.68 11.22 1.22 0.76 0.35 0.12 1.13 99.06
2.98
2.89
2.99
Total Fe expressed as FezOs; for oxidation of FeO.
density values in gm cm -3
; Loss on ignition (L.O.I.)
adjusted
397
I
Composition -volume diagram for change Al to A8
I
volmle
o-6 decrease
I
1.0 Volume Factor, fv
I
I
1.4
Yolumeincrease
Fig. 5. Mass balance calculation between samples Al and A8, plotted as loss or gain of material, relative to the unsheared sample (Al), against the volume factor.
host rock, at least within analytical error, but may have undergone a slight volume increase, that is, it is a zone of dilatation (Fig. 5). Since the rock density is nearly constant across the zone and there is an increase in the modal proportions of amphibole (which is denser than plagioclase) it seems likely that the amphibole in the shear zone is less dense than that in the host rock. This is consistent with the suggestion that this shear zone is a zone of finite dilatation. Correlating mineral and rock composition, and assuming an ideal two mineral system, it is possible to calculate approximate modal variations. This indicates that:
398
76% amphibole + 24% plagioclase --* 90% amphibole + 10% plagioclase in the shear zone, assuming all the minerals in the shear zone have the composition of the recrystallized grains; this is likely to lead to a slight overestimation of the amphibole. DISCUSSION
The observed changes in mineral chemistry in this study are those which, for basic rocks, are normally associated with increasing temperature in prograde regional metamorphism from low- to high-grade amphibolite facies. However, there is some disagreement as to the consistency of the observed changes in amphibole chemistry reported in the literature on prograde regional metamorphism (Miyashiro, 1973), and this will be discussed later. There are three possible mechanisms that may produce these variations in a small scale shear zone: (1) Shear heating within the shear zone may produce locally increased temperatures (Graham and England, 1976; Sibson, 1977; Nicolas et al., 1977; Scholz, 1979; Brun and Cobbold, 1980). Various’ductile shear zones and faults have been described where the immediately adjacent rocks have been metamorphosed to higher grades, and these have been interpreted as being due to increased temperatures as a result of shear heating along the fault for reviews see Scholz, 1979, and Brun and Cobbold, 1980). Such zones are of the order of tens to hundreds of kilometers long and are thought to have been active over long periods of time (in the order of 20 m.y.). In general, for significant shear heating to occur, either the shear stress on the slipping zone must be in excess of one kilobar, or the velocity of slip must be of the order of tens of centimetres per year (greately in excess of typical time-averaged slip-rates for major fault zones), and these conditions must be met for long periods of time (Scholz, 1979). If the localization of the chemical changes in the shear zone of width 5 m is to be attributed to a peaked thermal anomaly arising from internal heat generation by steady state shearing, a crude estimate for the duration of the heat generating episode can be obtained from the thermal constant for a slab with width equal to the half-width (I) of the shear zone: T, 2 12/K
where K is the diffusivity (Sibson, 1977). Taking 1 = 250 cm and K = lo-’ cm* set-‘, T, = 72 days. That is, the shear heating can only have lasted for around 72 days or the effects would have been experienced over a much wider zone. Accepting this duration for the heating episode, the temperature rise at the centre of the zone can be calculated taking likely extreme values for shear resistance and slip-rate (TV = 1 kbar and-u = 10 cm yr-‘, respectively). Then the power dissipated per unit area is Q = rf . u and the temperature increase after a time t is (Sibson, 1978):
A0 = 2.82 x 1O-7 Q! . t”*
399
(assuming the same value for diffusivity and a value of 2 X 10’ erg cm-’ ‘C-l for conductivity (c.g.s. units)), which gives a value of 0.2”C. Hence, even if high stresses do occur, and the displacement rate along the zone is high, the temperature rise generated will be insufficient to produce a localized noticeable effect. (2) Deformation may have occurred during prograde metamorphic conditions with mineral reequilibration only occurring in the area of high strain in the shear zone. In other words, enhanced diffusion rates were produced due to the deformation (Cohen, 1970). Although this may be of importance in low-grade environments where diffusion is slow (White and Knipe, 1978), and in higher grade shear zones involving an influx of fluid facilitated by the deformation (Brodie, 1980), it is unlikely to produce sharp chemical zones in high temperature, fluid deficient, isochemical environments where diffusion is more rapid. In addition, it is probable that the shear zone was not initiated during the prograde metamorphism but was formed in connection with movements on the later Insubric Line fault. In this case equilibration would have been to a lower grade mineral assemblage. (3) The deformation in the shear zone may lead to a reduction in the mean stress in addition to straining the mineral structure, if it was a zone of dilatation (Casey, 1980). The change in mean stress may lead to variations in the equilibrium distribution coefficients between amphibole and plagioclase similar to those observed for variations in temperature, In the absence of, or accompanying, dilatancyh accommodated by void formation, a tendancy to dilate following a reduction in the mean pressure could be facilitated by the recrystallized phases having lower densities. From electron microscopy it is found that recrystallization in the shear zone was probably syntectonic, so the recrystallized grains also reflect the changed distribution coefficients that operated. The mass balance calculations and density determinations are consistent with the shear zone being a zone of dilatation and therefore support this interpretation. APPLICATIONS
TO REGIONAL
METAMORPHISM
Since it was first observed that amphibole and plagioclase compositions vary in an apparently systematic fashion in mafic rocks from terrains of increasing metamorphic grade (e.g. Wiseman, 1934; James, 1955), various attempts have been made to calibrate these changes as indicators of temperature variations. Spear (1979) investigated the partioning of Na and Ca between plagioclase and the M4 site of the amphibole in prograde regional metamorphism and documented the change in partition coefficients with increasing temperature (grade) as more Ca-rich plagioclase coexists with more Na-rich amphibole. Variations in alkalies, Ti- and Al-content of amphiboles, have been documented from many regional metamorphic terrains. The Ti”’ content increases with temperature (Leake, 1965; Bard, 1970; Raase, 1974) and, in many areas, the alkali content of the vacant A-site also
400
increases (Shido and Miyashiro, 1959; Binns, 1965, 1969; Raase, 1974), thereby producing a more pargasitic or edenitic composition with increasing temperature. However, in other areas such as the Haast River area of New Zealand, very little variation in alkali content of the amphibole has been recorded (Cooper and Lovering, 1970). Changes in Al-content of amphiboles are less well defined: in some regions Al”’ and Al’” decrease with temperature (Shido and Miyashiro, 1959; Binns, 1969), while in others Al“’ increases (Bard, 1970). Variation in Al”’ may be a function of pressure rather than temperature (Raase, 1974) and comparing the amphibole analyses discussed in this paper with those on Raase’s graph of Al”’ against Si relative to pressure, indicates nearly constant pressure as might be expected. It has been suggested that some of the disparities in the observed changes in hornblende chemistry between different regional metamorphic terrains may be the result of the variation in pressure between the various facies series (Ernst, 1972): the amphibole from higher pressure facies series, such as the Sanbagawa region in Japan show lower TiOl and CaO and slightly higher SiO, + A1203 + Na,O content than those from similar rocks in lower pressure series (Haast River area, etc.). Hence there exists some inconsistency within the literature as to the interpretation of observed variations in hornblende composition in prograde regionally metamorphosed terrains. Thus the observation of similar variations in hornblende and plagioclase composition in a localized shear zone is likely to be significant. Irrespective of the cause of the compositional variations associated with the shearing reported in this paper, it seems likely that shearing during regional metamorphism plays an important role in determining the observed changes in amphibole and plagioclase chemistry. If this is generally true then some of the observed irregularities in the chemical variation, particularly in the amphiboles, during prograde regional metamorphism may be the result of variations in the shear stress. Unfortunately few of the authors who describe the variations in mineral chemistry in amphibolite facies metabasites have recorded the textural features of their samples, and vice versa. Consequently, it is not presently possible to ascertain from the studies reported in the preexisting literature what influence variations in shear stress may have on mineral chemistry. Further work is in progress to apply these ideas to amphibolite facies metagabbros in prograde regionally metamorphosed sequences of rocks. ACKNOWLEDGEMENTS
The use of the SRC supported HVEM within the Metallurgy Department is gratefully acknowledged together with NERC (Grant GR3/3848) for financial support in the electron microscopy. The mineral analyses were carried out at the NERC-microprobe centre at Imperial College. Dr. S.H. White and Dr. B. Gorman are thanked for discussion and criticizing the manuscript, and also Dr. R.H. Sibson for discussion on shear heating.
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