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Geometry of isograds: thermodynamic constraints on inversion
393
Tecronophysics, 201(1992) 393-399 Elsevier Science Publishers B.V., Amsterdam
Geometry of isograds: thermodynamic
constraints on inversion
D.S. Bhattacharyya Department
of Geology and Geophysics,
Indian Institufe of Technology, Kharagpur-721302,
India
(Received November 21, 1990; revised version accepted May ($1991)
ABSTRACT Bhattacharyya, D.S., 1992. Geometry of isograds: thermodynamic constraints on inversion. Tectonophysics,
201: 393-399.
Inverted isograds have been reported from metamorphic terrains ranging in age from Precambrian to Tertiary. Most of the workers believe that metamorphic inversion was caused by an inverted temperature gradient, associated with large-scale thrusting. However, &grads are not isotherms, and the former may develop at large angles to the latter; it is shown here that the orientation of isograds depends not only on the orientation of isotherms but also on the value of AT/AP of an isograd reaction and that of the temperature gradients. Accordingly, four different sets of conditions for inversion are recognised: two for inverted temperature gradients, one for a horizontal temperature gradient and one for a normal temperature gradient. These conditions have been worked out for four different isograds: staurolite-in, staurolite-out, muscovite breakdown, and partial melting of granitic compositions. It is shown that isograds may be in normal or inverted attitudes depending on the orientation and magnitude of the temperature gradient and also on the slope AT/AP of an isograd reaction. Published accounts of metamorphic inversion do not provide all of these data but explain them in terms of only an inverted temperature gradient, which may not be correct, and may need re-investigation.
Introduction Inverted isograds have been reported from many erogenic belts which range in age from Precambrian to Tertiary (Ray, 1947; Le Fort, 1975; St-Onge, 1981; Duebendorfer, 1988). In all these examples, inversions are associated with thrusting. In some instances, the thrust planes are steeply dipping and so also are the inverted isograds (Duebendorfer, 1988); in others, both are shallow dipping or even subhorizontal. In general, workers have argued that metamorphism and deformation are broadly synchronous: the isograds were developed at the peak of metamorphism and the inverted isograds are the result of inverted temperature gradients, associated with thrusting. The inversion of the temperature gradient is supposed to have been brought about by thrusting of a “hot” slab over a “cold” slab (Hubbard, 1989; Petcher, 1989; StHubli, 1989). Qualitatively, this explanation seems convincing; but, on closer scrutiny, it is realised that the explanation of inversion needs more careful ex0040-1951/92/$05.00
amination. First of all, an isograd is not an isotherm, and may develop at large angles to the latter; thus, one may ask whether inverted isotherms invariably lead to inverted isograds, or whether inverted isograds are the unique result of inverted isotherms. It should be realised that orientations of isograds are also controlled by the spacings of isotherms and slopes of reaction graphs in P-T space. All of these factors should be considered together in interpretating metamorphic inversions. The relationship of these parameters was discussed in an earlier paper (Bhattacharyya, 19811. A more general form of the relationship is given by the equation: AT 1 1 cos ce~Pg, =cot 8 (1) sin ff I I The positive and negative signs are for negative and positive slopes of AT/AP respectively. Pg is the lithostatic pressure gradient, 0.3 kbar/km (Runcorn, 1967); Tg is the value of the temperature gradient; and (Y and 8 are the angles of
0 1992 - Elsevier Science Publishers B.V. All rights reserved
Fig. 1. Construction of isogtad, A + B = C + D. T, and T, are isotherms, T2 > T,. S is the spacing of the isotherms and is inversely proportional to the temperature gradient. P, and Pz are isobars, Pz > P,. MN is the spacing of the isobars, and is inversely proportional to the pressure gradient due to lithostatic pressure, a = dip of isotherm; B = dip of isograd.
slopes of isotherms and isograds, measured in a fixed sense (Fig. 1). The conditions for vertical isograds (Fig. 2) can be derived by putting B = 90” in eqn. (1): 1 sin a,
asa,f*P [
TP
1 8%
= 0
Fig. 3. Four cases of inverted &grads: (a) normal temperature gradient; (b) horizontal temperature gradient; (cl inverted temperature gradient-_(a) to (cl for positive slope of AT/A P: (d) inverted temperature gradient, for negative slope of AT/A P.
I
(2) since l/(sin a,) cannot be zero. The subscript c denotes the conditions for vertical isograds oniy. It is thus evident that for a particular isograd with a fixed value of AT/A P, cos a, varies inversely with T,,, for a vertical isograd. Normal or inverted isograds result if the isograd deviates from the vertical attitude towards one side or the other. Hence, inverted isograds can be deduced from eqn. (2). Two types of graphs can be constructed, (a) 8-a and (b) ac-T& from eqns (I) and (2) respectively, for different isograd reactions (i.e.
Fig. 2. Vertical isograd, A + B =C + D. = 909 a, =r dip of isotherm for vertical isograd.
different AT/AP); from these, normal and inverted attitudes of isograds can be deduced. It is intended here to formulate the exact geometric conditions for inversion of isograds and then to apply them to specific cases.
Conditions for inverted isograds can be derived from the above discussions. There are four cases of inversions of isograds, the first three for positive slopes of AT/AP and the fourth for a negative slope of AT/AP. These are discussed below. Case 1. It is obvious from Fig. 2 that a normal metamorphic sequence will occur if the isogiad slopes to the right; if the isograd slopes to the left (Fig. 3a1, a lower-grade assemh@e (A + B) underlines the higher-grade assemblage (C + DI, i.e. the isograd is inverted. This happens if the spacing of the isotherm is greater than a critic& value, given by the Tgc of eqn. (2). In this situation, the temperature gradient is ~~~rd~ directed, but the &grad is inverted; isograd and isotherm dip in opposite directions. For subhorizontal iso-
GEOMETRY
395
OF ISOGRADS
grads, Tg should be very low or AT/AP very large. Case 2. It is apparent from Fig. 2 that for vertical isograds, as cy, increases, the spacing of the isotherms decreases (i.e. Tg increases) until, at (Y,= 90”, Tgc is infinitely large-which is absurd. But for a, = 90”, for any finite value of TB, the isograd always slopes towards the left (Fig. 3b), i.e. the isograd is inverted. For subhorizontal isograds, Tg should be very large or AT/AP very low. Case 3. If the isograds are further rotated clockwise from the vertical attitude, inverted isotherms are obtained: Tg is directed upward; the isograd is inverted; the isograd and isotherm dip in the same directions (Fig. 3~); and a! is then less than 8. Subhorizontal isograds would result from very low values of Tg or very large values of AT/AP, Case 4. This is applicable for negative slope of AT/AP. The only situation in which isograds are inverted is shown in Fig. 3d: LYis greater than 8. Subhorizontal isograds result from very low slopes of isotherms or extremely high values of Tg or very low values of AT/A P. The results are summarised in Table 1.
Four common isograd reactions Four isograd reactions are considered here for geometrical analysis of inversion. These are staurolite-in, staurolite-out, muscovite breakdown, and partial melting of granitic compositions. The first three have positive slopes and the fourth negative slopes of AT/AP. All of these are common in regionally metamorphosed terrains. For the staurolite-in isograd, the reaction is taken from Hoschek (1969): chlorite -+ muscovite = staurolite + biotite + quartz f H,O. The AT/AP value of the reaction is 8.3”C/kbar. For the staurolite-out isograd, the reaction is taken from Hoschek (1969): staurolite -t quartz + muscovite = sillimanite f biotite + H,O. The AT/A P value of the reaction is 28.6”C/kbar. For muscovite breakdown, the reaction is taken from Chatterjee and Johannes (1974): muscovite + quartz = K-feldspar + sillimanite + I-&O. The AT/AP value of the reaction is variable, and the average value is taken to be EiO”C/kbar. For partial melting of granitic ~om~sitions, the data are taken from Tuttle and Bowen (19581, Luth et al. (1964) and Huang and Wyllie (1975). The AT/AP value of the reaction is highly variable
TAEfLE 1 Summary of four cases of inversion Slope of AT/AP with T-axis
Cases and figures
Temperature gradient, Ta
Positive
Case 1 Fig. 4a
Downwardly directed, less than TEc
Case 2 Fig. 4b
Horizontal, any value
cU<@
Isotherms vertical
Case 3 Fig. 4c
Upwardly directed, any value
ff<6
Slopes same direction, slope of isotherm greater
Case 4 Fig. 4d
Upwardly directed, greater than TBc
a>$
Slopes same direction, slope of isotherm less
Negative
Relationship between a and B
Slopes (acute angles) of isotherms and isograds Opposite slopes
80 70 t
I
6% AP
LaAP
pOSItlYe
negot1ve
Fig. 4. Graphs of TsC versus (I~ for the vertical attitude of the four isograd reactions: (1) = staurolite-in; (2) - staurolite-out; (3) = muscovite breakdown; (4) = partial melting of granitic compositions. Figures indicate values of AT/AP. The marked side of a curve indicates conditions of inverted isograds.
and has a negative
slope with the temperature axis; its value is taken to be 35”C/kbar. These values of AT/AP, and of p, = 0.3 kbar/km, are
substituted in eqns. (1) and (2); and graphs of TBc-ac and a-8 (Figs. 4 and 5) are drawn for these isograd reactions. From these graphs sev-
170160-
zc
150140130120IIOIOOso. I v 80-
0
10
20
30
40
50
60
70
80
90
100
110 120
I30
140
150
I60
170 I80
Fig. 5. Graphs of 0 versus Q for the four isograds, (I), (2), (3) and (4). for T, = WC/km. Combinations of 0 and P for inverted isograds shown. Figures shown AT/AP values along the curves.
397
GEOMETRY OF ISOGRADS
Application of the model
Fig. 6. Diagrammatic section showing dispositions of &grads, discussed in model 3. Note the divergence of the isograds, and the normal attitude of isograds (I) and (4, and the inverted attitude of isograd (3) with the same T8.
era1 illustrative models of dispositions of isograds are worked out and presented below. ModeI 1. If Tg = 3O”C/km and is downwardly directed, and isotherms dip at 40” (point Q in Fig. 41, all the four &grads are normally disposed. Dips of isograds can be read from Fig. 5. Model 2. If TB= 3O”C/km and is upwardly directed, and isotherms dip at 130” (point R in Fig. 4), all the four isograds are inverted; they dip at slightly different angles (0, = 133.5”, e2 = 140.5”, 8, = 148.4*, @,= 119.9” for the four isograds respectively-see Fig, 5). However, the isograds may appear to be parallel in the outcrops. The situation is comparable to those depicted in Figs. 3c and d. yodel 3. If TB= 3O”C/km and is do~wardly directed, and isotherms dip at 73” (point S in Fig. 4), isograd (3) is inverted, isograd (2) is vertical, and isograds (I) and (4) are in normal attitudes. The dispositions of isograds are shown diagrammatically in Fig, 6: 8, = 78.2”, 8, = 90”, 8, = 108.1” and 0, = 56.4O (from Fig. 5). The divergence of isograds is more marked here. In fact, isograds with different values of AT/AP are bound to have different slopes. yodel 4. If Tg = 3O”C/km, very low dips of isograds can be calculated for (Y= 160”, 8i = 161.5, 8, = 164.5”, 6, = 167.5” and 0, = 150”. This gives very low dips of isograds ( < 30”) and they appear to be parallel in the outcrops. This is not a unique solution, but it gives an estimate of the conditions for low dips of isograds in inverted attitudes, as they are reported from the Himalayan orogen (discussed later).
The model is based on the relationships among five parameters, a, 8, AT/AP, Tg and Pg. Of these, Pg is the lithostatic pressure gradient of 0.3 kbar/km. For a particular &grad reaction, AT/AP is known from experimental data. Thus, it becomes imperative to have data on two of the other three parameters (ar, Tg and 0) in order to obtain the value of the remaining parameter. Unfortunately, published accounts of isograds do not provide these data. Hence, it is not possible to subject these cases to geometrical analysis. However, one example is cited below where the author successfully applied the geometrical principles underlying inversion of isograds. An inverted biotite isograd was mapped around Buxa Duars in the Eastern Himalayas (Bhattacharyya, 1981). The dip of the isograd was measured at 120” (i.e. 60” measured the other way). The reaction across the isograd was: stilpnome1ane + phengite = biotite f chlorite + H,O. The AT/A P value of the reaction is 8.3”C/km (Winkler, 1975). If we assume Tg = 3O*C/km, the dip of the isotherm (tw) can be read from curve (1) of Fig. 5, as 116” for 8 = 120”; this gives an inverted isograd for an inverted isotherm. However, if Tg has a lower value, curve (1) of Fig. 5 will be shifted towards curves (2) and (3). (It may be noted that a lower TB has the same effect as a higher AT/API. Thus, it is possible to obtain the inverted isograd (0 = 120”) for a = 90” (i.e. horizontal T,) when Tg = 4YC/km. However, such a low value of Tg is not realistic in metamorphic terrains. Hence, it is logical in this case to infer that the inverted isograd is the result of inverted isotherms. Inspection of curve (I) in Fig. 4 indicates that the inverted isograd would result from a wide range of values of Tg and a, but the value of cy is constrained by the value of 8; the value of Tg is accordingly constrained. Without precise data on Tg the model cannot be uniquely determined. Discussion It has been shown that the orientation of an isograd depends not only on the orientation of the temperature gradient but also on the magni-
tude of the temperature gradient and the slope of AY‘/Af’ of the reaction in P-T space. It is thus theoretically possible that a normal sequence of isograds develops even where the temperature gradient is inverted, as well as an inverted scquence developing where the temperature gradient is in a normal attitude. Thus, interpretation of inverted isograds should not be attempted (as is done in most published accounts), in terms of an inverted temperature gradient only. However, it is quite possible that some or many of the inverted sequences are truly the result of inverted temperature gradients. The majority of published accounts of metamorphic inversions do not provide data on the parameters mentioned here. This causes difficulty in explaining the inverted isograds. Several of the published accounts are discussed here to point out the flaws in their interpretations; such flaws arise out of inadequacy or lack of data, in particular on the dip of isograds (0) and temperature gradients CT,). St-Onge (1981) mapped staurolite, sillimanite, sillimanite plus orthoclase, and partial melting isograds, and demonstrated their inversion along the lower side of a funnel-shaped batholith; the dips of isograds are steep (values not given) and subparallel to the walls of the batholith; the temperature gradient is not known either in magnitude or orientation. While the pattern is closely similar to those depicted in Figs. 3c and d and may be the result of an inverted temperature gradient (as inferred by the author), other possibilities, such as inversion due to a horizontal temperature gradient (as depicted in Fig. 3b) cannot be ruled out. Without more precise data on the controlling parameters, the question remains open. Duebendorfer (1988) reported inverted isograds (chlorite, biotite, garnet and staurolite) associated with a Precambrian mylonite zone, with steep isograd dips (70” approximately). Although inversion could be result of an inverted temperature gradient (as concluded by the author), it could also result from a horizontal temperature gradient (see Fig. 3b) or even a normal temperature gradient (see Fig. 3a); the point can only be settled if the value of the temperature gradient is known.
Apart from these examples of steeply dipping inverted isograds, there arc also curious examples of shallow-dipping or subhorizontal inverted isograds, reported by many workers from the Himalayan orogen (Ray, 1947: Le Forte. 1975; Arita. 1983; Mohan et al., 1989). Pecher (19891 mapped inverted isograds (chlorite. biotite, garnet. kyanitc and sillimanite), associated with the Main Central Thrust of the Nepal Himalayas, and reported an inverted temperature gradient of 34”C/km. Stiiubli (1989) similarly mapped inverted isograds, associated with the Main Central Thrust in the Kisthwar window; he did not mention any value of temperature gradient. There are many similar instances of inverted isograds in the Lesser Himalayas. In all of these cases, dips of isograds, although not determined in the field, were inferred to be very low and parallel to the shallowdipping Main Central Thrust. The temperature gradient was determined in only a few cases, where it was found to be inverted; but. in the majority of cases, an inverted temperature gradient was simply inferred. The magnitude of the temperature gradient is generally not reported. The isograds along with the Main Central Thrust are shown to be folded, but folding is a later phenomenon. The majority of the authors concluded that inversion was due to an inverted temperature gradient, although such an inverted temperature gradient was mostly inferred and not determined. It is asserted here that it is possible that shallow-dipping inverted isograds could have resulted from a normal temperature gradient if the magnitude of the temperature gradient was sufficiently low, as shown in Fig. 3a; here, if the spacing of the isotherms increases (i.e. T, decreases), the dips of isograds become very shallow. Thus, while it is admitted that the standard interpretation of inverted isograds due to inversion or isotherms could be true, it is also possible that such inversions are the result of other controlling factors in a milieu of normally disposed isotherms. The problem can be settled if the requisite parameters are determined and then the geometrical models precisely constructed. It should also be noted that inversion of isotherms are conventionally associated with distortions
GEOMETRY
OF ISOGRADS
caused by thrusting. Karabinos and Ketcham (1989) demonstrated that thrusting along a shallow-dipping plane (dip 5-10”) at a rate of 5 cm/yr would distort the isotherms but would not invert them. It is hence necessary to be cautious in assuming that thrusting means inversion of isotherms and hence inversion of isograds. Acknowledgements All facilities for this work was provided by the Department of Geology and Geophysics, I.I.T., Kharagpur, India. The comments of the two anonymous referees have contributed greatly to the quality of the paper. References Arita, K., 1983. Origin of inverted metamorphism of the Lower Himalayas. Tectonophysics, 95: 43-60. Bhattachatyya, D.S., 1981. Geometry of isograds in metamorphic terrains. Tectonophysics, 73: 385-395. Bhattachatyya, D.S. and Das, K.K., 1983. Inversion of metamorphic zones in the Lower Himalayas, Gangtok. J. Geol., 91: 98-102. Chatterjee, N.D. and Johannes, W., 1974. Thermal stability and standard thermodynamic properties of synthetic 2M,muscovite. Contrib. Mineral. Petrol., 48: 89-114. Duebendorfer, E.M., 1988. Evidence for an inverted metamorphic gradient associated with a Precambrian suture, Southern Wyoming. J. Metamorph. Geol., 6: 41-63. Hoschek, G., 1969. The stability of staurolite and chloritoid and their significance in metamorphism of pelitic rocks. Contrib. Mineral. Petrol.. 22: 208-232.
399 Huang, W.L. and Wyllie, P.J., 1975. Melting reactions in the system NaAlSis04-KAlSI,0,-Si0, to 35 kb, dry and with excess water. J. Geophys. Res., 83: 737-745. Hubbard, M.S., 1989. Thermobarometric constraints on the thermal history of the Main Central Thrust zone and Tibetan slab, Eastern Himalayas. J. Metamorph. Geol., 7: 19-30. Karabinos, P. and Ketcham, R., 1989. Thermal structure of active thrust belts. J. Metamorph. Geol., 6: 559-570. LeFort, P., 1975. Himalayas: the collided range. Am. J. Sci., 275-A: l-44. Luth, W.C., Jahns, R.A. and Tuttle, O.F., 1964. The granite system at pressures of 4 and 10 kb. J. Geophys. Res., 69: 759-773. Mohan, A., Windley, B.F. and Searle, M.P., 1989. Geothermobarometry and development of inverted metamorphism in the Dajeeling-Sikkim region. J. Metamorph. Geol., 7: 95-110. Pecher, A., 1989. The metamorphism in the central Himalayas. J. Metamorph. Geol., 7: 31-41. Ray, S., 1947. Zonal metamorphism in the Eastern Himalayas. Q. J. Mineral. Metall. Sot. India, 21: 155-170. Staubli, A., 1989. Polyphase metamorphism and the development of the Main Central Thrust. J. Metamorph. Geol., 7: 73-93. St-Onge, M.R., 1981. Normal and inverted metamorphic isograds and their relations to syntectonic Proterozoic batholiths in the Wopmay orogen, Canada. Tectonophysics, 76: 295-316. Tuttle, O.F. and Bowen, N.L., 1958. Origin of granite in the light of experimental studies in the system NaAJSi,O,KAISi,O,-H,O. Geol. Sot. Am. Mem., 74. Winkler, H.G.F., 1975. Petrogenesis of Metamorphic Rocks, 4th edition. Narosa Publishing House, New Delhi, 334 pp.
Tecronophysics, 201(1992) 393-399 Elsevier Science Publishers B.V., Amsterdam
Geometry of isograds: thermodynamic
constraints on inversion
D.S. Bhattacharyya Department
of Geology and Geophysics,
Indian Institufe of Technology, Kharagpur-721302,
India
(Received November 21, 1990; revised version accepted May ($1991)
ABSTRACT Bhattacharyya, D.S., 1992. Geometry of isograds: thermodynamic constraints on inversion. Tectonophysics,
201: 393-399.
Inverted isograds have been reported from metamorphic terrains ranging in age from Precambrian to Tertiary. Most of the workers believe that metamorphic inversion was caused by an inverted temperature gradient, associated with large-scale thrusting. However, &grads are not isotherms, and the former may develop at large angles to the latter; it is shown here that the orientation of isograds depends not only on the orientation of isotherms but also on the value of AT/AP of an isograd reaction and that of the temperature gradients. Accordingly, four different sets of conditions for inversion are recognised: two for inverted temperature gradients, one for a horizontal temperature gradient and one for a normal temperature gradient. These conditions have been worked out for four different isograds: staurolite-in, staurolite-out, muscovite breakdown, and partial melting of granitic compositions. It is shown that isograds may be in normal or inverted attitudes depending on the orientation and magnitude of the temperature gradient and also on the slope AT/AP of an isograd reaction. Published accounts of metamorphic inversion do not provide all of these data but explain them in terms of only an inverted temperature gradient, which may not be correct, and may need re-investigation.
Introduction Inverted isograds have been reported from many erogenic belts which range in age from Precambrian to Tertiary (Ray, 1947; Le Fort, 1975; St-Onge, 1981; Duebendorfer, 1988). In all these examples, inversions are associated with thrusting. In some instances, the thrust planes are steeply dipping and so also are the inverted isograds (Duebendorfer, 1988); in others, both are shallow dipping or even subhorizontal. In general, workers have argued that metamorphism and deformation are broadly synchronous: the isograds were developed at the peak of metamorphism and the inverted isograds are the result of inverted temperature gradients, associated with thrusting. The inversion of the temperature gradient is supposed to have been brought about by thrusting of a “hot” slab over a “cold” slab (Hubbard, 1989; Petcher, 1989; StHubli, 1989). Qualitatively, this explanation seems convincing; but, on closer scrutiny, it is realised that the explanation of inversion needs more careful ex0040-1951/92/$05.00
amination. First of all, an isograd is not an isotherm, and may develop at large angles to the latter; thus, one may ask whether inverted isotherms invariably lead to inverted isograds, or whether inverted isograds are the unique result of inverted isotherms. It should be realised that orientations of isograds are also controlled by the spacings of isotherms and slopes of reaction graphs in P-T space. All of these factors should be considered together in interpretating metamorphic inversions. The relationship of these parameters was discussed in an earlier paper (Bhattacharyya, 19811. A more general form of the relationship is given by the equation: AT 1 1 cos ce~Pg, =cot 8 (1) sin ff I I The positive and negative signs are for negative and positive slopes of AT/AP respectively. Pg is the lithostatic pressure gradient, 0.3 kbar/km (Runcorn, 1967); Tg is the value of the temperature gradient; and (Y and 8 are the angles of
0 1992 - Elsevier Science Publishers B.V. All rights reserved
Fig. 1. Construction of isogtad, A + B = C + D. T, and T, are isotherms, T2 > T,. S is the spacing of the isotherms and is inversely proportional to the temperature gradient. P, and Pz are isobars, Pz > P,. MN is the spacing of the isobars, and is inversely proportional to the pressure gradient due to lithostatic pressure, a = dip of isotherm; B = dip of isograd.
slopes of isotherms and isograds, measured in a fixed sense (Fig. 1). The conditions for vertical isograds (Fig. 2) can be derived by putting B = 90” in eqn. (1): 1 sin a,
asa,f*P [
TP
1 8%
= 0
Fig. 3. Four cases of inverted &grads: (a) normal temperature gradient; (b) horizontal temperature gradient; (cl inverted temperature gradient-_(a) to (cl for positive slope of AT/A P: (d) inverted temperature gradient, for negative slope of AT/A P.
I
(2) since l/(sin a,) cannot be zero. The subscript c denotes the conditions for vertical isograds oniy. It is thus evident that for a particular isograd with a fixed value of AT/A P, cos a, varies inversely with T,,, for a vertical isograd. Normal or inverted isograds result if the isograd deviates from the vertical attitude towards one side or the other. Hence, inverted isograds can be deduced from eqn. (2). Two types of graphs can be constructed, (a) 8-a and (b) ac-T& from eqns (I) and (2) respectively, for different isograd reactions (i.e.
Fig. 2. Vertical isograd, A + B =C + D. = 909 a, =r dip of isotherm for vertical isograd.
different AT/AP); from these, normal and inverted attitudes of isograds can be deduced. It is intended here to formulate the exact geometric conditions for inversion of isograds and then to apply them to specific cases.
Conditions for inverted isograds can be derived from the above discussions. There are four cases of inversions of isograds, the first three for positive slopes of AT/AP and the fourth for a negative slope of AT/AP. These are discussed below. Case 1. It is obvious from Fig. 2 that a normal metamorphic sequence will occur if the isogiad slopes to the right; if the isograd slopes to the left (Fig. 3a1, a lower-grade assemh@e (A + B) underlines the higher-grade assemblage (C + DI, i.e. the isograd is inverted. This happens if the spacing of the isotherm is greater than a critic& value, given by the Tgc of eqn. (2). In this situation, the temperature gradient is ~~~rd~ directed, but the &grad is inverted; isograd and isotherm dip in opposite directions. For subhorizontal iso-
GEOMETRY
395
OF ISOGRADS
grads, Tg should be very low or AT/AP very large. Case 2. It is apparent from Fig. 2 that for vertical isograds, as cy, increases, the spacing of the isotherms decreases (i.e. Tg increases) until, at (Y,= 90”, Tgc is infinitely large-which is absurd. But for a, = 90”, for any finite value of TB, the isograd always slopes towards the left (Fig. 3b), i.e. the isograd is inverted. For subhorizontal isograds, Tg should be very large or AT/AP very low. Case 3. If the isograds are further rotated clockwise from the vertical attitude, inverted isotherms are obtained: Tg is directed upward; the isograd is inverted; the isograd and isotherm dip in the same directions (Fig. 3~); and a! is then less than 8. Subhorizontal isograds would result from very low values of Tg or very large values of AT/AP, Case 4. This is applicable for negative slope of AT/AP. The only situation in which isograds are inverted is shown in Fig. 3d: LYis greater than 8. Subhorizontal isograds result from very low slopes of isotherms or extremely high values of Tg or very low values of AT/A P. The results are summarised in Table 1.
Four common isograd reactions Four isograd reactions are considered here for geometrical analysis of inversion. These are staurolite-in, staurolite-out, muscovite breakdown, and partial melting of granitic compositions. The first three have positive slopes and the fourth negative slopes of AT/AP. All of these are common in regionally metamorphosed terrains. For the staurolite-in isograd, the reaction is taken from Hoschek (1969): chlorite -+ muscovite = staurolite + biotite + quartz f H,O. The AT/AP value of the reaction is 8.3”C/kbar. For the staurolite-out isograd, the reaction is taken from Hoschek (1969): staurolite -t quartz + muscovite = sillimanite f biotite + H,O. The AT/A P value of the reaction is 28.6”C/kbar. For muscovite breakdown, the reaction is taken from Chatterjee and Johannes (1974): muscovite + quartz = K-feldspar + sillimanite + I-&O. The AT/AP value of the reaction is variable, and the average value is taken to be EiO”C/kbar. For partial melting of granitic ~om~sitions, the data are taken from Tuttle and Bowen (19581, Luth et al. (1964) and Huang and Wyllie (1975). The AT/AP value of the reaction is highly variable
TAEfLE 1 Summary of four cases of inversion Slope of AT/AP with T-axis
Cases and figures
Temperature gradient, Ta
Positive
Case 1 Fig. 4a
Downwardly directed, less than TEc
Case 2 Fig. 4b
Horizontal, any value
cU<@
Isotherms vertical
Case 3 Fig. 4c
Upwardly directed, any value
ff<6
Slopes same direction, slope of isotherm greater
Case 4 Fig. 4d
Upwardly directed, greater than TBc
a>$
Slopes same direction, slope of isotherm less
Negative
Relationship between a and B
Slopes (acute angles) of isotherms and isograds Opposite slopes
80 70 t
I
6% AP
LaAP
pOSItlYe
negot1ve
Fig. 4. Graphs of TsC versus (I~ for the vertical attitude of the four isograd reactions: (1) = staurolite-in; (2) - staurolite-out; (3) = muscovite breakdown; (4) = partial melting of granitic compositions. Figures indicate values of AT/AP. The marked side of a curve indicates conditions of inverted isograds.
and has a negative
slope with the temperature axis; its value is taken to be 35”C/kbar. These values of AT/AP, and of p, = 0.3 kbar/km, are
substituted in eqns. (1) and (2); and graphs of TBc-ac and a-8 (Figs. 4 and 5) are drawn for these isograd reactions. From these graphs sev-
170160-
zc
150140130120IIOIOOso. I v 80-
0
10
20
30
40
50
60
70
80
90
100
110 120
I30
140
150
I60
170 I80
Fig. 5. Graphs of 0 versus Q for the four isograds, (I), (2), (3) and (4). for T, = WC/km. Combinations of 0 and P for inverted isograds shown. Figures shown AT/AP values along the curves.
397
GEOMETRY OF ISOGRADS
Application of the model
Fig. 6. Diagrammatic section showing dispositions of &grads, discussed in model 3. Note the divergence of the isograds, and the normal attitude of isograds (I) and (4, and the inverted attitude of isograd (3) with the same T8.
era1 illustrative models of dispositions of isograds are worked out and presented below. ModeI 1. If Tg = 3O”C/km and is downwardly directed, and isotherms dip at 40” (point Q in Fig. 41, all the four &grads are normally disposed. Dips of isograds can be read from Fig. 5. Model 2. If TB= 3O”C/km and is upwardly directed, and isotherms dip at 130” (point R in Fig. 4), all the four isograds are inverted; they dip at slightly different angles (0, = 133.5”, e2 = 140.5”, 8, = 148.4*, @,= 119.9” for the four isograds respectively-see Fig, 5). However, the isograds may appear to be parallel in the outcrops. The situation is comparable to those depicted in Figs. 3c and d. yodel 3. If TB= 3O”C/km and is do~wardly directed, and isotherms dip at 73” (point S in Fig. 4), isograd (3) is inverted, isograd (2) is vertical, and isograds (I) and (4) are in normal attitudes. The dispositions of isograds are shown diagrammatically in Fig, 6: 8, = 78.2”, 8, = 90”, 8, = 108.1” and 0, = 56.4O (from Fig. 5). The divergence of isograds is more marked here. In fact, isograds with different values of AT/AP are bound to have different slopes. yodel 4. If Tg = 3O”C/km, very low dips of isograds can be calculated for (Y= 160”, 8i = 161.5, 8, = 164.5”, 6, = 167.5” and 0, = 150”. This gives very low dips of isograds ( < 30”) and they appear to be parallel in the outcrops. This is not a unique solution, but it gives an estimate of the conditions for low dips of isograds in inverted attitudes, as they are reported from the Himalayan orogen (discussed later).
The model is based on the relationships among five parameters, a, 8, AT/AP, Tg and Pg. Of these, Pg is the lithostatic pressure gradient of 0.3 kbar/km. For a particular &grad reaction, AT/AP is known from experimental data. Thus, it becomes imperative to have data on two of the other three parameters (ar, Tg and 0) in order to obtain the value of the remaining parameter. Unfortunately, published accounts of isograds do not provide these data. Hence, it is not possible to subject these cases to geometrical analysis. However, one example is cited below where the author successfully applied the geometrical principles underlying inversion of isograds. An inverted biotite isograd was mapped around Buxa Duars in the Eastern Himalayas (Bhattacharyya, 1981). The dip of the isograd was measured at 120” (i.e. 60” measured the other way). The reaction across the isograd was: stilpnome1ane + phengite = biotite f chlorite + H,O. The AT/A P value of the reaction is 8.3”C/km (Winkler, 1975). If we assume Tg = 3O*C/km, the dip of the isotherm (tw) can be read from curve (1) of Fig. 5, as 116” for 8 = 120”; this gives an inverted isograd for an inverted isotherm. However, if Tg has a lower value, curve (1) of Fig. 5 will be shifted towards curves (2) and (3). (It may be noted that a lower TB has the same effect as a higher AT/API. Thus, it is possible to obtain the inverted isograd (0 = 120”) for a = 90” (i.e. horizontal T,) when Tg = 4YC/km. However, such a low value of Tg is not realistic in metamorphic terrains. Hence, it is logical in this case to infer that the inverted isograd is the result of inverted isotherms. Inspection of curve (I) in Fig. 4 indicates that the inverted isograd would result from a wide range of values of Tg and a, but the value of cy is constrained by the value of 8; the value of Tg is accordingly constrained. Without precise data on Tg the model cannot be uniquely determined. Discussion It has been shown that the orientation of an isograd depends not only on the orientation of the temperature gradient but also on the magni-
tude of the temperature gradient and the slope of AY‘/Af’ of the reaction in P-T space. It is thus theoretically possible that a normal sequence of isograds develops even where the temperature gradient is inverted, as well as an inverted scquence developing where the temperature gradient is in a normal attitude. Thus, interpretation of inverted isograds should not be attempted (as is done in most published accounts), in terms of an inverted temperature gradient only. However, it is quite possible that some or many of the inverted sequences are truly the result of inverted temperature gradients. The majority of published accounts of metamorphic inversions do not provide data on the parameters mentioned here. This causes difficulty in explaining the inverted isograds. Several of the published accounts are discussed here to point out the flaws in their interpretations; such flaws arise out of inadequacy or lack of data, in particular on the dip of isograds (0) and temperature gradients CT,). St-Onge (1981) mapped staurolite, sillimanite, sillimanite plus orthoclase, and partial melting isograds, and demonstrated their inversion along the lower side of a funnel-shaped batholith; the dips of isograds are steep (values not given) and subparallel to the walls of the batholith; the temperature gradient is not known either in magnitude or orientation. While the pattern is closely similar to those depicted in Figs. 3c and d and may be the result of an inverted temperature gradient (as inferred by the author), other possibilities, such as inversion due to a horizontal temperature gradient (as depicted in Fig. 3b) cannot be ruled out. Without more precise data on the controlling parameters, the question remains open. Duebendorfer (1988) reported inverted isograds (chlorite, biotite, garnet and staurolite) associated with a Precambrian mylonite zone, with steep isograd dips (70” approximately). Although inversion could be result of an inverted temperature gradient (as concluded by the author), it could also result from a horizontal temperature gradient (see Fig. 3b) or even a normal temperature gradient (see Fig. 3a); the point can only be settled if the value of the temperature gradient is known.
Apart from these examples of steeply dipping inverted isograds, there arc also curious examples of shallow-dipping or subhorizontal inverted isograds, reported by many workers from the Himalayan orogen (Ray, 1947: Le Forte. 1975; Arita. 1983; Mohan et al., 1989). Pecher (19891 mapped inverted isograds (chlorite. biotite, garnet. kyanitc and sillimanite), associated with the Main Central Thrust of the Nepal Himalayas, and reported an inverted temperature gradient of 34”C/km. Stiiubli (1989) similarly mapped inverted isograds, associated with the Main Central Thrust in the Kisthwar window; he did not mention any value of temperature gradient. There are many similar instances of inverted isograds in the Lesser Himalayas. In all of these cases, dips of isograds, although not determined in the field, were inferred to be very low and parallel to the shallowdipping Main Central Thrust. The temperature gradient was determined in only a few cases, where it was found to be inverted; but. in the majority of cases, an inverted temperature gradient was simply inferred. The magnitude of the temperature gradient is generally not reported. The isograds along with the Main Central Thrust are shown to be folded, but folding is a later phenomenon. The majority of the authors concluded that inversion was due to an inverted temperature gradient, although such an inverted temperature gradient was mostly inferred and not determined. It is asserted here that it is possible that shallow-dipping inverted isograds could have resulted from a normal temperature gradient if the magnitude of the temperature gradient was sufficiently low, as shown in Fig. 3a; here, if the spacing of the isotherms increases (i.e. T, decreases), the dips of isograds become very shallow. Thus, while it is admitted that the standard interpretation of inverted isograds due to inversion or isotherms could be true, it is also possible that such inversions are the result of other controlling factors in a milieu of normally disposed isotherms. The problem can be settled if the requisite parameters are determined and then the geometrical models precisely constructed. It should also be noted that inversion of isotherms are conventionally associated with distortions
GEOMETRY
OF ISOGRADS
caused by thrusting. Karabinos and Ketcham (1989) demonstrated that thrusting along a shallow-dipping plane (dip 5-10”) at a rate of 5 cm/yr would distort the isotherms but would not invert them. It is hence necessary to be cautious in assuming that thrusting means inversion of isotherms and hence inversion of isograds. Acknowledgements All facilities for this work was provided by the Department of Geology and Geophysics, I.I.T., Kharagpur, India. The comments of the two anonymous referees have contributed greatly to the quality of the paper. References Arita, K., 1983. Origin of inverted metamorphism of the Lower Himalayas. Tectonophysics, 95: 43-60. Bhattachatyya, D.S., 1981. Geometry of isograds in metamorphic terrains. Tectonophysics, 73: 385-395. Bhattachatyya, D.S. and Das, K.K., 1983. Inversion of metamorphic zones in the Lower Himalayas, Gangtok. J. Geol., 91: 98-102. Chatterjee, N.D. and Johannes, W., 1974. Thermal stability and standard thermodynamic properties of synthetic 2M,muscovite. Contrib. Mineral. Petrol., 48: 89-114. Duebendorfer, E.M., 1988. Evidence for an inverted metamorphic gradient associated with a Precambrian suture, Southern Wyoming. J. Metamorph. Geol., 6: 41-63. Hoschek, G., 1969. The stability of staurolite and chloritoid and their significance in metamorphism of pelitic rocks. Contrib. Mineral. Petrol.. 22: 208-232.
399 Huang, W.L. and Wyllie, P.J., 1975. Melting reactions in the system NaAlSis04-KAlSI,0,-Si0, to 35 kb, dry and with excess water. J. Geophys. Res., 83: 737-745. Hubbard, M.S., 1989. Thermobarometric constraints on the thermal history of the Main Central Thrust zone and Tibetan slab, Eastern Himalayas. J. Metamorph. Geol., 7: 19-30. Karabinos, P. and Ketcham, R., 1989. Thermal structure of active thrust belts. J. Metamorph. Geol., 6: 559-570. LeFort, P., 1975. Himalayas: the collided range. Am. J. Sci., 275-A: l-44. Luth, W.C., Jahns, R.A. and Tuttle, O.F., 1964. The granite system at pressures of 4 and 10 kb. J. Geophys. Res., 69: 759-773. Mohan, A., Windley, B.F. and Searle, M.P., 1989. Geothermobarometry and development of inverted metamorphism in the Dajeeling-Sikkim region. J. Metamorph. Geol., 7: 95-110. Pecher, A., 1989. The metamorphism in the central Himalayas. J. Metamorph. Geol., 7: 31-41. Ray, S., 1947. Zonal metamorphism in the Eastern Himalayas. Q. J. Mineral. Metall. Sot. India, 21: 155-170. Staubli, A., 1989. Polyphase metamorphism and the development of the Main Central Thrust. J. Metamorph. Geol., 7: 73-93. St-Onge, M.R., 1981. Normal and inverted metamorphic isograds and their relations to syntectonic Proterozoic batholiths in the Wopmay orogen, Canada. Tectonophysics, 76: 295-316. Tuttle, O.F. and Bowen, N.L., 1958. Origin of granite in the light of experimental studies in the system NaAJSi,O,KAISi,O,-H,O. Geol. Sot. Am. Mem., 74. Winkler, H.G.F., 1975. Petrogenesis of Metamorphic Rocks, 4th edition. Narosa Publishing House, New Delhi, 334 pp.