Abstract
A combined analytical and numerical evaluation of the uncertainties in P-T paths is made for three assemblages that propagates errors in the parameters: initial pressure, initial temperature, initial composition, change of composition of monitor parameters, endmember entropy, and endmember volume. Propagated errors along an isobaric heating path (ΔT=77°C) for assemblage 1 (Grt-Bt-Pl-Qtz-Ms-Chl-H2O), using as monitor parameters the mole fractions of almandine, spessartine, grossular, and anorthite, and ignoring uncertainties in thermodynamic properties, are approximately ±320 bars (1σ) and ±8.3°C (1σ) if rim compositional uncertainties of 5% in major cations are assumed, or ±2.5°C (1σ) and ±50 bars (1σ) if electron microprobe analytical uncertainties are assumed for compositions. The largest source of uncertainty is from the errors in the monitor parameters, and P-T path uncertainties can depend critically on which monitor parameters are used. If the mole fraction of annite is used as a monitor parameter in place of the anorthite content of plagioclase, then propagated uncertainties are worse than ±29°C (1σ) and ±5800 bars (1σ). P-T path uncertainties also depend on assemblage. 1σ precisions in assemblages 2 (Grt−Bt−Pl−Qtz−Ms−Sil−H2O) and 3 (Grt−Bt−Qtz−Kfs−Sil−H2O) using as monitor parameters the mole fractions of almandine, spessartine, grossular, and anorthite are calculated to be ±267 bars and ±43.4°C and ±372 bars and ±8.2°C respectively. Estimates of the accuracies in P-T paths that include potential errors in endmember entropy of ±1 J/mol·K and in endmember volume of ±1 cm3/mol are: ±324 bars and ±8.5°C (assemblage 1), ±341 bars and ±48.6°C (assemblage 2), and ±388 bars and ±9.7°C (assemblage 3). Use of different garnet, plagioclase, and muscovite activity models can change the length of a P-T path by as much as 15%, but does not typically change directions in P-T space significantly. Models that incorporate changes of fluid composition shorten P-T paths in assemblages 1 and 3 but do not change trajectories significantly. Assemblage 2 is virtually unaffected by fluid phase models. For the mineral assemblages considered here and using appropriate monitor parameters, propagated errors are small compared to the total path length, suggesting that the differential thermodynamic approach is a precise and accurate method for determining amounts of heating or thickening during metamorphism, and hence for interpreting orogenic processes.
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References
Berman RG (1988) Internally-consistent thermodynamic data for minerals in the system Na2O−K2O−CaO−MgO−FeO−Fe2O3−Al2O3−SiO2−TiO2−H2O−CO2. J Petrol 29:445–522
Berman RG (1990) Mixing properties of Ca−Mg−Fe−Mn garnets Am Mineral 75:328–344
Bohlen SR, Boettcher AL, (1981) Experimental investigations and geological applications of orthopyroxene geobarometry. Am Mineral 66:951–964
Burton KW, Boyle AP, Kirk WL, Mason R (1989). Pressure, temperature and structural evolution of the Sulitjelma foldnappe, central Scandinavian Caledonides. In: Daly JS, Cliff RA, Yardley BWD (eds) Evolution of Metamorphic Belts. Geol Soc Lond Spec Pub 43: 391–411
Chatterjee ND, Flux S (1986) Thermodynamic mixing properties of muscovite-paragonite crystalline solutions at high temperatures and pressures, and their geological applications. J Petrol 27:677–693
Chatterjee ND, Johannes W (1974) Thermal stability and standard thermodynamic properties of synthetic 2M1-muscovite, (KAl2(AlSi3)O10(H)2). Contrib Mineral Petrol 48:89–114
Eugster HP, Albee AL, Bence AE, Thompson JB, Waldbaum DR (1972) The two-phase region and excess mixing properties of paragonite-muscovite crystalline solutions. J Petrol 13:147–179
Ferry JM (1980) A comparative study of geothermometers and geobarometers in pelitic schists from south-central Maine. Am Mineral 65:720–732
Ferry JM, Spear FS (1978) Experimental calibration of the partitioning of Fe and Mg between biotite and garnet. Contrib Mineral Petrol 66:113–117
Florence FP (1991) Diffusional modification of garnet growth zoning and Acadian metamorphism and tectonic history in the Littleton area, Northwestern New Hampshire. Ph. D. Dissertation, Rensselaer Polytechnic Institute
Florence FP, Spear FS (1991) Effects of diffusional modification of garnet growth zoning on P-T path calculations. Contrib Mineral Petrol 107:487–500
Frost BR, Tracy RJ (1991) P-T paths from zoned garnets: some minimum criteria. Am J Sci 291:917–939
Hodges KV, Spear FS (1982) Geothermometry, geobarometry and the Al2SiO5 triple point at Mt. Moosilauke, New Hampshire. Am Mineral 67:1118–1134
Hodges KV, Crowley PD (1985) Error estimation and empirical geothermobarometry for pelitic systems. Am Mineral 70: 702–709
Hodges KV, McKenna LW (1987) Realistic propagation of uncertainties in geologic thermobarometry. Am Mineral 72: 671–680
Hodges KV, Royden L (1984) Geologic thermobarometry of retrograde metamorphic rocks: An indication of the uplift trajectory of a portion of the northern Scandinavian Caledonides. J Geophys Res 89:7077–7090
Holdaway MJ (1971) Stability of andalusite and the aluminum silicate phase diagram. Am J Sci 271:97–131
Holland TJB, Powell R (1990) An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: the system K2O−Na2O−CaO−MgO−MnO−FeO−Fe2O3−Al2O3−TiO2−SiO2−C−H2−O2. J Metamorphic Geol 8:89–124
Hubbard MS (1989) Thermobarometric constraints on the thermal history of the Main Central Thrust zone and Tibetan slab, eastern Nepal Himalaya. J Metamorphic Geol 7:19–30
Kerrick DM, Jacobs GK (1981) A modified Redlich-Kwong equation for H2O, CO2, and H2O−CO2 mixtures at elevated pressures and temperatures. Am J Sci 281:735–767
Kohn MJ, Spear FS (1991) Error propagation for barometers: 2. Application to rocks. Am Mineral 76:138–147
Kohn MJ, Orange DL, Spear FS, Rumble DR III, Harrison TM (1992) Pressure, temperature, and structural evolution of West-Central New Hampshire: Hot thrusts over cold basement. J Petrol 33:521–556
Kohn MJ, Spear FS, Dalziel IWD (1993). Metamorphic P-T paths from the Cordillera Darwin, a core complex in Tierra del Fuego, Chile. J Petrol (in press).
Koziol AM (1989) Recalibration of the garnet-plagioclase-Al2SiO5-quartz (GASP) geobarometer and applications for natural parageneses. EOS Trans Am Geophys Union 70:493
Kretz R (1983) Symbols for rock-forming minerals. Am Mineral 68:277–279
Menard T (1991) Metamorphism of calcic pelitic schists, Strafford Dome, Vermont, Ph.D. Dissertation, Rensselaer Polytechnic Institute
Newton RC, Charlu TB, Kleppa OJ (1980) Thermochemistry of the high structural state plagioclases. Geochim Cosmochim Acta 44:933–941
Ohmoto H, KerrickD (1977) Devolatilization equilibria in graphitic systems. Am J Sci 277:1013–1044
Orange DL (1985) Metamorphic petrology, pressure-temperature paths, and tectonic evolution of the Mount Cube quadrangle, New Hampshire and Vermont. MS Thesis, Massachusetts Institute of Technology
Reid MJ, Gancarz AJ, Albee AL (1973) Constrained least-squares analysis of petrologic problems with an application to lunar sample 12040 Earth Planet Sci Lett 17:433–445
Roddick JC (1987) Generalized numerical error analysis with applications to geochronology and thermodynamics. Geochim Cosmochim Acta 51:2129–2135
Selverstone J (1985) Petrologic constraints on imbrication, metamorphism, and uplift in the SW Tauern Window, Eastern Alps. Tectonics 4:687–704
Selverstone J, Spear FS (1985) Metamorphic P-T paths from pelitic schists and greenstones from the south-west Tauern Window, Eastern Alps. J Metamorphic Geol 3:439–465
Selverstone J, Spear FS, Franz G, Morteani G (1984) High-pressure metamorphism in the SW Tauern window, Austria: P-T paths from hornblende-kyanite-staurolite schists. J Petrol 25:501–531
Selverstone J, Morteani G, Staude J-M (1991) Fluid channelling during ductile shearing: Transformation of granodiorite into aluminous schist in the Tauern Window, Eastern Alps. J Metamorphic Geol 9:419–431
Spear FS (1986) PTPATH: a FORTRAN program to calculate pressure-temperature paths from zoned metamorphic garnets. Computers in Geoscience 12:247–266
Spear FS (1989) Petrologic determination of metamorphic pressure-temperature-time paths. In: Spear FS, Peacock SM Metamorphic pressure-temperature-time paths. (Short Course in Geology) pp 1–55 Am Geophys Union, 7:Washington, DC, USA
Spear FS, Ferry JM, Rumble D (1982) Analytical formulation of phase equilibria: The Gibbs' method. In: Ferry JM (ed) Characterization of Metamorphism through Mineral Equilibria (Reviews in Mineralogy) Vol. 10 Mineralogical Society of America, Washington DC, pp 105–152
Spear FS, Rumble D III (1986) Pressure, temperature and structural evolution of the Orfordville Belt, west-central New Hampshire. J Petrol 27:1071–1093
Spear FS, Selverstone J (1983) Quantitative P-T paths from zoned minerals: Theory and tectonic applications. Contrib Mineral Petrol 83:348–357
Spear FS, Selverstone J, Hickmott DD, Crowley P, Hodges KV (1984) P-T paths from garnet zoning: A new technique for deciphering tectonic processes in crystalline terranes. Geology 12:87–90
Spear FS, Hickmott DD, Selverstone J (1990a) The metamorphic consquences of thrust emplacement, Fall Mountain, New Hampshire. Geol Soc Am Bull 102:1344–1360
Spear FS, Kohn MJ, Florence FP, Menard T (1990b) A model for garnet and plagioclase growth in pelitic schists: Implications for thermobarometry and P-T path determinations. J Metamorphic Geol 8:683–696
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Kohn, M.J. Uncertainties in differential thermodynamic (Gibbs' method) P-T paths. Contr. Mineral. and Petrol. 113, 24–39 (1993). https://doi.org/10.1007/BF00320829
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DOI: https://doi.org/10.1007/BF00320829