A brief presentation on the summary of Armstrong and Tracy's paper published in 2000 on the one-dimensional thermal modeling of Vermont, U.S.A. This was presented by me as a part of an internal assessment in the penultimate semester of my postgraduate course in Geology, Presidency University, Kolkata.

1. One-dimensional thermal modeling of Acadian
metamorphism in southern Vermont, USA (2000)
BY - T . R . A R M S T R O N G & R . J . T R A C Y
PRESENTED BY - MAINAK GHOSH, PG - II

2. INTRODUCTION
• The basic concept in thermal modeling is – tectonic events such as thrusting or
folding take place on a time scale which is much shorter than that of thermal
relaxation. Therefore tectonic events will disturb the thermal structure of the crust, and
once tectonism has ceased this thermal perturbation will decay with time back towards
with a steady value.
• One-dimensional thermal (1DT) modeling described here is a forward technique – a
thermal perturbation in response to a tectonic event such as overthrusting is
imposed on a crustal thermal structure and allowed to decay with time.
(Spear,1992).

3. This paper compares modeled P±T ±t paths with those estimated
from geological and petrological data for rocks in the southern
pre-Silurian Vermont Sequence. P±T ±t paths calculated from the
1DT model can then be compared with those obtained from the
petrological methods in a test of the consistency of the thermal
model and the structure-based tectonic models and parameters.
OBJECTIVE OF THIS PAPER

4. Two different structural and metamorphic
domains in southern Vermont have been
examined in this study:
• Garnet-grade pre-Silurian rocks
along the east flank of the Rayponda
and Sadawga Domes (western
domain of Fig. 1), and
• Staurolite-grade to kyanite-grade
rocks, along the eastern flank of the
Athens Dome, approximately 5±10 km
farther east (eastern domain). Both
domains lie within the so-called Taconide
Zone (see Fig. 1), in which rocks were
both deformed and metamorphosed in
the Taconian (Ordovician) orogenic
episode.
STUDY AREA

5. EVALUATION OF MODEL PARAMETERS
• 40Ar /39Ar hornblende plateau ages from garnet-grade rocks on the east flank of
the Sadawga Dome in the western domain range from 388 to 376 Ma (Sutter &
Hatch, 1985)
• Based upon a thermobarometric estimate, the maximum temperature was
probably reached between 395 and 388 Ma.
• Geochronological and thermochronological data indicate that Acadian deformation
in the western domain occurred at least episodically over an age range of
approximately 25±30 Myr, starting with thrust-related crustal loading at around
400 Ma and ending with late dome-stage, post-peak metamorphic deformation at
approximately 375±370 Ma.
• Initially rapid and relatively high-strain post-metamorphic exhumation and related
cooling were succeeded by slower, low-strain exhumation – evidenced from minor
retrogression shown by peak metamorphic assemblages.

6. EVALUATION OF MODEL PARAMETERS
• Thermobarometric measurements of peak temperature and associated pressure
from garnet-grade and staurolite- or kyanite-grade rocks around the Athens Dome in the
eastern domain range from 550±25 °C to 600±25 °C, and 7.5 to 9.2 kbar
• 40Ar /39Ar hornblende plateaus from these rocks range in age from 376 Ma (staurolite-
grade) to 365 Ma (kyanite-grade).
• 40Ar /39Ar muscovite cooling ages of 365 to 340 Ma are similar to the younger end of
hornblende cooling age range, and indicate that these rocks underwent rapid cooling (and
presumably rapid exhumation) immediately after peak temperature was attained.
• K-feldspar 40Ar /39Ar plateau ages of 310 Ma from Silurian±Devonian rocks
immediately east of the Taconide Zone indicate slower subsequent exhumation
following muscovite closure.
• These ages yield integrated initial unroofing rates of 1.4 mm yr−1 (from the time of
peak temperature to Ar closure in hornblende, at about 500 °C), and a subsequent
integrated rate of 0.1 mm yr−1 (from hornblende closure to muscovite closure) for
Acadian post-peak cooling (Armstrong et al., 1992).

7. The structural evolution of the lithotectonic belts
(i) The onset of metamorphism of the Vermont Sequence, related to c. 400 Ma crustal
loading.
(ii) Upright fold interference development, high-strain deformation (early dome-stage
deformation);
(iii) Rapid exhumation and cooling;
(iv) subsequent lower strain deformation and slower cooling and exhumation (late dome-
stage deformation).

8. TECTONIC MODELING PARAMETERS
An initial set of tectonic input
parameters for use in the one-
dimensional thermal model (Table 1).
The parameters for both domains were
held fixed in order to observe how
changes in the thermal parameters
would affect the outcome of the model
calculations.
• All thermal modeling runs used an arbitrary 100 Myr total duration, beginning at t=0
with the onset of crustal loading -> constrained dome-stage and late dome-stage
deformation episodes -> post-deformational passive exhumation.
•In the western (older) domain, this exhumation phase lasts 70 Myr (30±100 Myr in
the model), whereas in the eastern domain (younger) this stage is constrained at 65
Myr duration.

9. •Modest variation in thermal input
parameters for different values of thermal
conductivity.
Using the garnet-grade (western domain)
tectonic parameters, the model-calculated
P/T results best fits the independently
measured thermobarometric P/T data for
that domain given in Table 2 (peak
temperature of 535 °C at 7.5 kbar, shown in
bold type in Table 2) with a thermal
conductivity of 2.75 W m-1 K-1
Modest changes in the average rock
density or in heat generation input
values produced only minimal shifts
of <10 °C and 0.2 kbar for the 35 km
crustal depth path (Table 2).
EVALUATION OF THERMAL PARAMETERS

10. Heat generation input values -
Comparison of model results with the
measured (thermobarometrically derived)
P±T data suggests that heat generation
values ranging from 2.0×10−6 to 3.0×10−6
J K-kg−1 (single value for constant basal
flux) and differential heat generation
values of 2.0×10−6 (top of modelled rock
column) and 2.5×10−6 (bottom of rock
column) are all acceptable.
Finally, because both western and eastern domains comprise the same lithotectonic
units and the estimated physical and thermal properties of the rocks should vary little
over the range of P±T conditions recorded in both domains, a single set of thermal
input parameters was selected for use with the different tectonic parameters.

11. EVALUATION OF TECTONIC PARAMETERS
STAGE 1 (OVERTHRUSTING EVENT):-
2 sets of values (from the garnet-grade model) yielded modeled P-T estimates comparable
with values derived from thermobarometry (marked in bold).
But only one set of comparable values (for rocks at 35 and 40 km initial depth) was
obtained from the particle paths associated with staurolite or kyanite grade model.

12. STAGE II (Crustal Residence) –
•Time period just prior to active tectonic exhumation and related deformational processes.
•Only one set of values (bolded) for each model fits the measured P±T data.
• Crustal residence of the staurolite- or kyanite-grade domain is 5 Myr longer than that of the
garnet-grade domain, extending until 390 Ma rather than 395 Ma, from a model starting time of
400 Ma.

13. STAGE III (DOME-STAGE DEFORMATION) :-
• Initial exhumation and dome-stage deformation.
• For duration of stage III uplifts, one set of values matches with measured thermobarometric
values for the garnet-grade domain – 15 Ma ending at 385 Ma.
• This value has been calculated using 2 values of exhumation rates (0.75 mm/yr and 1
mm/yr).

14. Only one calculated Stage III duration compares well with measured P±T ±t values
for the staurolite- or kyanite-grade domain: 20 Myr, ending at 380 Ma (Table 3).

15. The choice of different strain rate values for Stage III exhumation (staurolite- or kyanite-
grade) produced small to moderate shifts in calculated temperature and pressure –
•From 545 to 550 °C and from 7.3 to 8.1 kbar – small shifts.
•Slightly larger shifts in predicted 40Ar/39Ar muscovite closure ages (from 366 to 380 Ma
for staurolite-grade rocks and from 330 to 377 Ma for kyanite-grade rocks).
-> Only one strain rate value (−1.00×10-15 s-1) produced agreement in calculated and
measured P/T values and 40Ar/39Ar muscovite cooling ages.
-> 40Ar /39Ar hornblende cooling ages show little variation since Stage III exhumation
occurs approximately during the attainment of peak temperature conditions and close to
hornblende closure for Ar (about 500 °C).
Different Strain rate values in Stage III

16. Stage IV (EXHUMATION):-
• Large scale uplift and erosion after attainment of post-peak temperature.
• Stage IV features significantly post-date the attainment of peak temperature and most
40Ar/39Ar hornblende closure ages, but precede 40Ar /39Ar muscovite closure (largely due
to the presence of new muscovite within late-stage deformation planes), so stage IV must
post-date Stage III (modeled ages of 385 Ma for garnet-grade rocks and 380 Ma for
staurolite- or kyanite-grade rocks).

17. RESULTS AND DISCUSSION
• Results from the one-dimensional model
include two sets of modeled P±T paths shown
in Fig. 2(a,b) generated from calculations using
the repeated thermal and tectonic input
parameters from the garnet-grade (western)
and staurolite- or kyanite-grade (eastern)
domains.
In both domains, the model assumes a rapid
loading that is related to the onset of crustal
thickening at c. 400 Ma.
• In this diagram, Pressure-temperature-time
(P±T ±t) path derived from one-dimensional
thermal (1DT) modeling is shown. Path begins
at the onset of crustal loading (c. 400 Ma) of
New Hampshire Sequence rocks. The path
includes the attainment of peak pressure prior
to the attainment of peak temperature and its
associated pressure

18. Model temperature-time (T ±t) path for garnet-grade
rocks of the western domain, calculated from the
one-dimensional thermal model. The curve is
subdivided by the open circles that reflect the timing
of attainment of theoretical mineral Ar closure
temperatures.
Assumed theoretical critical temperatures are c. 500
°C for hornblende (Hbl), 350 °C for muscovite (Ms)
and 225 °C for K-feldspar (Kfs).

19. (a)Temperature-time (T ±t) paths for staurolite-grade
rocks (filled circles) and kyanite-grade rocks (open
circles) of the eastern domain. Each pair of adjacent
circles on either path brackets T ±−t segments used to
calculate cooling rates (in °C M/yr) shown adjacent to
each segment.
Model Ar closure ages for hornblende (Hbl) (at 500
°C), muscovite (Ms) (at 350 °C) and K-feldspar (Kfs)
(at 225 °C) are shown.
386 Ma and 384 Ma are the model ages for
attainment of maximum temperature for staurolite-
grade and kyanite-grade paths, respectively.
(b) Pressure (depth)-time (P±t) paths calculated for
staurolite-grade rocks (filled circles) and kyanite-
grade rocks (open circles) of the eastern domain.
Each pair of adjacent circles on either path brackets
specificP-t segments used to calculate uplift rates
(given in mm M/yr) and shown adjacent to each
segment.

20. CONCLUSION
Results form thermal modeling provide important aspects to the tectonothermal
models of this study area.
•Prediction of decompression prior to the attainment of peak temperature along
a`clockwise' P±T path, matches with estimates from geothermobarometry, and is in
contrast to the `anticlockwise' Acadian P±T path documented just to the east.
•Consistency in calculated with predicted results in durations of isobaric heating
events.
• Consistency in predicted differences of time for onset of exhumation (in thermal
model) and geologically based structural model which suggest west to east younging of
Acadian metamorphism.
• Regional variation in thermal evolution is ultimately controlled by the diachroneity of
deformational events.

21. Finally, the results of this study demonstrate that well-constrained thermal
modeling can provide estimates of continuous P-t and T -t evolution that are
a very powerful complement to P±T ±t data obtained by petrological and
geochronological techniques, and which are necessary for deciphering the
diachronous development of tectonic events that control thermal evolution in
complex orogens.
Thank You!