FIGURE CAPTIONS
Figure 1. Initial conditions
for reference model LHO-71 and all other models presented here. Upper panel
shows undeformed, rectangular, passive marker grid for the model crust;
solid vertical lines at 100 km intervals are numbered (positive on pro-side,
negative on retro-side) for comparison with the deformed grids shown in
Figs. 2-6. Upper crustal layer is in light grey; lower crustal layer is
white. Lower panel shows thermal structure of the model crust, with isotherms
at 100 ºC intervals; 700 ºC isotherm shown as a heavy line to
facilitate comparison between different models. Distribution of upper crustal
(A1) and lower crustal (A2)
heat-producing material corresponds to mechanically weak upper crust (0-20
km) and strong lower crust (20-35 km). Velocity vectors are shown as short
heavy lines. Model is started in conductive steady-state, i.e., in thermal
equilibrium with VP = 0. Model boundary conditions:
surface temperature = 0 oC, basal temperature, Ta
= 1350 oC; basal mantle heat flux, qm =
20 mW/m2; no horizontal heat flux at the
sides of the model; retro-side of model crust is fixed at x = 0 km (not
shown). At the start of the model, pro-lithosphere converges with velocity
VP = 1 cm/y, imposed at the base of the crust and
in the mantle, and vertically through the crust as a far-field boundary
condition. Similarly, the base and far-field of the retro-crust has VR
= 0. Pro-mantle lithosphere is subducted beneath stationary retro-lithosphere
at fixed detachment point, S. Erosion is proportional to surface slope.
The model is time-stepped by alternating mechanical and thermal steps.
Thermal steps solve the time-dependent heat balance equation with the current
velocity field determined dynamically within the crust and by the boundary
conditions. Radioactive upper and lower crust and the temperature field
are advected and the updated temperature field calculated for the entire
model region. In the frictional field, both the upper and lower crust deform
by incompressible plastic flow with an internal angle of friction, f
= 15º. In the ductile field, the upper crust deforms according
to the 'wet quartzite' flow law (Gleason & Tullis, 1995) and the lower
crust deforms according to 'dry Maryland diabase/10' flow law (modified
after Mackwell et al., 1998). Flow law parameters: h
= effective viscosity (Pa.s), B* = pre-exponential factor (Pa.s);
e. = strain rate (s-1),
n = stress exponent, Q* = activation energy (kJ/mol), R = gas constant
(8.314 J/ºKmol), T = ºK. Heat balance equation parameters: r
= density, Cp = heat capacity, K = thermal conductivity, k
= K/rCp = thermal diffusivity (all constant);
T(x,z,t) = temperature, t = time, A(x,z,t) = rate of heat production /
unit volume; v(x,z,t) = tectonic velocity (dynamic in crust, kinematic
in mantle); Ñ = d/dx
+ d/dz = gradient
operator. Parameter values and changes between models are given in Table
1.
Figure 2. Reference model
LHO-71 after 450 km (45 My) of convergence. Upper panel is the 'peak grade
profile', which shows the maximum temperatures (Tmax)
reached by points at or near the model surface at 45 My, and the times
at which these points reached Tmax, in My after the
start of the model. In this and all similar figures, My (millions of years
since model start) can be converted to Ma (millions of years before 'present')
by subtracting the My value for any point from the My value of the time-step
shown (45 My in this case). Note that outside the deformed zone, surface
Tmax does not change with time because there is no
exhumation, and the times of Tmax shown are not significant
in detail; some of these points are slightly below the model surface (0-2
km) and in these cases Tmax > 0. Middle panel is deformed
marker grid. Note development of lower crustal antiform on retro-side,
asymmetric upper crustal thickening on pro- and retro-sides, and offset
of originally vertical markers (compare with Fig. 1). Lower panel shows
thermal and velocity fields. Note elevation of crustal isotherms in vicinity
of thick upper crustal layer on the pro-side, relative depression of isotherms
where upper crust is thin above lower crustal antiform, and depression
and inversion of mantle isotherms above subduction zone.
Figure 3. Model LHO-66
after 450 km (45 My) of convergence, showing the effect of a mid-crustal
weak zone developed at the base of the upper crust in response to an extra
increment of temperature-dependent 'melt' weakening. The effective viscosity
of the upper crust undergoes a linear decrease from the flow law value
for the ambient T and s conditions to 1019
Pa.s over the temperature range 400-700 ºC, and the lower crust undergoes
the same viscosity change over the interval 600-900 ºC. The model
crust deforms according to the rheological model that yields the highest
strain rate (lowest effective viscosity) for the current conditions. For
T < 600 ºC, the upper crust deforms according to the wet quartzite
flow law, but where mid-crustal temperature exceeds ca. 600 ºC, the
linear viscosity decrease model yields a significantly lower effective
viscosity. This extra mid-crustal weakening is analogous to a reduction
in strength caused by a small amount of 'melt', fluid, or some other T-dependent
weakening process. The resulting crustal deformation (middle panel) is
very similar to that for LHO-71 (Fig. 2), except that there is a narrow
zone near the base of the pro-side upper crust where material is displaced
pro-ward relative to that above and below it. This 'channel flow' zone
is also evident as a reversal in the mid-crustal velocity field (lower
panel). Peak grade profile (upper panel) and thermal field (lower panel)
are almost identical to those for LHO-71 at the same time (Fig. 2).
Figure 4. Effect of post-convergent
extension on thermal and velocity fields, and on zone of mid-crustal reverse
channel flow. Upper panel of each pair shows the velocity field and 700
ºC isotherm for model LHO-77, and the lower panel shows the deformed
marker grid for the same time. Note the change in scale of velocity vectors
for the 60 and 90 My panels. Up to 45 My, LHO-77 is identical to LHO-66
(Fig. 3). Immediately after 45 My, VP is reduced to
zero, and thick crust flows outward in response to the gravitational potential
energy gradient. This causes extension (E) and thinning of the orogenic
core, and produces corresponding zones of contraction (C) on the flanks
of the orogen. Outward flow velocities are higher on the pro-side than
on the retro-side. Between 45 and 60 My, the 700 ºC isotherm migrates
upward into the crust because the cooling effect of subduction is removed;
the asymmetry of post-orogenic thermal relaxation reflects both the asymmetry
of thickened heat-producing material and asymmetry of syn-convergent isotherms.
The overall amount of extension is about 10%. In this model, upper crustal
thinning is not sufficient to exhume the mid-crustal channel.
Figure 5. Model HT-6 after
450 km (45 My) of convergence, showing the effect of focused erosion on
exhumation of the mid-crustal channel flow zone. Model thermal and mechanical
parameters are the same as for LHO-66 (Fig. 3) except that erosion rate
varies with time and distance as well as slope. From 0-675 km there is
no erosion; beyond 725 km erosion rate increases at 30 My from 4.4 x 103
x slope m/My to 4.6 x 104 x slope m/My; between 675 and 725 km there is
a linear increase in erosion rate from zero to the current value at 725
km. The lack of erosion on the retro-side of the model suppresses the formation
of the lower crustal antiform and produces a thick upper crustal layer
across the model (middle panel) along with a broad plateau. Mid-crustal
temperatures approach 600 ºC beneath the plateau, leading to reverse
channel flow on both the pro- and retro-sides of the system. The mid-crustal
channel is partially exhumed at 45 My in response to erosion at the pro-ward
margin of the plateau; the channel reaches the surface at c. 60 My (see
Fig. 6). Exhumation of the mid-crust on the pro-side of the system leads
to upward advection of isotherms in this region. The asymmetric peak grade
profile reflects variable exhumation across the erosion front; Tmax
increases up-section across the erosion front and declines toward the plateau.
Figure 6. Effect of focused
erosion on development and exhumation of the mid-crustal channel flow zone.
On the pro-side, the reversal in the mid-crustal velocity field associated
with channel flow is apparent by comparing the 30 My and 45 My panels.
On the retro-side, outward channel flow and convergence act in the same
direction, so that the retro-ward flow reaches a maximum in the mid-crustal
channel. Thickening at the toe of the pro-side channel is evident from
both the deformed grids and the velocity fields at 45 and 60 My; the channel
develops a 'pip' shape during exhumation in response to removal of overlying
material. By 60 My the channel is beginning to be exhumed on the pro-side
of the system. The velocity field beneath the central part of the plateau
after 45 My indicates uniform retro-ward displacement except near the detachment
point (heavy black dot). The 700 ºC isotherm migrates upward and outward
as the plateau widens.
Figure 7. Peak grade profiles
for models LHO-77 (upper panel) and HT-6 (lower panel) showing how the
Tmax distribution across the model surface changes as exhumation proceeds.
The profiles are shown for reference time 45 My, and for the times of the
bottom panels in Fig. 4 (LHO-77, 90 My) and Fig. 6 (HT-6, 75 My) respectively.
Labels are the times of Tmax for 45 My (upright) and
later (italics) profiles, with the earliest and latest times in each case
shown in bold. Arrows labelled P07, P13, etc. correspond to the points
for which P-T-t paths and particle trajectories are presented in Fig. 9;
their positions are shown at 90 My for LHO-77, and at 75 My for HT-6.
Figure 8. Summary cartoon
showing contrasting effects of extension and focused erosion on the evolution
and exhumation of the mid-crustal channel flow zone.
Figure 9. P-T-t paths
and particle trajectories for selected points from models LHO-77 (top set
of diagrams) and HT-6 (bottom set). Positions of points relative to peak
grade profiles at 90 My and 75 My respectively are shown in Fig. 7. P-T-t
diagrams show the stability fields of andalusite (a), kyanite (k), and
sillimanite (s), position of muscovite + quartz = K-feldspar + Al2SiO5
+ H2O reaction (m + q = kf + als + w), and minimum
melting curve for water-saturated granitoid rocks (wet melting). P-T-t
paths for each point are shown as heavy line with heavy dots at 15 My intervals;
labels are times in My since model start. Also shown are the values of
Tmax and Pmax with corresponding
P, T, and t (My since model start). Particle trajectories show changes
in lateral positions and depths of the same points during the model run;
symbols and labels as for the P-T-t paths, except that in some cases open
circles rather than dots have been used for clarity. Note that these diagrams
do not show either surface topography or Moho position, which change with
time. At the start of the models, P19 and P20 are vertically separated
by 7.5 km, and the initial positions of these points are the same in both
models. In LHO-77, convergence stops at 45 My and is followed immediately
by crustal extension. In model HT-6, both channel flow and the change to
a more rapid erosion rate begin at about 30 My.
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