Geology Reference
In-Depth Information
thermochronological cooling histories. Even with
50% uncertainties, however, statistically signifi-
cant changes in erosion rates can often be inter-
preted from thermochronological data derived
from multiple mineral systems. Moreover, these
thermochronological dates typically provide the
best, and commonly the only, means to define
average erosion rates at million-year time scales.
Whenever possible, an improved quantification
of the local geotherm should be attempted.
Sometimes nearby boreholes penetrate deeply
enough to provide a calibration of the coolest
part of the geotherm. Upper crustal isotherms
are sensitive to topographic variations. The
ridge-to-valley relief of mountains can be viewed
like fins on a radiator that are emitting terrestrial
heat to the atmosphere. If the fins are deep and
close together, they have little impact on any but
the isotherms very close to the surface. At large
topographic wavelengths, the isotherms up to
10-km depth or more will mimic the topography.
More rapid erosion rates cause a greater sensi-
tivity to smaller-scale topographic variations due
to the rapidity with which rocks (and their heat)
are advected toward the surface. Beneath high
summits, a given isotherm will be at a higher
altitude than beneath a valley (Fig. 7.20A), but
the near-surface geothermal gradient will be
lower beneath the summit than beneath the
valley bottom (Stüwe
et al.
, 1994; Braun, 2003).
Consider an example of an alpine landscape
with 4 km of local relief and a wavelength of
10 km between summits. If the topography is in
steady state, such that erosion and rock uplift are
everywhere in balance, a steady-state thermal
structure can be modeled as function of the ero-
sion rate (Fig. 7.20). In this particular example,
the erosion rate is 2 mm/yr. Despite a spatially
uniform erosion rate, the predicted age variations
at the surface for several thermochronometers
with different annealing or closure temperatures
are striking! The ages vary by a factor of 2-4,
with the lowest-temperature thermochronometer
being most affected (Fig. 7.20C). Cooling rates
for helium dates (closure temperature
∼
60
°
C in
this model) would be estimated to vary from over
150
°
/Myr in the valley bottoms to less than 40
°
C/
Myr at the summits. If an “average” geothermal
gradient were chosen, say 30
°
/km, as a basis for
Sub-Surface Temperatures
A
5
0
0
80
80
0
140
240
300
-5
erosion rate: 2 mm/yr
4
00
-10
B
Thermochronologic Ages
4
Zr
2
Ap
He
0
0
5
10
15
20
Distance (km)
400
C
300
200
Cooling
Profiles
100
age offset:
apatite FT
0
0
1
2
3
4
5
6
7
Time before exhumation (My)
Fig. 7.20
Topographically controlled isotherms,
cooling ages, and cooling profiles.
Modeled cooling age pattern of three thermochronometers
exhumed at the Earth's surface over two wavelengths of a
two-dimensional, V-shaped topography with 4 km of relief.
Lapse rate on the surface is set to 6.5
°
C/km. The erosion
rate is spatially uniform at 2 mm/yr, implying the landscape
has achieved a steady-state form, and the calculation is
carried out over several million years. The chronometers
are zircon (assumed fission-track closure temperature of
220
°
C), apatite (assumed fission-track closure temperature
of 110
°
C), and (U-Th)/He system (assumed apatite closure
temperature of 60
°
C). A. Thermal structure, including
upwarped isotherms below summits, but a lower
geothermal gradient than beneath valleys. Note the
spatial variation in ages despite a spatially uniform
erosion rate. B. Expected spatial pattern of the cooling
ages at the surface for the three chronometers. C. Cooling
histories taken by rocks exhumed in the central valley
(solid) and the central peak (dashed) of the topography.
As expected from the distance between the deep, flatter
isotherms and the surface (in A), the cooling age variation
inferred from zircon fission-track ages should tightly
mimic the topography. As the closure temperature lowers,
the influence of the topography on the thermal structure
increases, both lowering the amplitude of the cooling
age contrast from peak to valley and imparting a
nonlinearity. This influence will be larger in the higher-
erosion cases.
