Geology Reference
In-Depth Information
Cooling-Age Distribution
A
z
s
(z
x
-z
c
)
(dz/dt)
t
cx
(z) =
z
x
z
v
(z
s
-z
v
)
geothermal
gradient
(dT/dz)
Fig. 7.30
Cooling ages as a function
of relief and hypsometry.
A. Model for predicting the distribution
of cooling ages (
t
c
) derived from a range
with a given relief expressed as the
difference between the summit (
z
s
) and
valley (
z
v
) elevations. A linear age-eleva-
tion relationship predicts ages anywhere
within the landscape. Closure tempera-
ture (
T
c
) occurs at depth
z
c
.
B. Probability distribution of detrital
cooling ages reflects a convolution of
the hypsometry of the range with the
age-elevation curve. Modified after
Brewer
et al.
(2003).
T
c
z
c
closure
temperature
0 My
erosion rate (dz/dt)
t
cv
t
cs
cooling age (t
c
)
B
Hypsometry
Age Range
Age Distribution
x
z
s
z
v
z
v
z
s
t
cv
t
cs
t
cv
t
cs
elevation
age
age
et al.
, 2006). This method can also both con-
strain the
18
O/
16
O ratio of the water from which
the carbonate grew and underpin a correlation
between soil temperature and the isotopic com-
position of the water. In theory, this correlation
enables discrimination between the effects of
altitude changes versus those due to climate.
and preserves its signature after it has been
eroded from the bedrock. One such tracer relies
on cooling ages because many mountain ranges
display a generally layer-cake stratigraphy of
ages. A sand sample eroded from such a range
should contain a suite of individual grain ages
that span the exposed topography and its asso-
ciated ages (Stock and Montgomery, 1996). If a
linear gradient of cooling ages within the paleo-
topography is assumed (as is typical for many
thermochronometers; Fig. 7.20) and erosion was
spatially uniform, then the frequency distribution
of ages should mimic the hypsometry, i.e., the
frequency distribution of elevation, within the
source catchment (Fig. 7.30). With the advent of
high-precision and relatively inexpensive tech-
niques for dating individual grains, it has become
practicable to date hundreds of detrital grains.
For any given catchment, if the goal is to capture
at least 95% of the paleorelief, then a minimum of
about 120 grain ages is required (Vermeesch,
2004). For a linear dependence of age on eleva-
tion, changes in relief and/or erosion rate will
Paleorelief
As rivers cut down into newly rising mountains,
the topographic relief commonly grows. Although
relief can be independent of elevation, relief has
been used as an indicator of erosion rates (Fig.
7.3A). Clearly combinations of relief and drain-
age spacing control average slope angles, and
relief affects the way storms interact with topog-
raphy to produce orographic rainfall (Bookhagen
and Burbank, 2006, 2010). Consequently, recon-
structions of paleorelief can provide a valuable
window on former landscapes.
In order to define paleorelief, a tracer is needed
that is sensitive to relative or absolute elevation
