Geology Reference
In-Depth Information
spectrometer (AMS), several of which have been
converted from use in physics and defense
industries for application in this field.
concentration,
N
, is so low everywhere within
the rock that the rate of growth is essentially
linear at the local production rate,
P
, i.e.,
N
=
Pt
.
Because
P
falls off exponentially with depth (see
Box 3.1), an exponential concentration profile
develops,
N
=
P
0
t
e
−
z
/
z
*
, where
P
0
is the production
rate at the surface and
z
* represents the depth in
the rock at which the production rate is
P
0
/e. If
a sample is collected from the surface (
z
= 0), and
we know the local production rate at the surface,
then measurement of
N
allows solution for the
exposure time,
t
. As the concentration builds up,
however, the second term in Eqn 3.4, representing
decay, begins to play a larger role. This decay
results in a decline in the rate of increase in
concentration, until ultimately a balance is
achieved between new production and decay.
This “secular equilibrium,” represented by
d
N
/d
t
= 0, limits the concentration to a maximum
of
N
=
P
/
l
(see Box 3.1). Note that, in these
circumstances, when the sample has reached
secular equilibrium, no information about the
exposure time can be extracted from a
measurement of
N
. Happily for the geomorphic
community interested in dating surfaces in the
Quaternary period (roughly 1.8 million years
long), this secular equilibrium takes several
half-lives to be achieved. Because
10
Be and
26
Al
have half-lives on the order of one million years
(see table within Box 3.1), they remain useful
throughout the Quaternary and, in fact, well
into the Pliocene. Dating of glacially polished
surfaces (e.g., Nishiizumi
et al.
, 1989) in the
Sierra Nevada is one example of dating surfaces
that have seen negligible erosion since
deglaciation - although recent work reveals that
one must be cautious to find sites in which
inheritance from past interglacials has been
fully removed (Dühnforth
et al.
, 2010). Exposure
dating of fluvial strath terraces along the Indus
River, on which the fluvial polish is still intact
and where the fluted and potholed nature of
the fluvially carved bed has clearly not
degenerated since abandonment of the strath, is
another example of dating a surface considered
to be pristine (Burbank
et al.
, 1996b).
More commonly, the rock surface being
sampled is eroding at some rate that we would
like to determine. This erosion can take place on
In situ
CRNs
In situ
CRNs have been used in two distinct set-
tings: bare bedrock surfaces, where one is inter-
ested in either or both the exposure age of the
surface and the erosion rate of it; and deposi-
tional surfaces. Each setting poses its own dilem-
mas, requiring differing sampling strategies.
But, commonly, there's no other game in town.
Bedrock surfaces
Consider a bare bedrock surface exposed to the
full cosmic-ray flux (no blocking by nearby out-
crops or valley walls). The CRN concentration in
a parcel of rock is dictated by the differential
equation describing both production and decay
of CRNs in the parcel:
d
N
/d
t
=
P
−
l
N
(3.4)
where
N
is the number of CRNs per unit volume
of rock,
t
is time,
P
is the production rate, and
l
is again the decay constant, which reflects
the probability of decay of the nuclide in a
unit of time and is related to the half-life by
t
1/2
= log(1/2)/l.
l
. Much of the complexity in the
interpretation of the measured CRN concentra-
tions resides in the history of the production
rate,
P
, to which the parcel has been subjected.
Let us address a few simple examples.
Consider a bare bedrock surface exposed at
t
= 0 by a thick bedrock landslide. This approach
to dating will equally well apply to a sample
obtained from within the headscarp, or from a
boulder on the surface of the landslide that we
can safely assume to have been at great depth
prior to the slide we would like to date. Assume
that the rock involved is much older than the
half-life of the CRN we wish to employ, assuring
that all CRNs produced in a prior exposure at
the surface have decayed. In other words, the
“inheritance” is negligible. As it is bombarded
with cosmic rays, CRNs will begin to accumulate
within the rock, most rapidly at the surface,
more slowly at depth. At early times, the
