Geology Reference
In-Depth Information
Table 3.2
Absolute dating methods.
Method
Useful range
Materials needed
References
Radioisotopic
14
C
35 ka
Wood, shell
Libby (1955), Stuiver
(1970)
U-Th
10-350 ka
Carbonate (corals,
speleothems)
Ku (1976)
Thermoluminescence (TL)
30-300 ka
Quartz or feldspar silt
Berger (1988)
Optically stimulated
luminescence (OSL)
30-300 ka
Quartz silt
Aitken (1998)
Cosmogenic
In situ
10
Be,
26
Al
0-4 Ma
Quartz
Lal (1988), Nishiizumi
et al.
(1991)
He, Ne
unlimited
Olivine, quartz
Cerling and Craig (1994)
36
Cl
0-4 Ma
Phillips
et al.
(1986)
Chemical
Tephrochronology
0-several Ma
Volcanic ash
Westgate and Gorton
(1981), Sarna-Wojcicki
et al.
(1991)
Amino acid racemization
0-300 ka, temperature
dependent
Paleomagnetic
Identification of reversals
>700 ka
Fine sediments,
volcanic flows
Cox
et al.
(1964)
Secular variation
0-several Ma
Fine sediments
Creer (1962, 1967),
Lund (1996)
Biological
Dendrochronology
0-10 ka, depending upon
existence of a local master
chronology
Wood
Fritts (1976), Jacoby
et al.
(1988), Yamaguchi
and Hoblitt (1995)
Sclerochronology
0-1000 yr
Coral
Buddemeier and Taylor
(2000)
random instant, the probability of such decay
depends on the parent-daughter pair. The lower
the probability of decay at any instant, the longer
it will take for a population of parent atoms to
decay to half its size, and vice versa. The time
required to reduce the parent population by half
defines the
half-life
. Mathematically, the process
is captured in the differential equation
d
N
/d
t
= −
l
N
atoms, d
N
/d
t
is the rate of change of this num-
ber, and the decay constant
l
expresses the
probability of decay of any parent atom at any
instant. The solution to this equation is an
exponential function:
N
=
N
0
e
−
lt
(3.2)
where
N
0
is the initial abundance of the parent
atom at time
t
= 0. You can easily see that the
time,
t
, it takes for the decay of the population
from
N
0
to
N
0
/e (recalling that e = 2.718…, this
is roughly
N
0
/3) is 1/
t
. The half-life, found by
solving for the time at which
N
=
N
0
/2,
is
t
1/2
= −ln(1/2)/l,
l
, or 0.693/
l
. In Table 3.2, we
(3.1)
This equation is a commonly used example of a
first-order linear differential equation found in
the front of many introductory differential equa-
tion textbooks. Here
N
is the number of parent
