Braun J., van der Beek P., Batt G. Quantitative Thermochronology: Numerical Methods for the Interpretation of Thermochronological Data
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148 Detrital thermochronology
predicts that source-area relief is increasing by focussed incision of the valleys,
leading to the observed predominance of ‘young’ ages ≤4Myr in the detrital
sample. These young ages would then reflect variable denudation rates, whereas
the spread in older ages could be explained by invoking the observed age–
elevation gradient. Optimum analysis of detrital grain-age populations, taking
into account the possibility of non-uniform denudation rates and transient relief,
requires sophisticated modelling approaches such as those outlined in Chapter 7,
combined with inversion techniques as discussed in Chapter 8.
9.5 Interpreting partially reset detrital samples
Whereas the high-temperature zircon fission-track or mica Ar–Ar systems are gen-
erally better suited for monitoring long-term variations in exhumation rate of the
source area, the lower-temperature apatite fission-track and (U–Th)/He systems
allow testing for shorter-term variations in exhumation rates. Because of their rel-
atively low closure temperatures, however, these systems are also correspondingly
more sensitive to the thermal evolution of the basin itself. Typically, stratigraph-
ically higher samples that have not been buried deep enough for partial resetting
to occur will retain a source signal, whereas deeper samples will record the burial
and exhumation history of the basin sediments themselves (e.g., Rohrman et al.,
1996). Therefore, as samples from deeper downsection are analysed, their infor-
mation content on source-area denudation is gradually erased and replaced by
information on the burial and exhumation history of the sedimentary basin.
The problem of retrieving information from partially reset samples has been
analysed quantitatively for the apatite fission-track system, which is widely used
by the petroleum industry for studies of the thermal evolution of sedimentary
basins (Rohrman et al., 1996; Carter and Gallagher, 2004). Given minimal controls
on the depositional history and kinetic properties of the apatites studied, both
the pre-depositional (source area) and the post-depositional (sedimentary basin)
thermal history can, in principle, be recovered from detrital apatite fission-track
samples by inverting their track-length distributions (Carter and Gallagher, 2004).
In practice, however, the potentially large variations in source-area denudation
rates, as well as in the annealing kinetics of the sampled grains, make this approach
challenging. Nevertheless, important information on the thermal history both of
the source area and of the basin can be gained by inspecting the component
(‘peak’) ages if data are sampled continuously downsection.
An example of such an approach is shown in Figure 9.10, where detrital apatite
fission-track (AFT) data from the Karnali River section (western Nepal) have
been plotted as a function of the initial stratigraphic depth of the samples. The
Karnali section exposes Miocene–Pliocene (16–5-Myr-old) Himalayan foreland
9.5 Interpreting partially reset detrital samples 149
0
1000
2000
3000
4000
5000
6000
0 2 4 6 8 10 12 14
Apatite FT Age (Myr)
Stratigraphic Depth (m)
Central Age
Minimum Age
Stratigraphic Age
Fig. 9.10. Variations of apatite fission-track central age (black diamonds) and
minimum peak age (white squares) with stratigraphic depth in the Karnali River
section through Siwalik sediments in western Nepal. The continuous black line
is the stratigraphic age (after Gautam and Fujiwara, 2000). The initial strati-
graphic depth was estimated by extrapolating the average sedimentation rates
to the present day. Note the constant ∼2Myr lag time between stratigraphic
and minimum apatite fission-track (FT) ages in the upper part of the section
≤2500 m and the consistent 2 Myr minimum age for the lowest four samples,
providing an estimate for the final exhumation of the section along the Main
Frontal Thrust.
basin sediments of the Siwalik group (e.g., Gautam and Fujiwara, 2000). These
are exposed at present because of tilting and exhumation along the Main Frontal
Thrust, the currently active frontal thrust of the Himalayan system. Samples from
the upper part of the section (down to a paleo-depth of ∼2500m) have AFT
ages that increase downsection; both the central age and the peak age of the
youngest component (the ‘minimum’ age) are older than the stratigraphic age.
These samples have not been annealed since deposition and retain the source-area
information. Their minimum AFT age displays a constant lag time of ∼2Myr
since ∼75 Myr ago, which is indicative of maximum source-region exhumation
rates of ∼15kmMyr
−1
, similar to the longer-term rates measured by detrital
zircon fission-track analysis of these samples.
For the stratigraphically lower samples, AFT ages decrease downsection and
are younger than the stratigraphic age: these samples have been partially annealed
during burial in the basin. The transition from unannealed to partially annealed
samples represents the exposed top of the ‘fossil’ apatite partial annealing zone
(PAZ) at ∼60
C (compare with Figures 3.8 and 3.10). The paleo-geothermal
gradient can be inferred from the estimated structural depth of this transition; in the
150 Detrital thermochronology
case of Figure 9.10, a pre-exhumational geothermal gradient of 15–20
Ckm
−1
within the basin is inferred, which is notably in accord with vitrinite reflectance
data and present-day heat-flow measurements in wells from the Ganges foreland
basin. Alternatively, if the geothermal gradient within the basin is known, the
depth to the top of the paleo-PAZ can be used to infer the amount of denudation
following the approach outlined in Figure 1.6 (e.g., Cederbom et al., 2004).
The base of the paleo-PAZ is represented by the transition from partially to fully
annealed samples; for cases in which final exhumation of the samples was rapid,
fully annealed samples will be characterised by constant thermochronological
ages downsection that represent the age of final exhumation (cf. Figures 3.10
and 1.6). The base of the paleo-PAZ is not exposed in the Karnali section shown
in Figure 9.10 but the minimum ages can be used to place limits on the timing
of final exhumation. In particular, the annealed AFT samples from the lowermost
part of the section have a consistent minimum age peak of 2 ±04Myr and
therefore suggest that the onset of exhumation of this part of the Siwaliks along
the Main Frontal Thrust occurred at that time. Using a similar approach on well
samples, Cederbom et al. (2004) showed that the molasse foreland basin of the
central Alps records 1–3 km of exhumation since 5 Myr ago, which they relate
to isostatic rebound of the basin due to widespread and rapid denudation of the
mountain belt.
10
Lateral advection of material
When one is applying a physical interpretation to thermochronological
data as outlined here, the geographical distribution of deformation,
denudation and thermal structure, and the interaction of particles with
these laterally variable parameters justify careful consideration. In
this chapter, we will investigate the consequences of lateral variation
in denudation rates and lateral motion of material points on ther-
mochronological age distributions.
10.1 Lateral variability in tectonically active regions
Thermochronological ages at the surfaces of eroded regions reflect an integration
of the denudation rates experienced between the isotopic closure of a sample and
its subsequent exposure. Crustal structure and kinematics (Beaumont et al., 1992,
1996; Koons, 1994), thermal structure (Koons, 1987; Lewis et al., 1988; Hyndman
and Wang, 1993; Batt and Braun, 1997; Ehlers et al., 2001) and regional exhuma-
tion rates (Wellman, 1979; Zeitler et al., 1982; Brandon et al., 1998; Ehlers et al.,
2003) can all have strong lateral gradients across tectonically active regions. Any
material traversing this variable framework is thus subject to an accompanying
range of conditions during its residence within the deforming region that will
influence the development of the apparent thermochronological age.
Material denudation, and the uplift and deformation with which it is commonly
associated, are driven, fundamentally, by lateral motion between crustal blocks.
Far from being an exceptional occurrence, lateral motion of material dominates the
overall kinematics experienced in many tectonically active regions, with samples
experiencing tens or even hundreds of kilometres of lateral translation during
progressive uplift and exhumation from mid-crustal depths (Beck, 1991; Jamieson
et al., 1996; Walcott, 1998; Brandon and Vance, 1992; Brandon et al., 1998), and
151
152 Lateral advection of material
0.4
(b)
A
B
C
A′
2
3
B′ DC′
0.6
T
c
1
T
c
3
T
c
2
0.4
1
Relative distance
Relative distance
0.4
Relative time in the past
(c)
A
B
D
1
2
3
0.6
C
(a)
A′
B′
D
C′
0.4
1.0
Relative depth
0.8
0.2
0.6
0.0
0.0
Relative temperature
0.2
0.8
0.4
1.0
1.00.80.2 0.60.0
0.0
Relative denudation rate
0.2
0.8
0.6
0.4
1.0
1.00.80.2 0.60.0
0.0
0.2
0.8
0.4
1.0
Relative temperature
1.00.80.2 0.60.0
Fig. 10.1. The thermochronological significance of material convergence rela-
tive to the denudational and thermal framework of a deforming region. Note that,
although figurative, the processes and effects illustrated are derived from pub-
lished (Batt and Braun, 1997, 1999; Batt et al., 2001) and unpublished numerical
modelling work of the authors. (a) The assumed variation in erosion rate across
the area of interest. (b) The regional thermal structure, and the material path taken
by three selected particles during their passage through the deforming region.
Arbitrary closure isotherms are shown for three nominal thermochronometers, as
discussed in the text. (c) Variations in temperature experienced over time by the
three particles illustrated in panel (b). Note the progressive acceleration in cool-
ing rate. This is caused by spatial, rather than temporal, variation in exhumation
rate (panel (a)), and thus illustrates the caution required in attaching dynamic
significance to such features.
hence integrating tectonic and surface conditions over potentially great distances
(Figure. 10.1).
10.2 Exhumation and denudation in multi-dimensional space
As defined in Chapter 1, exhumation refers to the unroofing history of an actual
rock, defined as the vertical distance traversed relative to the Earth’s surface,
whereas denudation, taken in the broad generic sense of Ring et al. (1999), relates
to the removal of material at a particular point at or under the Earth’s surface, by
tectonic processes and/or erosion, and is more correctly viewed as a measure of
material flux.
10.3 Consequences of lateral motion for thermochronology 153
In the one-dimensional case in which the regional character is uniform, or
particles are exhumed purely vertically, the terms denudation and exhumation are
practically synonymous, except for the subtle distinction in the frame of reference.
For cases in which lateral transport plays an important role, in contrast, the
exhumation record derived from thermochronological constraints is not directly
interchangeable with spatial parameters such as erosion or tectonic unroofing
(Morris et al., 1998) (see Figure 10.1).
10.3 Consequences of lateral motion for thermochronology
Integrated effects on individual ages
The potential thermochronological consequences of lateral motion relative to a
variable tectonic framework are schematically illustrated in Figure 10.1. Mate-
rial is assumed to be traversing a region experiencing deformation and erosion
where denudation rates vary laterally. For simplicity, the thermal structure is
shown as uniform, with a linear geothermal gradient, but the detail of this is not
critical to the basic phenomena under discussion here. Sample 1 (the main path
illustrated) cools progressively through the closure temperatures of three arbi-
trary thermochronometers during its exhumation, experiencing effective closure
at points A, B, and C respectively, with A
′
,B
′
and C
′
marking the corresponding
points at the surface directly above each of these sites. Upon its eventual exposure
at the surface, the apparent ages of sample 1 for each of these three chronometers
reflect the average exhumation rate experienced between the relevant point of
closure (A, B, or C) and exposure of the sample at point D. Owing to the spatial
variation in denudation rate, the exhumation rate experienced varies through time
as the sample traverses the deforming region. As a consequence, none of the
chronometers indicated will directly reflect the denudation rate either at point D
or at the location at which its respective closure occurred.
Consequences for spatially dispersed datasets
Lateral variation in the character of exhumation paths has equally significant
consequences for the integrated interpretation of spatially dispersed thermochrono-
logical data, where physical significance is ascribed to variations in ages between
data collected at different localities across a region.
When one is sampling age–elevation profiles (cf. Sections 1.2 and 6.2), tectonic
behaviour is interpreted from age variations along transects in areas of high relief
(Wagner and Reimer, 1972; Wagner et al., 1977; Fitzgerald and Gleadow, 1988;
Fitzgerald et al., 1995). Conceptually, this approach is based on treating samples
as if they all came from a single column of rock, but, in practice, the collection of
samples dispersed over 1000 m or more of elevation difference usually involves
154 Lateral advection of material
lateral separation of material by kilometres to tens of kilometres, even in areas of
intense relief.
At longer spatial wavelengths, authors of some tectonic studies ascribe physical
or temporal significance to geographic variations in the apparent age of samples
collected across deformed and exhumed regions at the scale of entire orogens
(Brandon and Vance, 1992; Tippett and Kamp, 1993; Batt et al., 2000, 2004;
Cockburn et al., 2000; Ehlers et al., 2003).
These approaches benefit from considering lateral variation in kinematics since
each point exposed on the surface experiences a different exhumation path, and
hence reflects a separate set of interactions with the variable thermal and denuda-
tional character of the region. This phenomenon is illustrated in Figure 10.1 by
the contrasting histories experienced by samples 1, 2 and 3. Although the regional
framework of denudation rates remains stable, these samples experience differing
exhumation histories as they traverse the region between isotopic closure and
eventual exposure.
This effect introduces ambiguity into the interpretation of spatial variability in
thermochronological ages, since any variation observed between geographically
separate samples can reflect either temporal variations in behaviour (e.g.,
diachronous deformation episodes or changes in exhumation rate over time)
or variations in the kinematic framework (e.g., structural variation or laterally
variable surface processes), or some combination of the two.
The significance of such ‘tectonic assembly’ of varying thermochronological
trends has long been recognised in modelling studies examining regional tectonic
evolution (Stüwe et al., 1994; Jamieson et al., 1996, 2002; Batt and Braun, 1997;
Harrison et al., 1998), and has led to a wide acceptance of the importance of
explicit structural control as an element in thermochronological studies (Stockli
et al., 2001; Ehlers et al., 2003).
10.4 Scaling of lateral significance with closure temperature
The higher the temperature at which a system closes, the deeper in the crust
and the earlier closure occurs, the greater the lateral distance that will subse-
quently be travelled prior to exposure at the surface, and the wider the potential
range of lateral variation which could thus be incorporated into the observed age
(see Figure 10.1). Conversely, the lower the temperature of closure, the less sensi-
tive a thermochronometer is to lateral variation in orogenic character, and the more
sensitive it is to local denudation conditions, surface processes and topographic
effects. When subject to lateral motion through the denuding region, it follows
that different thermochronometers do not just constrain varying timescales or lev-
els of sensitivity, but also provide insight into fundamentally different aspects of
the character and evolution of tectonically deformed regions.
10.5 Evaluation of the significance of lateral variation 155
10.5 Evaluation of the significance of lateral variation
The consequences of lateral variations in particle paths for the development of
the thermochronological record do not mean that one-dimensional interpretations
cannot provide valid tectonic insights in some, or indeed many, cases – but the
potential impacts of spatially variable structural and erosional character first need
to be considered in order to evaluate their relative significance.
Regional estimation of significance: the factor
Before embarking on time- and processing-intensive deconvolution of the ther-
motectonic implications of individual samples, a useful first step is to consider
the approximate level of influence that lateral motion might be expected to exert
within a particular dataset. A simple guide to the potential consequences of lateral
particle motion during the buildup of thermochronometric ages can be derived
from comparison of the spatial variability in denudation rate f
,
f
=
max
−
min
max
$
(10.1)
where
max
and
min
are the maximum and minimum denudation rates across the
region and
is the length scale over which this variation occurs. The horizontal
length scale
X
over which the sample has travelled between closure at depth and
exposure at the surface (Figure 10.2) is
X
= v
h
t
s
(10.2)
where v
h
is the rate of horizontal motion across the region and t
s
is the sample
age (Batt and Brandon, 2002). Multiplied together, these give a dimensionless
number ,
=
X
f
(10.3)
that indicates the relative variation in exhumation rate potentially experienced by
a sample between thermochronological closure and its exposure at the surface.
If either the variability in denudation rate
max
−
min
or the horizontal veloc-
ity v
h
is small, tends towards zero, and neglecting the thermochronological
consequences of lateral motion may be reasonable. Conversely, high values of
approaching or even exceeding 1, that is, reflecting a nominal 100% varia-
tion in exhumation rate between closure and surface exposure, indicate that a
wide range of exhumation rates could potentially be integrated by the given
thermochronometer, with corresponding influence on the observed ages.
156 Lateral advection of material
Closure isotherm
Relative denudation rate
0.0
0.2
0.8
0.6
0.4
1.0
v
h
λ ∆ε
ε
min
ε
max
λ
X
E
x
h
u
m
a
t
i
o
n
t
r
a
j
e
c
t
o
r
y
Fig. 10.2. An illustration of the physical parameters relevant to evaluation of
the significance of lateral transport in interpreting thermochronological data.
A particle passing through a system experiencing exhumation will integrate
lateral variation in character over a characteristic length scale,
X
, that can be
derived by combining the average lateral rate of motion through the system with
the total time recorded between closure and exposure of the particle given by
its apparent age for a given chronometer. The relative significance of this length
scale is assayed by comparison with the wavelength of spatial variation in the
relevant parameter (in the case illustrated, exhumation rate) within the system,
and the total variation in conditions within this range.
Deconvolving lateral effects on the thermochronological record
In the absence of strong dynamic forcing or the transient effects of magmatic
intrusions, temperature increases with depth in the crust, with isotherms approxi-
mately parallel to topography near the surface and becoming progressively more
subdued with depth (as treated in detail in Chapters 4–6). It follows that, despite its
consequences for the integrated thermal history experienced by material travers-
ing a tectonically active region, long-term lateral motion is notoriously difficult
to isolate in the thermochronological record, since such movement is largely par-
allel to broad-scale thermal structure and thus does not produce a significant and
predictable cooling effect (see, for instance, Figure 13.4 later).
The most effective resolution to this ambiguity is derived through numerical
simulations that incorporate the two- and three-dimensional kinematics of tectonic
deformation and denudation, and thus allow the thermochronological record to be
interpreted in the context of the overall motion experienced.
10.5 Evaluation of the significance of lateral variation 157
An example of such a simulation will be treated in Chapter 13. In brief, geologi-
cal and structural controls, together with requirements for conservation of material,
enable one to make a reasonable approximation of the past and present mode of
deformation of many deformed and denuded regions. Numerical models based on
such kinematic frameworks can be used to solve for the evolving thermal structure
of the deforming region (Koons, 1987; Beaumont et al., 1996; Batt and Braun,
1997). The physical and thermal coupling of these models enables the tracking
of selected material points through the model domain, and the assessment of how
a given exhumation path interacts with the evolving thermal structure, enabling
thermal histories, and their implications for different thermochronometers, to be
calculated for individual particles.
The multi-variate models needed to incorporate the dynamic interplay of heat
flow, kinematics and sample mineralogy that goes into producing a thermochrono-
logical age cannot usually provide a unique interpretation for specific age data
(e.g., Quidelleur et al., 1997). Rather, such models are used to provide insights into
how various aspects of tectonic deformation and accompanying denudation are
ultimately integrated into the thermochronological record, thus helping to choose
between competing hypotheses, and guiding interpretation of the physical causes
behind observed regional patterns in thermochronological data (Shi et al., 1996;
Beaumont et al., 1996; Batt and Braun, 1999; Batt et al., 2001; Ehlers et al., 2001).
Case study: the Olympic Mountains
The Olympic Mountains (Figure 10.3) are the topographically highest and most
deeply exhumed segment of the Cascadia forearc high of western North America.
The Olympics were the earliest part of the forearc to become emergent, c. 12 Myr
ago (Brandon and Calderwood, 1990), and the mountainous topography of the
range has been sustained since that time by continued accretion of material
from the subducting Juan de Fuca Plate and within-wedge deformation (Brandon
and Calderwood, 1990; Brandon et al., 1998). The Cascadia accretionary wedge
(Figure 10.3) is composed predominantly of sedimentary material built up by this
progressive accretion (Clowes et al., 1987; Brandon and Calderwood, 1990). This
sedimentary wedge underlies most of the offshore continental margin, reaching
thicknesses of 30 km, but is sub-aerially exposed only in the Olympic Mountains
(Stewart, 1970; Rau, 1973; Tabor and Cady, 1978).
In common with many accretionary complexes, there is a general paucity of
age-diagnostic fossils within the sandstones of the Cascadia accretionary wedge.
In the absence of reliable paleontological age control, thermochronological data
have long been the prime means applied to constraining the tectonic evolution