Quantifying the effect of recent relief changes on age–elevation relationships

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Abstract

The effect that recent relief changes may have on the distribution of rock ages with elevation is investigated for a range of thermochronometers. From the solution of the heat transport equation in a crustal block undergoing uplift and surface erosion, the temperature history of rock particles that are exhumed at the Earth’s surface today is computed. These T-t paths are then used to calculate apparent isotopic ages for the (U–Th)/He system in apatite, characterized by a low (≈70°C) closure temperature. The results show that recent relief changes strongly affect the distribution of ages with elevation (notably the slope of the age–elevation relationship). The calculations presented here predict that, in most situations, regions that have undergone a steady decrease in surface relief in the recent past should be characterized by an inverted age–elevation relationship, that is older ages should be found near valley bottoms and younger ages near summit tops. It is also shown how the wavelength of the topography, the geothermal gradient, the exhumation rate and the duration of the relief reduction event affect this result.

Introduction

Regions of past or present tectonic uplift are subject to more or less rapid erosion. This leads to rock exhumation and cooling. This cooling has been documented by thermochronometry, from estimates of the time at which a given mineral has passed through a given temperature (called the closure temperature of the chronometer). As shown by many authors [1], [2] and illustrated in Fig. 1a, rocks that are exhumed near a mountain top have cooled through the closure temperature before rocks that are exhumed near the bottom of a valley. The difference in time is greater for high temperature systems (Fig. 1a) than for low temperature ones (Fig. 1b). This is because the thermal perturbation caused by a finite surface topography decreases exponentially with depth [3]. The amplitude of this perturbation can be parameterized by the vertical deflection of the closure temperature isotherm relative to the amplitude of the surface topography. As shown in Fig. 1b, we call this ratio α. Deep within the crust, isotherms are not affected by surface topography and α=0; in the vicinity of the surface, the isotherm follows exactly the surface topography and α=1.

Consequently, in an actively uplifting and eroding area characterized by a finite topography, there should be a well-defined relationship between height and apparent age for any thermochronometer [1]. In slowly eroding areas and/or for high closure temperature chronometers (α≈0), the slope of this relationship is equal to the exhumation rate. In rapidly eroding environments or for thermochronometers characterized by a low closure temperature (0<α<1), the closure temperature isotherm is perturbed by the surface topography and the slope of the age–elevation relationship (AER) gives an overestimate of the real exhumation rate [4].

This point is illustrated in Fig. 2 where fission track age–elevation data from the Huayna Potosi Pluton (Bolivian Andes) are shown. One set of ages comes from fission track analysis of apatite (circles) which has a closure temperature of ≈115°C, the other comes from FT analysis of zircon (triangles) which has a closure temperature of ≈250°C. The slope of the AER is significantly greater for the apatite ages compared to the zircon dataset. Neglecting the effect of the finite amplitude topography on the underlying temperature field, one would predict that the exhumation rate has significantly increased from 0.15 km Myr−1 to 2.2 km Myr−1 between the time the rocks cooled through the 250°C isotherm, i.e. 25–45 Myr ago, and the time they cooled through the 115°C isotherm, i.e. 6–16 Myr ago. Conversely, this dataset can also be interpreted as evidence for steady exhumation at 0.1–0.2 km Myr−1 during the past 45 Myr. In this scenario, the difference in slope between the two age–elevation datasets is a direct consequence of the thermal perturbation caused by the finite amplitude topography, which is significantly larger at depths of 1–2 km (where the apatite FT ages were set) than at depths of 5–6 km (where the zircon FT ages were set).

AERs have been documented in a large number of tectonically active areas such as the European Alps [5], the Andes [6], Alaska [7], and the Southern Alps of New Zealand [8], as well as in regions of past tectonic activity such as the Transantarctic Mountains [1], the Sierra Nevada [9] or Southeastern Australia [10]. In all areas, age increases with elevation, as predicted by the so-called ‘thermal topography’ argument described above.

The argument relating the slope of an AER to exhumation rate is based, however, on the assumption that surface topography does not evolve with time. As illustrated in Fig. 1c, it is clear that recent changes in surface relief amplitude (i.e. that took place since the rocks cooled through the closure temperature) have a strong effect on the slope of the AER. We assume that local changes in relief amplitude can be represented by a single parameter, β, defined as the ratio of present-day relief to past relief, i.e. at a time defined by the ‘mean age’ of rocks for a given thermochronometer. Our purpose here is to investigate whether AERs can provide information on the current rate of change of surface relief, especially for the newly developed thermochronometer (U–Th)/He in apatite, which, because of its low closure temperature, is regarded by many as the most likely candidate among the various thermochronometric systems to provide constraints on the rate at which surface processes are able to respond to more or less rapid changes in tectonic and/or climatic environment [11].

Many questions have recently been raised relating tectonics, relief and climate. For example, the current debate on the effect of Cenozoic climate change on the recent evolution of the Earth’s surface relief remains clearly open. Molnar and England [12] and, more recently, Peizhen et al. [13] have argued that the rapid cooling experienced by the Earth’s atmosphere over the last 2–3 Myr has been accompanied by increased erosion rates and a net increase in topographic relief, especially in large tectonically active areas such as the Himalayas and the Andes. According to Molnar and England [12], this relief production has led to uplift of mountain peaks by isostatic compensation and may have, therefore, caused, or at least enhanced, the climate shift by promoting precipitation. The debate is whether this feedback mechanism exists. Some have produced arguments based on geomorphological considerations [14], [15] that increased precipitation and/or a cooler climate should lead to a reduction (or, at most, a very small increase) in topographic relief; others have provided direct evidence, from cosmogenic radionuclide concentrations in the Sierra Nevada, that, locally, relief has increased in the last 3 Myr [16] but that, because of the small lateral extent of many mountain ranges, this has not led to substantial isostatically induced peak uplift. Other thermochronological data [17] indicate that the Sierra Nevada was characterized by substantial and probably much greater surface relief some 60–80 Myr ago and that the area has experienced a net decrease in relief since [17]. That different datasets/methods provide support to apparently conflicting opinions on the evolution of surface relief suggests that a better understanding of how surface topography influences thermochronometric data is needed.

Here the evolution of the temperature beneath an evolving, finite amplitude surface topography is computed, from which synthetic AERs can be derived. To achieve this, a newly developed numerical method to solve the basic partial differential equation governing heat transfer in the crust is used [18]. AERs are predicted for a range of parameter values representing different initial conditions (geothermal gradient), tectonic situations (rate of exhumation) and landforms (wavelength and rate of change of the surface topography).

Section snippets

Relief change and AER

The main purpose of the work presented here is to determine how finite amplitude topography and changes in surface relief affect the temperature distribution in the underlying crust, and how this information can be retrieved from AERs obtained for low temperature thermochronometers such as (U–Th)/He in apatite. To achieve this, the transient, two-dimensional heat transfer equation is solved, which may be written as [19]:ρc∂T∂t+v∂T∂z=∂xk∂T∂x+∂zk∂T∂z+ρAwhere T(x,z,t) is the temperature, ρ is

Sensitivity to model parameters

The variation of AER slope with relative relief change for a given closure temperature is also a function of the assumed model parameters. These include the wavelength of surface topography (λ), the exhumation rate (v), the average geothermal gradient (T/L) and the time scale of surface relief change (δ). To demonstrate this dependence, a number of sets of experiments were performed in which the amplitude of the relative change in relief, β, is systematically varied from 0.5 to 2. In each set,

Discussion

In this paper, a recently developed numerical method has been used to solve the heat transfer equation in the lithosphere undergoing uplift and erosion including the effects of a finite amplitude, time-varying surface topography. It is shown that the slope of AERs obtained by thermochronometry of rocks sampled in a region of finite relief is sensitive not only to the mean exhumation rate and the shape of the surface topography, but also to the rate of change of surface landform. This result

Acknowledgements

The author would like to thank A. Gleadow, M. Brandon, and F. Schlunegger for very constructive reviews of this manuscript.[AH]

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