1996; Farley 2000), has allowed direct inference of the temperature history of the host rocks, and a more indirect inference of denudation chronologies.
14
Reviews in Mineralogy & Geochemistry Vol. 58, pp. 375-387, 2005 Copyright © Mineralogical Society of America
Exploiting 3D Spatial Sampling in Inverse Modeling of Thermochronological Data Kerry Gallagher1, John Stephenson1, Roderick Brown2, Chris Holmes3, Pedro Ballester1 1
Dept. of Earth Sciences and Engineering Imperial College London South Kensington, London, SW7 2AS, England 2
Division of Earth Sciences Gregory Building University of Glasgow Glasgow, G12 8QQ, Scotland 3 Dept. of Statistics University of Oxford 1 South Parks Road Oxford, OX1 3TG, England
INTRODUCTION The development of quantitative models for fission track annealing (Laslett et al. 1987; Carlson 1990; Laslett and Galbraith 1996; Ketcham et al. 1999) and more recently, helium diffusion in apatite (Wolf et al. 1996; Farley 2000), has allowed direct inference of the temperature history of the host rocks, and a more indirect inference of denudation chronologies (see Kohn et al. this volume, and references therein). An example of a model prediction of AFT parameter and (U-Th)/He age for a specified thermal history is given in Figure 1. Various approaches exist to extract a thermal history model directly from the data, and these focus around inverse modeling (Corrigan 1991; Gallagher 1995; Issler 1996; Willett 1997; Ketcham et. al. 2000). The user specifies some constraints on the thermal history (e.g., upper and lower bounds on the temperature time, and heating/cooling rate), and then typically some form of stochastic sampling is adopted to infer either the most likely thermal history (ideally with some measure of the uncertainty of the solution), and/or a family of acceptable thermal histories. In both the forward and inverse approaches, the thermal history is typically parameterized as nodes in time-temperature space, with some form of interpolation between the nodes. Over recent years, one of the major applications of low temperature thermochronology has been the study of long term denudation as recorded in the cooling history of surface samples. More recently, some studies have specifically tried to link relatively short term, local estimates of denudation (e.g., from cosmogenic surface exposure dating) to these longer term estimates (Cockburn et al. 2000; Brown et al. 2001; Reiners et al. 2003). The step from the thermal history to denudation chronology is less direct that inferring the thermal history from the data, in that we need to make some assumptions in order to convert temperature to depth. This may involve an assumption that a 1D steady state with a constant temperature gradient over time is appropriate, or alternatively that a full 3D diffusion-advection model is required. The latter situation is not particularly amenable to an inversion approach, although recent applications have been made with a restricted number of parameters, to identify plausible solutions to relatively specific questions, such as the timing of relief development (Braun 1529-6466/05/0058-0014$05.00
DOI: 10.2138/rmg.2005.58.14
376
Gallagher, Stephenson, Brown, Holmes & Ballester
7 &
(-;TVKLS /DVOHWWHWDO 'XUDQJR
]
/L79A
]
(-;7(A
7LPH 0D
+H$JH 0D
2EV$)7$JH 0D 1RRI WUDFNV
