Abstract
Abstract. Thermochronometry provides one of few methods to quantify rock exhumation rate and history, including potential changes in exhumation rate. Thermochronometric ages can resolve rates, accelerations, and complex histories by exploiting different closure temperatures and path lengths using data distributed in elevation. We investigate how the resolution of an exhumation history is determined by the distribution of ages and their closure temperatures through an error analysis of the exhumation history problem. We define the sources of error, defined in terms of resolution, model error and methodological bias in the inverse method used by Herman et al. (2013) which combines data with different closure temperatures and elevations. The error analysis provides a series of tests addressing the various types of bias, including addressing criticism that there is a tendency of thermochronometric data to produce a false inference of faster erosion rates towards the present day because of a spatial correlation bias. Tests based on synthetic data demonstrate that the inverse method used by Herman et al. (2013) has no methodological or model bias towards increasing erosion rates. We do find significant resolution errors with sparse data, but these errors are not systematic, tending rather to leave inferred erosion rates at or near a Bayesian prior. To explain the difference in conclusions between our analysis and that of other work, we examine other approaches and find that previously published model tests contained an error in the geotherm calculation, resulting in an incorrect age prediction. Our reanalysis and interpretation show that the original results of Herman et al. (2013) are correctly calculated and presented, with no evidence for a systematic bias.
Highlights
Thermochronometry provides one of few methods to quantify rock exhumation histories
Where exhumation occurs by surface processes, the exhumation rate is equivalent to a surface erosion rate, and we will use these two terms interchangeably in this paper
We have dissected the possible source of errors and shown that, neglecting measurement errors, which should not be systematic, there are three potential sources of error: (1) model errors due to the parameterization including spatial correlation smoothing; (2) model errors due to incorrect prediction of the near-surface geotherm; and (3) resolution errors that result from inadequate data coverage of space and time
Summary
Thermochronometry provides one of few methods to quantify rock exhumation histories. Part of its success stems from the large number of thermochronometer systems available (Reiners and Brandon, 2006; Reiners et al, 2005) as well as the development of numerical models able to convert thermochronometric data into constraints on cooling associated with exhumation by surface or tectonic processes Models are an integral part of thermochronometric data interpretation as they are needed for computing cooling histories. Willett et al.: Bias and error in modelling thermochronometric data from parent–daughter loss relationships with a complex thermal history as well as for converting cooling histories into exhumation histories. Cooling or exhumation histories provide direct constraints on kinematics or tectonic processes and rates of surface erosional processes Cooling or exhumation histories provide direct constraints on kinematics or tectonic processes and rates of surface erosional processes (e.g. Grasemann and Mancktelow, 1993; Seward and Mancktelow, 1994; Brandon et al, 1998; Batt et al, 2000; Moore and England, 2001; Willett and Brandon, 2002; Ehlers et al, 2003; Lock and Willett, 2008; Campani et al, 2010; Herman et al, 2010; Barnes et al, 2012; McQuarrie and Ehlers, 2015)
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