Commun. Comput. Phys., 9 (2011), pp. 129-146.


Quantifying Tectonic and Geomorphic Interpretations of Thermochronometer Data with Inverse Problem Theory

G. Bao 1, Y. Dou 5, T. A. Ehlers 2, P. Li 3, Y. Wang 4, Z. Xu 1*

1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.
2 Institut fuer Geowissenschaften, Universitat Tuebingen, Germany.
3 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.
4 Department of Mathematics, Fudan University, Shanghai, China.
5 Department of Mathematics, Harbin Institute of Technology, Harbin, China.

Received 9 January 2010; Accepted (in revised version) 27 April 2010
Available online 5 August 2010
doi:10.4208/cicp.090110.270410a

Abstract

Thermochronometer data offer a powerful tool for quantifying a wide range of geologic processes, such as the deformation and erosion of mountain ranges, topographic evolution, and hydrocarbon maturation. With increasing interest to quantify a wider range of complicated geologic processes, more sophisticated techniques are needed. This paper is concerned with an inverse problem method for interpreting the thermochronometer data quantitatively. Two novel models are proposed to simulate the crustal thermal fields and paleo mountain topography as a function of tectonic and surface processes. One is a heat transport model that describes the change of temperature of rocks; while the other is surface process model which explains the change of mountain topography. New computational algorithms are presented for solving the inverse problem of the coupled system of these two models. The model successfully provides a new tool for reconstructing the kinematic and the topographic history of mountains.

AMS subject classifications: 86A22, 35R37, 35Q80, 86A60

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Key words: Thermochronology, heat equations, inverse problem, variational method, iterative method, surface processes.

*Corresponding author.
Email: bao@math.msu.edu (G. Bao), dou@math.msu.edu (Y. Dou), tehlers@me.com (T. A. Ehlers), lipeijun@purdue.edu (P. Li), zhengfu@math.msu.edu (Z. Xu)
 

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