Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T16:29:13.944Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 August 2015

G. Bao ,
Y. Dou ,
T. A. Ehlers ,
P. Li ,
Y. Wang  and
Z. Xu
G. Bao*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Y. Dou*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin, China
T. A. Ehlers*
Affiliation:
Institut fuer Geowissenschaften, Universitat Tuebingen, Germany
P. Li*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Y. Wang
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA Department of Mathematics, Fudan University, Shanghai, China
Z. Xu*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
*
Email:bao@math.msu.edu
Email:dou@math.msu.edu
Email:tehlers@me.com
Email:lipeijun@purdue.edu
Corresponding author.Email:zhengfu@math.msu.edu
Get access

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.

Keywords

86A2235R3735Q8086A60Thermochronologyheat equationsinverse problemvariational methoditerative methodsurface processes
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 1 , January 2011 , pp. 129 - 146
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Alik, I.Z., Gerald, S., Igor, T. and Alexander, K., Inverse problem of thermal convection: numerical approach and application to mantle plume restoration, Physics of the Earth and Planetary Interiors. 145(2004), 99–114.Google Scholar
[2]Baldwin, S.L., Monteleone, B.D., Webb, L.E., Fitzgerald, P.G., Grove, M. and Hill, E.J., Pliocene eclogite exhumation at plate tectnoic rates ineastern Papua New Gunea, Nature. 431(2004), 263–267.Google Scholar
[3]Braun, J. and Sambridge, M., A new method based on irregular spatial discretization, Basin Research. 9(1997), 27–52.CrossRefGoogle Scholar
[4]Bukhgeim, A.L., Introduction to the Theory of Inverse Problems, The Netherland: VSP. 2000.Google Scholar
[5]Colton, D., The approximation of solutions to the backwards heat equation in a nonhomo-geneous medium, J. Math. Anal. Appl. 72(1979), 418–429.Google Scholar
[6]Choulli, M. and Yamamoto, M., Some stability estimates in determing sources and coefficients, J. Inv. Ill-posed Problems. 14(2006), 355–373.Google Scholar
[7]Dodson, M.H., Closure temperature in cooling geochronological and petreological systems, Contrib. Minerol. Petrol. 40(1973), 259–274.CrossRefGoogle Scholar
[8]Ehlers, T.A., Farley, K.A., Apatite(U-Th)/He thermochronometry: methods and applications to problems in tecnoics and surface processes, EPSL-Frontiers. 206(2003), 1–14.CrossRefGoogle Scholar
[9]Ehlers, T.A., Farley, K.A., Rusmore, M.E. and Woodsworth, G.J., Apatite(U-Th)/He signal of large magnitude and accelerated glacial erosion: Southwest Britishi Columbia, Geology. 34(2006), 765–768.CrossRefGoogle Scholar
[10]Elden, L., Time discretization in the backward solution of parabolic equations, Math. Comput. 39(1982), 53–84.Google Scholar
[11]Gallagher, K., Evolving thermal histories from fission track data, Earth Planet Sci Lett. 136(1995), 421–435.CrossRefGoogle Scholar
[12]Haenel, R., Rybach, L. and Stegena, L., Handbook of Terrestrial Heat-Flow Density Determination, Kluwer Academic Publishers, 1988.Google Scholar
[13]Herman, F., Braun, J., Senden, T.J. and Dunlap, W.J., (U-Th)/He thermochronometry: Mapping 3D geometry using micro-x-ray tomography and solving the associated production-diffusion equation, Chemical Geology. 242(2007), 126–136.Google Scholar
[14]Ismail-Zadeh, A.T., Talbot, C.J. and Volozh, Y.A., Dynamic restoration of profiles across diapiric salt structures: numerical approach and its applications, Tectonophysics. 337(2001a), 21–36.Google Scholar
[15]Isakov, V, Inverse Problems for Partial Differential Equations, Springer, New York, 1998.CrossRefGoogle Scholar
[16]Ivanov, V.K., Vasin, V.V. and Tanana, V.P., Theory of Linear Ill-Posed Problems and Its Applications [in Russian], Nauka, Moscow, 1978.Google Scholar
[17]Lutz, T.M. and Omar, G., An inverse method of modeling thermal histories from apatite fission track data, Earth Planet. Sci. Lett. 104(1991), 181–195.Google Scholar
[18]Persson, P. and Strang, G., A simple mesh generator in Matlab, SIAM Rev. 46(2004), 329–345.Google Scholar
[19]Tikhonov, A.N. and Arsenin, V.A., Solution of Ill-posed Problems, Winston, Washington, DC, pp255. 1977.Google Scholar
[20]Shuster, D.L. and Farley, K.A., 4He/3He themochronometry: theory, practice, and potential applications, Rev. in Mineralogy and Geochemistry. 58,(2005), 181–203.CrossRefGoogle Scholar
[21]Whipp, D.M. and Ehlers, T.A., Influence of goundwater flow on thermochronometer derived exhumation rates in the Nepalese Himalaya, Geology. 35(2007), 851–854.Google Scholar
[22]Wolf, R.A., Farley, K.A. and Silver, L.T., Assessment of (U-Th)/He thermochronometry: the low tempratrue history of the San Jacinto Mountains, California. Geology. 25(1997), 65–68.Google Scholar
[23]Yamamoto, M. and Zou, J., Simultaneous reconstrction of the intial temtperature and heat radiative coefficient, Inverse Problems. 17(2001), 1181–1202.Google Scholar