Numerical reconstruction of the initial temperature of diapiric structures in the Earth: effect of the heat diffusion
A. Ismail-Zadeha,b,*, A. Korotkiic, G. Schubertd, I. Tsepelevc
a Geophysical Institute, Karlsruhe University, Hertzstr. 16, Karlsruhe 76187, Germany bInternational Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Warshavskoye sh. 79-2, Moscow 113556, Russia cInstitute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, S. Kovalevskoy ul. 16, Ekaterinburg 620219, Russia dDepartment of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, 3806 Geology Building, 595 Charles Young Drive East, Los Angeles, CA 90095-1567, USA
ABSTRACT
We present a numerical approach to three-dimensional reconstruction of the evolution of thermal diapiric structures (e.g. hot plumes in the Earth's mantle) backwards in time. This approach is based on a search for the temperature and flow in the geological past by minimizing differences between the present-day temperature and that predicted by forward models of the evolution of diapiric structures for an initial temperature guess. We use the Eulerian spline FEM, FDM, and variational method to solve the coupled heat, momentum, and continuity equations with the appropriate boundary and initial conditions. The relevant numerical algorithm is tested with respect to the Rayleigh number and viscosity.
Keywords:
3-D thermal convection; Data assimilation; Variational method; Eulerian spline FEM; FDM