MATHEMATICAL MODELLING OF MAGMA SOLIDIFICATION AND LITHOSPHERE THINNING

Abstract

Study of heat generated within the Earth, dissipated from its surface and coming from the mantle provides useful information about continental rifting, lithosphere thinning, metamorphic transformation and other tectonic processes. Phase boundary movement is a useful tool to study these, and many other geophysical and geological problems. Phase boundary movement methods can also be applied to formulate magma-solidification problems of simple and complex type. In this formulation, the energy balance condition on the phase boundary (Stefan condition) is used to determine changes in the status of domain of the problem. These problems are highly non-linear due to the non-linear Stefan condition on the boundary. The initial and boundary conditions of Neumann, Dirichlet, or of mixed type increase the complexity in solving the non-linear systems. Analytical treatments through approximation have earlier been applied to analyse some problems by many researchers. Numerical techniques such as finite difference and finite element methods are gaining popularity these days to solve a given physical system. The, Fourier series method has been used to describe lithosphere thinning due to basal heat flux at the LAB (lithosphere-asthenosphere boundary). Here the results are presented for some general heat flux which may suit geological and geophysical situations better. Magma solidification is discussed using analytical methods as well as numerical methods. Here a more general Rayleigh-Nusselt relationship is used to describe the solidification process occurring in magma chambers. In this thesis, we have used the Fourier method to solve two problems on lithosphere thinning. Four other problems are solved using concepts of fluid mechanics and numerical techniques. Results are developed numerically in three problems and analytically in one problem. The chapterwise details of the thesis are given below.