A linear approximation to the solution of a one-dimensional Stefan problem and its geophysical implications

TLDR: In this paper, the motion of a phase boundary in the Earth caused by temperature and pressure excitations at the Earth's surface is determined under a linear approximation using a sum of convolutions of pressure and temperature Green's functions with the corresponding excitations.

Abstract: Summary. The motion of a phase boundary in the Earth caused by temperature and pressure excitations at the Earth’s surface is determined under a linear approximation. The solution is found as a sum of convolutions of pressure and temperature Green’s functions with the corresponding excitations. The Green’s functions are given under the form of Laplace transforms that can be inverted either by numerical evaluation of a branch cut integral or by inversion of a series expansion. This solution is a generalization of a solution previously derived by Gjevik. This latter solution is the first term in the series expansion. The relaxation times associated with the phase boundary motion are of the order of 105-107yr for the olivine-spinel phase transition and of 106-107yr for the basalt-eclogite transition. The linear approximation remains valid for long times only if the phase boundary moves slowly.