Open AccessA linear approximation to the solution of a one‐dimensional Stefan problem and its geophysical implications
Author(s) -
Mareschal Jean Claude,
Gangi Anthony F.
Publication year - 1977
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1977.tb03716.x
Subject(s) - laplace transform , stefan problem , mathematical analysis , phase transition , linear approximation , relaxation (psychology) , mathematics , series (stratigraphy) , boundary (topology) , phase boundary , phase (matter) , physics , geology , nonlinear system , thermodynamics , quantum mechanics , psychology , social psychology , paleontology
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 10 5 –10 7 yr for the olivine—spinel phase transition and of 10 6 –10 7 yr for the basalt—eclogite transition. The linear approximation remains valid for long times only if the phase boundary moves slowly.