According to recent estimates, the continental mid‐crust contains 35–40 per cent amphibolites. Heating of the crust by an underlying mantle plume, for example beneath continental rifts, high plateaus, and areas of intraplate volcanic activity, releases water. Dehydration of amphibole‐bearing rocks at depths of 20–40 km occurs mainly in the temperature range 650–700 °C, and this releases about 0.4 wt per cent of water.  Seismic tomography studies of the crust in the Kirgyz Tien Shan Range, where the age of the tectonic activity is less than 30 Ma, revealed a low‐velocity zone in the mid‐crust. The velocity of P waves was 0.4 km s−1 lower than in normal crust. MT sounding data in the region show the existence of a low‐resistivity layer with an average resistivity of about 25 Ω m at the depth of the low‐velocity layer. The spatial correlation of the observed anomalous layers and calculated effect of fluid phase on seismic and electric parameters of rocks suggests the presence of aqueous fluids released by the heating of the mid‐crust.

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The movement of a phase-change boundary in the Earth is determined by the solution of a non-linear boundary value problem (Stefan-like problem). It is equivalent to the solution of a non-linear integral equation. Approximate linear and non-linear asymptotic solutions to a variety of Stefan-like problems are derived and compared. If the amplitude of the phase boundary motion is small, the integral equation is linearized and analytical solutions are obtained by Laplace transform techniques. Series expansions converge asymptotically to the exact solution at small t regardless of the amplitude of the phase boundary motion. Solutions were derived for three different boundary value problems describing the motion of a phase boundary in the lithosphere or at the lithosphere-asthenosphere boundary: (i) motion of a phase-change boundary under change in surface pressure, (ii) motion of a phase boundary under change in heat flow at the lithosphere asthenosphere boundary and (iii) change in temperature at the base of the lithosphere. The comparison shows that, for the first two problems, the linear and the non-linear solutions are close at small values of f and the linear approximation remains valid even when the amplitude of the phase boundary motion is large.

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