Quasi-static thermoelastic deformation in an elastic half-space: theory and application to InSAR observations at Izu-Oshima volcano, Japan

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We derive closed analytical solutions for quasi-static thermoelastic deformation in responseto instantaneous point and spherical heat sources in an elastic half-space. Since we can takeadvantage of the solutions for an infinite medium, the derivation of solutions for a semi-infinitemedium is straightforward. We examine the spatial and temporal evolution of thermoelasticdeformation for point and spherical heat sources. We applied the solution to a radar interferometricobservation of post-eruptive deformation associated with the 1986 fissure eruptionat Izu-Oshima volcano, Japan. Assuming a spherical heat source at a depth of 240 m with avolume of 1.15 × 107 m3 and a temperature step 103 K, the predicted rate of post-eruptiveground movement agrees with the observed rate within observational errors. Also, the sameparameter values allow us to compute the co-eruptive ground displacement by the effect ofmass intrusion, whose amplitude is consistent with the observed height (45 m) of the newlyformed cone. The derived solutions can be applied to transient ground displacements observedat active volcanoes, and allowus to evaluate the heat amount of magma intruded at very shallowdepths.
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