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

Abstract

We derive closed analytical solutions for quasi-static thermoelastic deformation in response to instantaneous point and spherical heat sources in an elastic half-space. Since we can take advantage of the solutions for an infinite medium, the derivation of solutions for a semi-infinite medium is straightforward. We examine the spatial and temporal evolution of thermoelastic deformation for point and spherical heat sources. We applied the solution to a radar interferometric observation of post-eruptive deformation associated with the 1986 fissure eruption at Izu-Oshima volcano, Japan. Assuming a spherical heat source at a depth of 240 m with a volume of 1.15 × 107 m3 and a temperature step 103 K, the predicted rate of post-eruptive ground movement agrees with the observed rate within observational errors. Also, the same parameter values allow us to compute the co-eruptive ground displacement by the effect of mass intrusion, whose amplitude is consistent with the observed height (45 m) of the newly formed cone. The derived solutions can be applied to transient ground displacements observed at active volcanoes, and allow us to evaluate the heat amount of magma intruded at very shallow depths. © 2005 RAS.