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Abstract

Geodetic observations such as GNSS and InSAR have detected posteruptive crustal deformations. Those deformations are generally interpreted by a combination of several geophysical processes. One of such processes is viscoelastic relaxation of the lower crust and mantle, which occurs on time scale of years. The stress change within the viscoelastic layer which is caused by the coeruptive (i.e., elastic) deformation continues to relax until a new equilibrium is attained. The new equilibrium reflects the effects of self-gravitation of the Earth. In other words, a new isostatic state is realized when the stress dissipation is completed. This mechanism is common with glacial isostatic adjustment (GIA) and postseismic relaxation. In modeling posteruptive deformations, however, the effects of self-gravitation have often been neglected. In previous work, we developed a spectral finite element approach that accounts for self-gravitation and applied it to the GIA and postseismic relaxation. In this study, we apply the same approach to posteruptive deformation and theoretically evaluate the effects of self-gravitation. We derive a weak formulation associated with the source condition of horizontal and vertical opening. The validity of the formulation is verified with comparison with an analytic solution for the coeruptive deformation. Preliminary computational results show that the self-gravitation reduces the longer-wavelength deformation, which is consistent with the case of postsesmic deformation. In the presence of gravity, the long-term height of caldera could decrease in order to achieve isostacy, compared with the case excluding it.