Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Analysis of a Mogi-type model describing surface deformations induced by a magma chamber embedded in an elastic half-space

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      Motivated by a vulcanological problem, we establish a sound mathematical approach for surface deformation effects generated by a magma chamber embedded into Earth's interior and exerting on it a uniform hydrostatic pressure. Modeling assumptions translate the problem into classical elasto-static system (homogeneous and isotropic) in an half-space with an embedded cavity. The boundary conditions are traction-free for the air/crust boundary and uniformly hydrostatic for the crust/chamber boundary. These are complemented with zero-displacement condition at infinity (with decay rate). After a short presentation of the model and of its geophysical interest, we establish the well-posedness of the problem and provide an appropriate integral formulation for its solution for cavity with general shape. Based on that, assuming that the chamber is centred at some fixed point \(\bm{z}\) and has diameter \(\varepsilon>0\), small with respect to the depth \(d\), we derive rigorously the principal term in the asymptotic expansion for the surface deformation as \(\varepsilon=r/d\to 0^+\). Such formula provides a rigorous proof of the Mogi point source model in the case of spherical cavities generalizing it to the case of cavities of arbitrary shape.

      Related collections

      Most cited references 18

      • Record: found
      • Abstract: not found
      • Article: not found

      Elastic stress and deformation near a finite spherical magma body: Resolution of the point source paradox

       D. F. McTigue (1987)
        Bookmark
        • Record: found
        • Abstract: not found
        • Article: not found

        Deformation from inflation of a dipping finite prolate spheroid in an elastic half-space as a model for volcanic stressing

          Bookmark
          • Record: found
          • Abstract: not found
          • Article: not found

          Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy

            Bookmark

            Author and article information

            Journal
            2016-06-20
            1606.06060

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            35C20, 31B10, 35J25, 86A60
            Roma01.Math
            math.AP

            Analysis

            Comments

            Comment on this article