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

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          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.

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          Most cited references 18

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

           D. F. McTigue (1987)
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            Deformation from inflation of a dipping finite prolate spheroid in an elastic half-space as a model for volcanic stressing

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              Surface deformation due to inflation of an arbitrarily oriented triaxial ellipsoidal cavity in an elastic half-space, with reference to Kilauea volcano, Hawaii

               Paul M. Davis (1986)
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                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

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