### Abstract

Motivated by a vulcanological problem, we establish a sound mathematical approach for surface deformation e ects 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 a half-space with an embedded cavity. The boundary conditions are traction-free for the air/crust boundary and uniformly hydrostatic for the 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 centered at some fixed point z and has diameter r > 0, small with respect to the depth d, we derive rigorously the principal term in the asymptotic expansion for the surface deformation as ε = r/d → 0^{+}. Such a 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.

Original language | English (US) |
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Pages (from-to) | 223-255 |

Number of pages | 33 |

Journal | Journal de l'Ecole Polytechnique - Mathematiques |

Volume | 4 |

DOIs | |

State | Published - Jan 1 2017 |

### Fingerprint

### Keywords

- Asymptotic expansions
- Double layer potentials
- Lamé operator
- Single

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Analysis of a mogi-type model describing surface deformations induced by a magma chamber embedded in an elastic half-space.** / Aspri, Andrea; Beretta, Elena; Mascia, Corrado.

Research output: Contribution to journal › Article

*Journal de l'Ecole Polytechnique - Mathematiques*, vol. 4, pp. 223-255. https://doi.org/10.5802/jep.42

}

TY - JOUR

T1 - Analysis of a mogi-type model describing surface deformations induced by a magma chamber embedded in an elastic half-space

AU - Aspri, Andrea

AU - Beretta, Elena

AU - Mascia, Corrado

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Motivated by a vulcanological problem, we establish a sound mathematical approach for surface deformation e ects 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 a half-space with an embedded cavity. The boundary conditions are traction-free for the air/crust boundary and uniformly hydrostatic for the 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 centered at some fixed point z and has diameter r > 0, small with respect to the depth d, we derive rigorously the principal term in the asymptotic expansion for the surface deformation as ε = r/d → 0+. Such a 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.

AB - Motivated by a vulcanological problem, we establish a sound mathematical approach for surface deformation e ects 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 a half-space with an embedded cavity. The boundary conditions are traction-free for the air/crust boundary and uniformly hydrostatic for the 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 centered at some fixed point z and has diameter r > 0, small with respect to the depth d, we derive rigorously the principal term in the asymptotic expansion for the surface deformation as ε = r/d → 0+. Such a 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.

KW - Asymptotic expansions

KW - Double layer potentials

KW - Lamé operator

KW - Single

UR - http://www.scopus.com/inward/record.url?scp=85034838159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034838159&partnerID=8YFLogxK

U2 - 10.5802/jep.42

DO - 10.5802/jep.42

M3 - Article

VL - 4

SP - 223

EP - 255

JO - Journal de l'Ecole Polytechnique - Mathematiques

JF - Journal de l'Ecole Polytechnique - Mathematiques

SN - 2429-7100

ER -