An Elastic Model for Volcanology

1. Front Matter

   Pages i-x

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2. From the Physical to the Mathematical Model

   • Andrea Aspri

   Pages 1-10

3. A Scalar Model in the Half-Space

   • Andrea Aspri

   Pages 11-51

4. Analysis of the Elastic Model

   • Andrea Aspri

   Pages 53-118

5. Back Matter

   Pages 119-126

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This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth’s interior. From a mathematical perspective, these modeling assumptions manifest as a boundary value problem that has long been known by researchers in volcanology, but has not, until now, been given a thorough mathematical treatment. This mathematical study gives an explicit formula for the solution of the boundary value problem which generalizes the few well-known, explicit solutions found in geophysics literature. Using two distinct analytical approaches—one involving weighted Sobolev spaces, and the other using single and double layer potentials—the well-posedness of the elastic model is proven. An Elastic Model for Volcanology will be of particular interest to mathematicians researching inverse problems, as well as geophysicists studying volcanology.

• Mathematical geophysics
• Mathematical geosciences
• Mathematical geophysics book
• Mathematical modeling geophysics
• Mogi model
• linear elasticity
• magma chamber
• hydrostatic pressure
• Mogi model
• Neumann boundary problem
• Half-space model
• Magma chamber
• Geophysics research math
• Math research volcanoes
• Math magma
• asymptotic expansions
• single and double layer potentials
• neumann function
• stability estimates
• weighted sobolev spaces

• Austrian Academy of Sciences, Johann Radon Institute for Computational, Linz, Austria

  Andrea Aspri

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