About this book
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