An Elastic Model for Volcanology

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 approachesone involving weighted Sobolev spaces, and the other using single and double layer potentialsthe 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.

Presents a much-needed mathematical treatment of the linear elastic model to explain deformation effects generated by inflating or deflating magma chambers Proves the well-posedness of the linear elastic model using two distinct analytical approaches Generalizes existing mathematical models of magma chambers to cavities of generic shape

Inhalt
Preface.- From the physical to the mathematical model.- A scalar model in the half-space.- Analysis of the elastic model.- Index.