Inversion Formulas for the Linearized Problem for an Inverse Boundary Value Problem in Elastic Prospection

Abstract

The problem of determining an unknown pair $\gamma = ( {\lambda ,\mu } )$ of Lamé parameters inside a body by its Dirichlet-to-Neumann data map $\Lambda ( \gamma )$ is considered. Using explicit exact solutions for the case of constant $\gamma $, it is seen that the deflection h between $\gamma + h$ and $\gamma $ is uniquely determined by the first-order approximation of $\Lambda ( {\gamma + h} )$ at $\gamma $.