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

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