About the stability of the inverse problem in 1-D wave equations—application to the interpretation of seismic profiles

@article{Bamberger1979AboutTS,
  title={About the stability of the inverse problem in 1-D wave equations—application to the interpretation of seismic profiles},
  author={Alain Bamberger and Guy Chavent and Patrick Lailly},
  journal={Applied Mathematics and Optimization},
  year={1979},
  volume={5},
  pages={1-47}
}
AbstractThis paper is devoted to the study of the following inverse problem: Given the 1-D wave equation:(1) $$\begin{gathered} \rho (z)\frac{{\partial ^2 y}}{{\partial t^2 }} - \frac{\partial }{{\partial z}}\left( {\mu (z)\frac{{\partial y}}{{\partial z}}} \right) = 0 z > 0,t > 0 \hfill \\ + boundary excitation at z = 0 + zero initial conditons \hfill \\ \end{gathered} $$ how to determine the parameter functions (ρ(z),μ(z)) from the only boundary measurementY(t) ofy(z, t)/z=0.This inverse… 

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