A numerical method for the explanation of sensitivity: The case of the identification of the 2D stratified elastic medium

The authors analyse the sensitivity of parameters involved in coupled acoustic/elastic equations to surface marine seismic data. This analysis is conducted by linearising the forward map (namely the map between a model of the subsoil and the pressure recorded at the surface) and then by introducing generalised inverses, constructed from a singular value decomposition of the Jacobian of this forward map. They apply this method of investigation to horizontally stratified media. They thus answer the questions of scaling and coupling between the different parameters. They analyse the power of resolution for each, and examine the influence of factors such as the type of medium around which linearisation is carried out, or the change of norm on the parameter space. They go on to examine the limits of validity of the linearisation.