Inverse scattering theory for wave equations in stratified media
It is proved that the scattering matrix at a fixed positive energy determines uniquely the wave velocity which is assumed to depend asymptotically on one variable (the vertical coordinate). The velocity approaches its limit at infinity at an exponential rate. This limit is a piecewise constant velocity which depends on the vertical coordinate only and has just one jump (that is, it is a step function).
scientific article; zbMATH DE number 1054114