Theory of a Method of Ultrasonic Investigation of Stratified Media: Acoustic Impediography.

The use of broandband signals in ultrasonic echography leads to a new step of this investigation method: the quantitative one, or ultrasonic impediography. The original Jones' technique which is only valid for softly varying media. By a full reformulation of the theory. Transforming the equation governing acoustic propagation in inhomogeneous media into a Schroedinger equation, can solve this inverse scattering problem of quantum mechanics by using the Gelfand-Levitan or the Jost-Kohn procedure. The acoustic impedance profile is thus recovered from the impulse response of the medium. It is shown that the first iterate gives the same theoretical formula as the one already used by Jones, while higher order iterates will automatically take into account multiple reflections, insuring the validity of the method for all general cases.