Inverse scattering for the reflectivity function

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Abstract
An inverse method for elastic, electromagnetic, or acoustic waves in a stratified half‐space is presented. Rather than transforming the wave equation to one for which quantum inverse scattering methods can be applied in solving for a potential q(τ), we transform to one where it is suitable to solve for a ‘‘reflectivity function,’’ or local reflection coefficient, γ(τ). We show that γ(τ) can be discontinuous, thus improving a result of Balanis, and that discontinuities of γ(τ) match those of the impulse response R(t). We also show the relationship between the scattering kernel of this method and the scattering kernel of the quantum inverse scattering theory.