On the measurement operator for scattering in layered media
Peter C. Gibson
Inverse Problems & Imaging 2017, 11(1): 87-97 doi: 10.3934/ipi.2017005

We describe new mathematical structures associated with the scattering of plane waves in piecewise constant layered media, a basic model for acoustic imaging of laminated structures and in geophysics. Using explicit formulas for the reflection Green's function it is shown that the measurement operator satisfies a system of quasilinear PDE with smooth coefficients, and that the sum of the amplitude data has a simple expression in terms of inverse hyperbolic tangent of the reflection coefficients. In addition we derive a simple geometric description of the measured data, which, in the generic case, yields a natural factorization of the inverse problem.

keywords: Layered media discontinuous coefficients 1D scattering measurement operator inverse problems

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