# American Institute of Mathematical Sciences

January  2017, 11(1): 87-97. doi: 10.3934/ipi.2017005

## On the measurement operator for scattering in layered media

 Dept. of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J1P3, Canada

Received  February 2016 Revised  September 2016 Published  January 2017

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.

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