### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3aUW14. A robust method for computing the reflection coefficient from a
multilayered bottom with shear.

**Evan K. Westwood
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*Defence Res. Establishment Pacific, FMO Victoria, BC V0S 1B0, Canada
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**Scott J. Levinson
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*Univ. of Texas at Austin, Austin, TX 78713-8029
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An analytic method for computing the plane wave reflection coefficient
from a multilayered ocean bottom with shear has been developed. The
compressional (p-) and shear (s-) wave sound speeds may either be constant in a
layer or have a gradient (in which case coupling is ignored). Propagator
matrices that involve exponentials or Airy functions are used to solve for the
p-wave and s-wave displacement potentials at the top of each layer in terms of
the same quantities at the bottom of each layer. Several key steps are critical
to making the calculations robust: (1) Reflection coefficients (p-p, p-s, s-s,
and s-p), rather than potentials, are computed at the top of each layer, (2)
numerically unstable Wronskian terms are replaced by their analytic formulas in
the p-s and s-p reflection coefficients, and (3) exponential factors common to
the p-s and s-p reflection coefficients are kept track of separately. Analytic
derivatives of the reflection coefficients with respect to angle and frequency
have been derived and implemented. The method requires very little computer
storage, and the analytic form is computationally efficient compared to
numerical methods, especially as the frequency increases. [Work supported by
the ARL Independent Research and Development Program.] [sup a)]On leave from
Appl. Res. Lab., The University of Texas at Austin.