Evan K. Westwood
Defence Res. Establishment Pacific, FMO Victoria, BC V0S 1B0, Canada
Scott J. Levinson
Univ. of Texas at Austin, Austin, TX 78713-8029
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.