Make a direct numerical implementation of the expression in (2.146) for the wavenumber representation of the field in an ideal waveguide. Allow the horizontal wavenumber to be complex.
a. For sound speed 1500 m/s and depth 100 m, compute the wavenumber kernel at 20 Hz for source and receiver both at depth 36 m. Sample the kernel at 200 points equidistantly placed over the interval where kw is the water wavenumber. Let the imaginary value of the horizontal wavenumber be kw=100 to avoid the modal singularities.
b. Determine the wavenumber interval for which your code produces a result which is qualitatively consistent with
c. Describe the nature of the numerical problem, and rewrite into a form which remedies the problem. Implement it and compare your result to (qualitatively).