Assume you have to make a simple wavenumber integration code for propagation in Pekeris waveguides.
a. Make a subroutine which computes the wavenumber kernel, or depth-dependent Green’s function, along a contour below the positive real wavenumber axis. Make sure your code is numerically stable for large wavenumbers,
b. Check your code by qualitatively reproducing the kernels You decide to use FFP integration with a contour offset equal to the wavenumber sampling interval
c. What is the associated minimum attenuation of the wrap-around?
d. Using this offset, perform a numerical convergence analysis for the integration by computing the transmission loss at 46 m depth and 10 km range for the Pekeris waveguide in assuming an attenuation of 0.5 dB/in the bottom. Note: You don’t have to use FFT integration for this, use simple trapezoidal rule integration. e. Repeat the convergence analysis without contour offset and discuss the difference in convergence rate.