% A random smooth medium: many weak scatterers rather than one strong one.
%
% The speed field is a sum of 60 plane waves with random directions, random
% wavenumbers around kc (radians per metre), and random phases — a
% band-limited Gaussian random field, built here with an ordinary MATLAB loop
% because a scene is evaluated once on the CPU and has the whole language
% available, not the element-wise subset a compiled step is held to.
%
% A pulse crossing this does not scatter once and leave: it scatters weakly
% and repeatedly, and what comes out the far side is a spread-out coda rather
% than a clean wavefront. Turn `amp` down and the medium becomes transparent;
% turn it up and the direct arrival disappears into the noise.
%
% The field is windowed to the interior so the absorbing layer stays uniform.
% Structure inside the sponge would scatter sound back into the domain from
% the very place that is supposed to be swallowing it.
function [c, sig] = medium(x, y, L, npts, c0, amp, kc, seed)
  nm = 60;
  rng(seed);
  g = zeros(npts, 1);
  for k = 1:nm
    th = 2*pi*rand();
    kk = kc * (0.5 + rand());
    ph = 2*pi*rand();
    g = g + cos(kk * (cos(th)*x + sin(th)*y) + ph);
  end
  g = g / sqrt(nm);

  r = sqrt(x.^2 + y.^2);
  window = 0.5 * (1 - tanh((r - 0.28*L) / (0.03*L)));

  c = c0 * (1 + amp * (g .* window));
  sig = sponge(x, y, L, 0.2*L, 1700);
end