acoustic wave propagation underwater in matlab

main.m
% Define simulation parameters
dx = 1; % grid spacing in meters
dz = 1; % depth spacing in meters
dt = 1e-4; % time step in seconds
f = 1000; % frequency in Hz
c0 = 1500; % sound speed in m/s
rho = 1000; % water density

% Create 2D grid
x = 0:dx:1000;
z = 0:dz:1000;
[X, Z] = meshgrid(x, z);

% Define source frequency and location
source_freq = 1000; % Hz
source_location = [500, 500]; % meters

% Calculate sound speed profile in water
S = ones(size(X))*c0; % constant sound speed
for k=1:10
    zc = (k-0.5)*100;
    S = S + 100*sin(2*pi*source_freq/c0*(Z-zc));
end

% Define initial pressure field
P = zeros(size(X)); % zero initial pressure
P_prev = P; % previous pressure field

% Main loop for time stepping
for t=1:10000
    % Compute spatial derivatives of pressure field
    dPdx = (P - circshift(P, [0, -1])) / dx;
    dPdz = (P - circshift(P, [-1, 0])) / dz;
    
    % Compute temporal derivative of pressure field
    dPdt = (P - P_prev) / dt;
    
    % Apply the parabolic wave equation
    P_next = 2*P - P_prev + (c0^2/rho)*(dt^2)*(dPdx.^2 + dPdz.^2) - (c0^2/rho)*dt^2*dPdt;
    
    % Apply the source
    P_next(source_location(1), source_location(2)) = P_next(source_location(1), source_location(2)) + sin(2*pi*f*t*dt);
    
    % Update the pressure field
    P_prev = P;
    P = P_next;
end

% Plot the final pressure field
imagesc(x, z, P');
colorbar;
title('Acoustic Pressure Field');
xlabel('Horizontal Distance (m)');
ylabel('Depth (m)');
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