This is to be done in Matlab

You will develop a 2D finite difference model to simulate the propagation of an acoustic wave. The model is to contain two layers that are separated by a reflecting / transmitting interface. The model specifications are given below.

This is what I have so far

%% Initiate Model % Initiate spatial dimension x: number of grid points, step size % Initiate time t: number of time steps, step size % Model parameters: wave velocity, calculate courant number % Initiate displacement matrix: U(x, t) = zeros

xmin = 0; x_max = 101; xn = 500; x = linspace(0,x_max,xn) t_steps = 1000; t_step_size = 0.001; V = 500 C = (t_step_size/x_step_size)* V; U(x,t) = zeros(x_max,t_steps);

%Initial Condition / Source Parameters % Set source frequency % Generate sinusoid for one period / cycle at x=0; y = sin(2*pi*t/T - 2*pi*x/lambda)

%FD Solution (explicit: forward marching in time recommended) % loop over time % loop over space % calculate displacements U for C

%Visualisation of Results % Plot(x, U(x, t) ) for certain t -> snapshots % Use getframe and movie -> movie of wave propagation

1.) Test Cases Build suite of test cases that will be used to benchmark your code. These are to be based on analytical 'textbook' solutions. You should develop at least two test cases and one should test the behaviour of the wave-field at the internal interface. Show that the test cases are appropriate for a 2D model of acoustic wave propagation. 2.) Pseudo Code The pseudo code should contain all major elements of your code. Loops or other iterations over matrix elements should be detailed. 3.) Finite Difference Model Minimum Model Size 100 100 Time> 1000 steps Wavelet Source at one grid point (i.e. no entire boundary) Acoustic wave equation to be solved with time-marching five-point centred grid scheme. (More sophisticated schemes like nine-point centred grid or staggered-grid are permitted) One internal interface allowing reflection and transmission Absorbing boundaries (this will be considered an advanced feature) * .) Visualisation Synthetic seismogram with shot gather receiver/source configuration Snapshots of the wave-field at pertinent time steps * * 1.) Test Cases Build suite of test cases that will be used to benchmark your code. These are to be based on analytical 'textbook' solutions. You should develop at least two test cases and one should test the behaviour of the wave-field at the internal interface. Show that the test cases are appropriate for a 2D model of acoustic wave propagation. 2.) Pseudo Code The pseudo code should contain all major elements of your code. Loops or other iterations over matrix elements should be detailed. 3.) Finite Difference Model Minimum Model Size 100 100 Time> 1000 steps Wavelet Source at one grid point (i.e. no entire boundary) Acoustic wave equation to be solved with time-marching five-point centred grid scheme. (More sophisticated schemes like nine-point centred grid or staggered-grid are permitted) One internal interface allowing reflection and transmission Absorbing boundaries (this will be considered an advanced feature) * .) Visualisation Synthetic seismogram with shot gather receiver/source configuration Snapshots of the wave-field at pertinent time steps * *