Homework 1

Programming part (extra credit)

For extra credit, you can modify the wave modeling program to include anisotropic wave propagation effects. The program below (slightly modified from the original version by Paul Sava) implements wave modeling with equation

$$S^2(\mathbf{x})\,\frac{\partial^2 P}{\partial t^2} = \nabla^2 P + F(\mathbf{x},t)\;,$$ (15)

where $F(\mathbf{x},t)$ is the source term. The implementation uses finite-difference discretization (second-order in time and fourth-order in space). Stepping in time involves the following computations:

$$\mathbf{P}_{t+\Delta t} = \left[ \nabla^2 \mathbf{P}_t - F(\... ...}) \Delta t^2 + 2 \mathbf{P}_{t} - \mathbf{P}_{t-\Delta t} \;,$$ (16)

where $\mathbf{P}$ represents the propagating wavefield discretized at different time steps.

Your task is to modify the code to implement your anisotropic equation (14). You will test your implementation using a constant velocity example shown in Figure 2.

wave
Figure 2. Wavefield snapshot for propagation from a point-source in a homogeneous medium. Modify the code to make wave propagation anisotropic.

1. Change directory to geo384w/hw1/code
2. Run

   scons wave.vpl
   

   to compile and run the program and to observe a propagating wave on your screen.
3. Open the file afdmc.c in your favorite editor and modify it to implement the wave operator from equation (14).
4. Run

   scons wave.vpl
   

   again to compile and test your program. If you want to add additional tests, modify the file SConstruct.
5. When you are satisfied with your results, run

   scons lock
   

   to lock the figures.

Homework 1