From modeling to full waveform inversion: A hands-on tour using Madagascar

Your exercise

• It works so slow! How to speeed up? $\rightarrow$ CUDA (Yang et al., 2015, Mgpufwi.cu) + MPI high performance computing (Jeff)?

• How to improve the poor resulting velocity model in Figure 6? A better initial model by less smoothing? Increase the number of iterations? Estimate a good step length to satisfy the Wolf condition? Estimate Hessian $\rightarrow$ Truncated newton (Métivier et al., 2014)+ Source encoding+ Good preconditioning?

• Derive the adjoint equation for first order wave equation system

  $$\begin{cases}\partial_t p=\kappa \nabla\cdot \mathbf{v}+ f_p \\ \rho \partial_t \mathbf{v}= \nabla p \end{cases}$$ (10)

  
  
  where $\kappa=\rho v^2$ .
• Write a forward simulation code based on sponge boundary condition using the above system

• Derive your gradient expressions for velocity and density

• code your multiparameter FWI for inverting $v$ and $\rho$