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Friday Questions

Questions on numerical methods applied to wave propagation

  • What is the key motivation to use Chebyshev polynomials instead of Fourier series for wave simulations?
  • What are the properties of basis functions used in pseudospectral methods (PSM)?
  • Discuss the two derivative methods (fft, matrix) used in PSM, advantages, disadvantages?
  • What are the differences on dispersion for FD and PS operator (qualitatively) as a function of wave number k?
  • What is the expression of the derivative (1st,2nd, etc) operator in the k-domain?
  • What role has the convolution theorem in this context?
  • Write the 1D velocity-stress formulation, why is it used so often in comparison with the displacement-stress formulation?
  • What types of boundary conditions can occur in computational seismology?
  • Why do we use grid stretching in Chebyshev methods?
  • What are the advantages and disadvantages of FD and PS methods?
  • What types of grids are used in FD methods? Is there a difference between irregular and unstructured grids?
  • What is the difference between explicit and implicit schemes, advantages, disadvantages?
  • What criterion usually determines the time step in wave calculations, what are the dependencies?
  • What is grid dispersion, what is grid anisotropy?
  • In a FD grid, in which propagation direction is the solution most accurate and why?
  • Why do staggered grids pose problems when treating material anisotropy?
  • Do we use the wave equation in spherical coordinates for whole planet problems?
  • Name approaches to simulate the traction-free condition (free surface)!
  • How can attenuation be incorporated in time-domain modelling?
  • What does PML stand for and what are the basic underlying principles?
  • Why is there a problem with waveforms in 2D wave calculations?
  • What is the meaning of assembly in SEM?
  • How can improve the accuracy of FD calculations in strongly heterogeneous media?
  • What are the main differences and physical implications between FD/PSM and F/SEM?
  • What are the differences in source implementations (forces, moments)?