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)?