Syllabus
1. Approximation of derivatives by difference operators
2. Partial differential equations and their approximation by difference equations (in particular elastodynamic equation)
3. Numerical dispersion, stability and the order of accuracy of a stencil, computational demands
4. Explicit and implicit stencils, heterogeneous stencils, approximation of material discontinuities and free-surface condition
5. Finite-difference method on regular and irregular grids
6. Acoustic and elastodynamic equations formulated in displacements on standard grids; stress-velocity formulation on staggered grids
7. Optimum operators and increasing stencil accuracy
8. Realizing the source and attenuation using a volume force
9. Artificial boundary conditions on the edges of the computational domain: non-reflecting boundaries, tapers and symmetry conditions
10. Hybrid formulation used for injecting physical field into computational domain
Annotation
A practical guide to the finite-difference modelling in geophysics with a view to wave propagation in complex 3D media.