I.3 Absorbing Boundary Conditions

Interior Pivots of FD Stencil ok Boundary Pivots of FD Stencil force stencil at t to be outside ?? 20-50 pt wide damping zone @ boundaries. Set d=0 @ edge. ? ? ? ? ? ? ? ? I.3 Absorbing Boundary Conditions

20:nx-20 20:ny-20 Damp d by exp(-ar) within damping zone (1 at interior of damp zone and .92 at outermost point. t ij Fortran Code with ABC’s FD Approx. to 2-D Acoustic Wave Equation fort=1:nt for i=1:nx for j=1:ny t t t t t t t+1 t-1 t p p p p p - 2 p - 2 + p 2 p + 2 p c t - 2 = i+1j ij-1 + ij ij+1 ij + ij i-1j ij ij y 2 2 x end end end t + F

c < dx dt What past values influenced this pt? 2dt dt 0 Time 2-2 FD 1-D Stability Condition Actual Speed Choose dt s.t. Slowest Numerical Speed Space

2dt dt 0 Time 2-2 FD 1-D Stability Condition Actual Speed c < dx Choose dt s.t. dt Slowest Numerical Speed V=2dx/2dt=dx/dt Space

2 Slowest Numerical Speed 2-2 FD Stability Condition Actual Speed c < dx Choose dt s.t. dt 2

2-2 FD Stability Condition

V = 2 dx/2dt 2-2 FD Stability Condition 0 dt 2dt V = 2dx/2dt=dx/dt

2 Slowest Numerical Speed 2-2 FD Stability Condition Actual Speed c < dx Choose dt s.t. dt 2

2-2 FD Dispersion Condition dx < 0.1  Choose dx s.t. Avoid coarsely sampling wavefield to avoid spatial aliasing

I.3 Absorbing Boundary Conditions