In this page is showned a numerical simulation of the diffraction of a cylindrical wave in a 2D-media. In an homogeneous domain, a layer with varying height perturbs the spreading of a cylindrical wave and creates diffracted waves.

The computation is made on a regular grid with 1500 points in each direction. An explicit numerical scheme provides the wave at time ndt on each point of the grid from its values at time (n-1) dt and (n-2)dt. The wave is created by mean of a second term added to the point of the grid corresponding to the location of the source. 3000 time steps have been performed. On the boundary, wide angle absorbing boundary conditions allow us to make the waves go outside the computationnal domain with very few spurious reflections.

velocity model	t=300dt

t = 600 dt	t= 900 dt	t= 1200 dt

t =1500 dt	t= 1800 dt	t= 2100 dt

Ref: F.Collino, high order absorbing boundary conditions for wave propagation models: straight line boundary and corner cases, in Second international conference on mathematical and numerical aspects of wave propagation, Ed E.Kleinmann et al., SIAM, 1993

In the following experiments, a ponctual source is generated at the vicinity of the surface of an elastic homogeneous media. In the first experiment, we impose the displacements to vanish at the surface while in the second one the normal stresses are null. One can see in both cases two cylindrical waves propagating with two different velocities (Pressure wave and Shear wave). However, only in the second case, one observes most of the energy propagating along the surface with a velocity roughly equal to the velocity's shear waves; this wave is the Rayleigh wave and belongs to the family of the guided wave.

Null surface displacements:

t1	t2
t3	t4

Free surface stresses:

t1	t2
t3	t4