# Unwanted Oscillation in FDM simulation of elastic wave equation

I am using staggered grid FDTD for solving elastic wave equation. A description of which can be found at (geodynamics.usc.edu/~becker/teaching/557/reading/Virieux1987.pdf). I have generated a synthetic seismogram (description below) using it.

Synthetic seismogram : To generate a synthetic seismogram, a source is placed at top and an array of receiver is laid along the surface. A synthetic seismogram can be visualize as in this youtube animation (www.youtube.com/watch?v=_Gjr5EWNIQk)

My Problem is the spurious oscillations generated in FDTD simulation for elastic wave. I have taken care of grid dispersion which requires 10 grid points per wavelength (minimum). still I feel there is a lot of dispersion in it. The model I have taken is a homogeneous elastic model with absorbing (damp) type boundary conditions along all the edges.

Vp = 2000 m/s; Vs = 1500 m/s;

Grid spacing: dx = dv = 5m;

time sampling: dt = 1msec

Source: Ricker (20Hz).

Following is the response of at one receiver (k/a trace) and a snap of wave

EDIT 1

Presently I don't have privileged to add more than two link so I edited and joined two pics of traces for soft and hard types of sources.

The corrected trace after applying pressure source (soft type) is shown now. But still there are wriggles trailing the wave

• Add some internal damping. Apr 15 '16 at 19:41
• @stali could you please elaborate or give any reference for it. Apr 15 '16 at 19:44
• Search for descriptions of von Neumann-Richtmyer artificial viscosity. Apr 16 '16 at 21:21
• Thanks to paul for deleting the reply I added by mistake. @Biswajit I checked for literature but nobody has mentioned this in case of synthetics seismogram generation. BTW, I checked my code and one problem i found is the application of hard source (i.e. sigma(i,j)= src(t)). It was forcing the node to stress and thus causing some spurious oscillations.Now I have added soft pressure source which is additive in nature i.e. sigma(i,j)= sigma(i,j) +src(t). Still some oscillations are remaining. Apr 17 '16 at 21:27
• I know you said that the you made sure to use enough grid points per wavelength, but do the oscillations seem to be grid-related at all? Apr 18 '16 at 1:04