Description of the problem given by Jean-David Benamou. We give here the solution found using our Lattice Boltzmann model for wave propagation. The method was originally developped for wave propagation prediction in urban environment and is described in a submitted paper (to IEE). A short presentation of our method can be found here but if you want more details please feel free to see our preprint.

The purpose is to calculate the propagation of a pulse (located in the underground) in a 2D inhomogeneous medium and to record the time of reception at the surface. Our solution takes about 3 minutes CPU time (not very optimized and included the generation of the resulting image) on a SunSparc 10 and was very easy to implement: about 100 lines F90 code!

The medium looks like following; the cross indicates the source and the surface is the upper horizontal border of the domain. The data file gives for every points the local speed of sound.

Our seismograms of this problem is (left with hard velocity and right with smooth velocity field) shown below. The vertical axis is the time, expressed in iteration, a better understanding of the media parameter is necessary in order to determined the real time in seconds.

For comparison, see the seismogram given by the simulation of the wave equation from Francis.Collino@inria.fr.

If you are intereseted in further comparing our method other methods, or if you are interested in the row data of my seismogram, or for any other information, please don't hesitate to contact me.