A particle view of dispersive wave propagation

Kristopher A. Innanen

We have shown elsewhere that simple seismic wave phenomena may be modeled with sets of (notional) particles which drift freely and collide. To extend this (scalar) modeling idea to incorporate attenuation, we merely replace each single particle with a large number of particles, each moving with a velocity drawn from a suitable distribution. Numerical examples demonstrate the qualitative correctness of this model; quantitatively it is supported by arguments due to Samuel Bickel, who points out that the constant Q impulse response is equivalent to one of the one-side probability density functions we choose from which to draw particle velocities.