Particle swarms for numerical wave equation

Michael P. Lamoureux, Heather K. Hardeman-Vooys

Motivated by the possibility of computation speed-ups using massive parallelization on fast graphical processing units, we investigate the use of particle swarms to produce a numerical simulation of seismic wave motion in heterogeneous media in 2D and 3D.

It is well known that Brownian motion of particles bouncing about at random forms a useful model for diffusion of heat. In the limit as particle numbers go to infinity, the Brownian motion leads to the diffusion equation: a second order, linear, parabolic partial differential equation. A similar model with correlated, but still random, particle motion leads to the acoustic wave equation in dimensions one, two and three.

Focusing on the Green’s function for individual source and receiver pairs in a seismic experiment, we aim to compute the numerical simulation of wave motion using large numbers of independently acting particles to recover the source/receiver response without modelling the entire seismic waveform in the experiment. We present the mathematics behind the theory of the particle simulation as well as a few numerical studies.