Dispersion analysis and computational efficiency of elastic lattice methods for seismic wave propagation

Discrete particle methods or elastic lattice methods represent a 3D elastic solid by a series of interconnected springs arranged on a regular lattice. Generally, these methods only consider nearest neighbour interactions, i.e. they are first-order in space. These interconnected springs interacted through a force term (Hooke's Law for an elastic body), which when viewed on a macroscopic scale provide a numerical solution for the elastodynamic wave equations. Along with solving the elastodynamic wave equations these schemes are capable of simulating elastic static deformation. However, as these methods rely on nearest neighbour interactions they suffer from more pronounced numerical dispersion than traditional continuum methods. By including a new force term, the numerical dispersion can be reduced while keeping the flexibility of the nearest neighbour interaction rule. We present results of simulations where the additional force term reduces the numerical dispersion and increases the accuracy of the elastic lattice method solution. The computational efficiency and parallel scaling of this method on multiple processors is compared with a finite-difference solution to assess the computational cost of using this approach for simulating seismic wave propagation. We also show the applicability of this method to modelling seismic propagation in a complex Earth model.