1. A computer-implemented wave field simulation method that comprises: (a) applying at least one signal to a grid comprising a plurality of model cells, the grid forming a model space, each model cell having a plurality of stress values associated with a plurality of stress nodes and a plurality of velocity values associated with a plurality of velocity nodes staggered from the stress nodes; (b) propagating the at least one signal as a wave into the model space by alternately updating the stress values and the velocity values to obtain a time-dependent wave field associated with the signal; wherein said updating stress values includes, for each model cell: determining spatial derivatives of the velocity values for the model cell; interpolating the spatial derivatives to multiple stress nodes within the model cell; and for each stress node within the model cell, combining the spatial derivatives associated with that stress node to update at least one stress value associated with that stress node, wherein at least one of (a) through (b) is performed on a computer.