A simplification in the calculation of motions near a propagating dislocation

From Haskell's (1969) integral representations for the near-field displacements due to a propagating strike-slip and dip-slip dislocation, a solution is obtained for a dislocation “line source” by an analytic integration in the direction of the fault propagation. This reduces the numerical integration from a surface integral required for the usual evaluation of the near-field motion, to a one-dimensional integration over the fault width. Since the dislocation function modeled here is a Heaviside step function, these results may be extended to any arbitrary source time-function by convolving these displacements with the time derivative of the desired source function.