A note on causality problems in the numerical solution of elastic wave propagation in cylindrical coordinate systems

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Abstract
Harkrider noted the presence of noncausal, nonpropagating near-field terms in the cylindrical shear wave potentials for dislocation sources. He stated that these noncausal terms drop out when the total displacement field is calculated using both SV and SH shear wave potentials. When calculating realistic far-field radial and tangential displacement time histories, one must be careful in how the higher order distance terms are truncated in order to avoid the presence of noncausal terms in the time histories. Examples of this effect for tangential displacements due to a 90° dip-slip dislocation source as well as a 90° vertical strike-slip source are given to demonstrate the numerical problem.