The elastodynamic near field

Summary. The elastodynamic fields of point forces and shear dislocations of finite source duration are analysed with the aim of establishing the frequency and time‐domain characteristics of the field in the near‐source region. Criteria are obtained for amplitude dominance in regions where the source–sensor distance is much smaller than the wavelength. It is shown that in the frequency domain , the Green's tensor (and hence the displacement field of a single point force) attenuates like R −1 in the near‐source region and there exists no region in which the ‘near‐field’ term becomes dominant such that the ‘far‐field’ term can be neglected. Hence, there is no real ‘near‐field’ term for the elastodynamic Green's tensor. The near‐field terms of the displacements, velocities and accelerations excited by a shear dislocation attenuate like R −2 , since the R −3 and R −4 terms tend to be eliminated due to mutual cancellation of P and S motions in the near‐source region. In the time domain , the corresponding near field of the displacement field is defined for the steady amplitude interval (away from transients) R /β < t < R /α+ T by the condition R ≤βT where β is the shear velocity and T is the source's duration. The relative strengths of all other arrivals will depend on the particular time window under consideration. The particle motion patterns due to a single force in the near‐source region are shown to be similar to rotating hyperbolas with an axis along the force direction, which are quite different from the ‘smoke ring’ motion patterns of the so‐called ‘near‐field’ term itself.