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.