Dynamic response of an elastic and viscoelastic full‐space to a spherical source

Abstract The dynamic response due to a spherical source of radius a embedded in an elastic and viscoelastic full‐space is investigated at a distance R from the source. Previous solutions to the elastic case are extended to incorporate realistic source pressure functions. The elastic solution is then cast in a scale independent form in order to generalize the application. The results show that the near‐field of the spherical source may be defined by R/a < 5. For this region the particle velocity and displacement decrease as R −2 , and the risetime decreases as R −1 . However. in the far‐field region ( R/a > 5) the particle velocity and displacement decrease as R −1 , and the risetime is independent of R . A non‐constant Q model is developed to model viscoelastic attenuation and a complete analytical solution for wave propagation is obtained by cascading the separate mechanisms of geometric attenuation and viscoelastic attenuation. A comparison of our analytical model with the results of dynamic finite element modelling shows excellent agreement. This suggests that the method of cascading the separate transfer functions is a valid approach for wave propagation in viscoelastic media.

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