SH line-source near-field singularity ($u\sim -F(t)\log r/(2\pi \mu )$)

Integrating the shear-horizontal wave equation with force $F(t){\delta }^{(2)}(\mathbf{x})$ over a shrinking circle gives $2\pi \mu r{\partial }_{r}u\to -F(t)$. Thus the local displacement field has the displayed logarithmic singularity. This is a fixed-time near-source limit, distinct from the wavefront limit underlying SH ray-tube amplitude transport.