Point-moment elastodynamic displacement ($u_i=M_{kj}\ast {\partial }_{y_j}{G}_{ik}$)

Integrating the equivalent dipole body force against the elastodynamic Green tensor by parts gives the displayed time convolution. For a fixed seismic moment tensor shape $M_{kj}=K_{kj}V(t)$, its $R^{-1}$ terms are $[\mathbf{e}(\mathbf{e}\cdot K\mathbf{e})\dot{V}(t-R/\alpha )/{\alpha }^3+(K\mathbf{e}-\mathbf{e}(\mathbf{e}\cdot K\mathbf{e}))\dot{V}(t-R/\beta )/{\beta }^3]/(4\pi \rho R)$. Derivatives of the angular projectors and the retarded near-field integral additionally produce $R^{-2}$ and $R^{-4}$ coefficients, yielding the final static field after the source stops.