= Normal-mode response to a step seismic moment
{title2=$a_\alpha=C_\alpha[1-\cos(\omega_\alpha\tau)]H(\tau)/\omega_\alpha^2$}
For mass-normalized <normal modes>, an instantaneous step in a point <seismic moment tensor> excites mode $\alpha$ with $C_\alpha=\mathbf M:\mathbf e_\alpha^*(\mathbf x_s)$ and $\tau=t-t_s$. Convolving the causal oscillator <Green's function> with the step gives $a_\alpha=C_\alpha[1-\cos(\omega_\alpha\tau)]H(\tau)/\omega_\alpha^2$. The expression contains a static response and undamped oscillations; attenuation requires an extension of the conservative model.
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