Tensile-crack seismic source (source code)

= Tensile-crack seismic source
{title2=$M_{ij}=V(t)(\lambda\delta_{ij}+2\mu n_in_j)$}

A small planar crack of area $S$ opening normally by $d(t)$ has volume change $V=Sd$ and the displayed <seismic moment tensor>. Its principal dipoles are $\lambda V,\lambda V,(\lambda+2\mu)V$: two act in the crack plane and the largest acts normally for positive opening and ordinary positive Lamé parameters. The definition follows by contracting the isotropic <elastic stiffness tensor> with two copies of the crack normal.