 Tensile-crack seismic source

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.