= Solution
Complete the crack normal to an orthonormal basis $(\mathbf e_1,\mathbf e_2,\mathbf n)$ with the first two vectors in the crack plane. The <seismic moment tensor> is diagonal in this basis:
$$
\boxed{M=V\left[\lambda\mathbf e_1\mathbf e_1^{\mathsf T}
+\lambda\mathbf e_2\mathbf e_2^{\mathsf T}
+(\lambda+2\mu)\mathbf n\mathbf n^{\mathsf T}\right]}.
$$
Each term gives an <elastic force dipole>, $f_i=-D e_i e_j\partial_j\delta$: two equal and opposite forces in direction $\mathbf e$, separated along $\mathbf e$, with moment $D$. Hence there are two identical in-plane dipoles of strength $\lambda V$ and one normal dipole of strength $(\lambda+2\mu)V$. For positive opening and ordinary positive <Lamé parameters>, all are extensional and the normal one is larger by $2\mu V$.
More generally, stable isotropic <linear elasticity> requires $\mu>0$ and $3\lambda+2\mu>0$. These imply $\lambda+2\mu>|\lambda|$, so the normal dipole has greater magnitude even if an auxetic material has negative $\lambda$ and compressive in-plane dipoles. The point source has zero net force, because it differentiates a delta function, and zero net torque, because its moment tensor is symmetric. Its normal moment distinguishes opening from a pure shear dislocation.
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