 Shear-horizontal wave

A shear-horizontal wave propagating in the $x$ direction has displacement perpendicular to the sagittal $xy$ plane, for example $\mathbf{u}=w(x,y,t){\mathbf{e}}_z$. It is divergence-free and obeys the scalar shear-wave equation $w_{tt}=c_S^2(w_{xx}+w_{yy})$.