Linked from
The 12 pages that link to Shear modulus, each with the reason it gives.
P wavesRelated: Together with compressibility and density, it governs P-wave speed in solids.
S-waveRelated: It determines whether a material can support S-waves and helps set their speed.
Seismic momentRelated: Rock rigidity enters the seismic-moment calculation as the shear modulus.
Seismic velocityRelated: It and density set shear-wave speed in an isotropic solid.
Love waveRelated: It helps determine the speed of the horizontally polarized motion in each layer.