An SH wave travels upward through mantle rock ( , ) and meets a welded

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Stress, strain and elastic waves in the Earth

Problem

An SH wave travels upward through mantle rock (ρ1=3300 kg m−3\rho_1 = 3300\,\mathrm{kg\,m^{-3}}, vS1=4500 m s−1v_{S1} = 4500\,\mathrm{m\,s^{-1}}) and meets a welded, horizontal interface with crustal rock (ρ2=2700 kg m−3\rho_2 = 2700\,\mathrm{kg\,m^{-3}}, vS2=3300 m s−1v_{S2} = 3300\,\mathrm{m\,s^{-1}}) above it, at an angle of incidence i1=20∘i_1 = 20^\circ from the normal. ((a)) Find the transmission angle i2i_2 in the crust using Snell's law for horizontal slowness. ((b)) Find the displacement reflection coefficient R=(Z1−Z2)/(Z1+Z2)R = (Z_1-Z_2)/(Z_1+Z_2) and transmission coefficient T=2Z1/(Z1+Z2)T = 2Z_1/(Z_1+Z_2), with Zj=ρjvSjcos⁡ijZ_j = \rho_j v_{Sj}\cos i_j.

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