A ray travels toward a horizontal welded interface

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

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

Problem

A ray travels toward a horizontal welded interface. Set up axes with

x

horizontal in the vertical plane containing the ray (the plane of incidence),

y

horizontal and perpendicular to that plane (along the strike of the interface), and

z

vertically downward. The ray makes an angle

i = 35^\circ

with the

z

axis (the normal to the interface), so its propagation direction is the unit vector

\hat{\mathbf{k}} = (\sin i,\ 0,\ \cos i).

((a)) Give the unit polarisation vector of the P wave travelling along this ray. ((b)) Give the unit polarisation vector of the SH wave travelling along this ray, and state in one sentence why this component alone cannot generate P or SV motion at the interface. ((c)) Give a unit polarisation vector of the SV wave travelling along this ray (choose the one with a positive

x

component).

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