Reflexion/ Transmission of a plane wave on a plane interface

On a plane interface between two elastic half-space, P and SV waves propagating in the (x, z) pare related by Snell’s law and
the law of continuity of displacement components x u and z u and constraints zz σ and zx σ on both sides of the interface. An
incident wave P or wave SV generates two P or SV reflected waves and two transmitted waves P or SV. The four continuity
equations are written in the form of a matrix multiplied by a vector transmission-reflection coefficient, defined for potential
movement of the particles. For an planar boundary between fluids with different characteristic impedances, there is continuity of
z u and zz σ on both sides of the interface and the shear zx σ in the medium must vanish at the interface (fluid media involving
only perfect no viscosity, so that was normal stresses, not shear stress 0 xz σ = ). As soon as the angle of incidence exceeds a
critical value of incidence, the wave for which the value of incidence is greater than 30°
becomes evanescent. The reflectiontransmission
coefficients become complex.

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