Reflectance Function for Layered Media

Referring to Fig. 10a, the relations among a particle velocity, a particle displacement, and a stress are as follows  

The potential of a longitudinal wave in water is expressed as follows  

The potentials of longitudinal and shear waves in the thin film are expressed as follows  

The boundary conditions are (1) whenz = 0, Z-axis components of the particle velocities are equal, (2) Z-axis components of stresses applied to the Z plane ate equal, and (3) X-axis components of stresses applied to the Z plane are equal, and their values are zero. Then we have the following equations  

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