The decaying factor is given by the expression
where represents the total number of boundary reflections,
and is the reflection coefficient at the th reflection.
The case with no reflections () corresponds to .
Generally speaking, boundaries can be one of four types:
The calculation of the reflection coefficient for an elastic medium (see Fig.4.1)
is given by the following expression:
- Absorvent: the wave energy is transmitted completely to the medium above the boundary,
so = 0 and ray propagation is terminated at the boundary.
- Rigid: the wave energy is reflected completely on the boundary,
with no phase change, so = 1.
- Vacuum: the wave energy is reflected completely on the boundary,
with a phase change of radians, so = -1.
- Elastic: the wave energy is partially reflected, with being a complex value and
where the units of attenuation should be given in dB/.
Ray reflection on an elastic media.
In general the reflection coefficient is real when
and the angle of incidence is less than the critical angle ,
with given by the expression
attenuation is negligible when
and for small the energy transfered to shear waves in the elastic medium is only a small fraction
of the total energy transfered.
Orlando Camargo Rodríguez