Mode conversion

Mode conversion is the transformation of a wave at an interface into other wave types (modes).

[1][2] Mode conversion occurs when a wave encounters an interface between materials of different impedances and the incident angle is not normal to the interface.

[1] Thus, for example, if a longitudinal wave from a fluid (e.g., water or air) strikes a solid (e.g., steel plate), it is usually refracted and reflected as a function of the angle of incidence, but if some of the energy causes particle movement in the transverse direction, a second transverse wave is generated, which can also be refracted and reflected.

Snellius' law of refraction can be formulated as:[1]

For example, if one radiates a longitudinal wave at a shallower angle than that of total reflection onto a boundary surface, it will be totally reflected, but in addition a surface wave traveling along the boundary layer will be generated.

In general, mode conversions are not discrete processes, i.e. a part of the incident energy is converted into different types of waves.

The amplitudes (transmission factor, reflection factor) of the converted waves depend on the angle of incidence.

[3] In seismology, a wave conversion specifically refers to the conversion between P and S waves at discontinuities.

[4] Body waves are reflected and refracted when they hit a boundary layer within the earth.

Here, P-waves can be converted into S-waves (PS-wave) at interfaces, as well as vice versa (SP-wave).

[5] Here applies analogously for an incident P-wave:

The change in amplitudes can be described with the zoeppritz equations.

An incident longitudinal wave (L1) is reflected and transmitted at an interface of two solids as a longitudinal wave (L1' and L2), but also partially as a transverse wave (S1 and S2).
An (longitudinal) P-wave is partially reflected and transmitted (PSt and PPt) as a (transverse) S-wave (PSr) and (longitudinal) P-wave (PPr). The nomenclature is as follows: First letter stands for the wave type of the causal wave (primary wave) and the second letter for the type of secondary waves generated after mode conversion.