Surface Rayleigh waves generation

[Nikkey098]

Good day,

I do not fully understand the physical mechanism of formation of Rayleigh waves at the free surface. While their derivation is quite clear and obey free-boundary conditions, it is not clear their physical mechanism.

Could you please correct me in my discussion. Incident P-wave can transform to reflected P and SV waves. When the angle of incidence of P wave reaches 2nd critical angle, both outgoing P and SV waves propagate along the surface forming Rayleigh wave. So, P-wave by itself can form Rayleigh wave. At the same time, incident SV wave can transform to reflected P and SV waves. When the angle of incidence of SV wave (again) reaches second critical angle - both outgoing P and SV waves propagate along the surface forming Rayleigh wave.

Can then Rayleigh wave be formed by interference of both incident P and SV waves on the free surface or Rayleigh waves are formed only separately by incident P or SV waves? Does it mean that right under the epicenter Rayleigh waves cannot form but at some distance from it in order to reach second critical angles?

Thank you

 

[davenn]

Could you please correct me in my discussion. Incident P-wave can transform to reflected P and SV waves.

Yes

When the angle of incidence of P wave reaches 2nd critical angle, both outgoing P and SV waves propagate along the surface forming Rayleigh wave.

No, The P and S and or Sv waves travel back down into the Earth in a curved path to again curve back up towards the surface at some more distant point.

So, P-wave by itself can form Rayleigh wave.

Not of any consequence

At the same time, incident SV wave can transform to reflected P and SV waves. When the angle of incidence of SV wave (again) reaches second critical angle - both outgoing P and SV waves propagate along the surface forming Rayleigh wave.

again, as above, no, P and S waves don't propagate along the surface to any extent

Can then Rayleigh wave be formed by interference of both incident P and SV waves on the free surface or Rayleigh waves are formed only separately by incident P or SV waves?

again, as above, the generation of surface waves by that interaction

Rayleigh are create right at the epicentre of the quake ( with is at the surface directly above the focus)
as a result of interaction of the P and S waves radiating out from the quake focus.

Any interaction of P, S and or Sv waves at any distance from the epicentre, the amplitude of Rayleigh
is going to be very minimal compared to those generated at the epicentre. This is because the amplitude
of P and S (Sv) waves are going to be highly attenuated with distanceDave

 

[Nikkey098]

Thank you for the answer,

I think I misinterpreted and do not fully understand 2 different phenomena:

1. Surface wave generated by incident P wave falling at second critical angle. As stated https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/modepropagation.htm, for example:
"Surface waves are generated when a longitudinal wave intersects a surface near the second critical angle and they travel at a velocity between .87 and .95 of a shear wave." Is that what happens when P wave or SV wave fall at second critical angle? That is what probably confused me, because mentioned velocity is generally belong to Rayleigh wave speed.

2. Second phenomena is a constructive interference of body waves at the free surface what can lead to the generation of Rayleigh wave.

Rayleigh are create right at the epicentre of the quake ( with is at the surface directly above the focus)
as a result of interaction of the P and S waves radiating out from the quake focus.

Could you please explain what kind of interaction is meant here? What are the physical conditions for interaction of body waves at the surface to generate Rayleigh wave (in comparison with surface wave phenomenon #1 above)?

Thank you in advance!