Surface Rayleigh waves generation

In summary, P-wave by itself can form Rayleigh waves. 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. This happens when the angle of incidence of SV wave is greater than 2 degrees.
  • #1
Nikkey098
2
0
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
 
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  • #2
Nikkey098 said:
Could you please correct me in my discussion. Incident P-wave can transform to reflected P and SV waves.

Yes

Nikkey098 said:
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.

Nikkey098 said:
So, P-wave by itself can form Rayleigh wave.

Not of any consequence

Nikkey098 said:
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

Nikkey098 said:
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
 
  • #3
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.
davenn said:
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!
 
Last edited:

1. What are Surface Rayleigh waves?

Surface Rayleigh waves, also known as Rayleigh waves or ground roll, are a type of seismic surface waves that travel along the surface of the Earth. They are named after the British physicist Lord Rayleigh, who first described them in the late 19th century.

2. How are Surface Rayleigh waves generated?

Surface Rayleigh waves are generated by the interaction of P-waves and S-waves at the surface of the Earth. When these waves meet, they create a rolling motion that propagates along the surface. This rolling motion is what we perceive as a surface wave.

3. What factors affect the generation of Surface Rayleigh waves?

The generation of Surface Rayleigh waves is affected by several factors, including the type of seismic source, the geological structure of the subsurface, and the frequency of the seismic waves. Surface Rayleigh waves are most commonly generated by earthquakes, but can also be produced by man-made sources such as explosions.

4. How do scientists study and measure Surface Rayleigh waves?

Scientists use seismometers, which are sensitive instruments that measure ground motion, to study and measure Surface Rayleigh waves. By analyzing the characteristics of the waves, such as their amplitude and frequency, scientists can gain valuable insights into the properties of the Earth's subsurface.

5. What are the applications of studying Surface Rayleigh waves?

Studying Surface Rayleigh waves can provide valuable information about the Earth's subsurface, such as the thickness and composition of different layers. This information is crucial for various industries, including oil and gas exploration, earthquake hazard assessment, and civil engineering projects. Surface Rayleigh waves can also be used to monitor the effects of natural disasters, such as earthquakes and landslides.

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