Interpreting Body Wave-Surface Wave Energy Transfer with Vectors & Tensors

[james k]

Homework Statement

Hi, as part of my final year project I am investigating how rayleigh surface waves are generated by transverse body waves. I've seen how Kolsky derives these waves by slving the wave equation for this type of waveform. My supervisor wants me to describe the energy transfer between the body wave and the surface wave by a tensor - vector relation.

Homework Equations

I think it should go something like this, : [boundary tensor]*[body wave vector] = [rayleigh wave vector]
What i need to know is what the the vectors and tensors actually represent and what should their elements be? How can I interpret this physically?

any help would be greatly appreciated, I've have searched everywhere for help with this but to no avail.
thanks James

The Attempt at a Solution

 

[Valkarie]

The vectors and tensors represent the directions, amplitudes, and phase differences of both the body wave and the surface wave. The elements of the tensor would depend on the properties of the medium that the waves are travelling through. The tensor-vector relation physically represents the energy transfer between the two waves. This can be interpreted as the energy from the body wave being transferred to the Rayleigh wave as they interact with each other.

 

[piercas]

I can help you understand the physical interpretation of the vectors and tensors in this energy transfer equation. In this context, the vectors represent the direction and magnitude of the energy transfer, while the tensors represent the relationship between the body wave and the surface wave.

The elements of the vectors and tensors will depend on the specific properties of the materials involved in the wave propagation, such as their elastic constants and density. The boundary tensor, in particular, represents the interface between the two materials and how it affects the energy transfer between them.

To interpret this physically, you can think of the body wave as a wave that travels through the interior of a material, while the surface wave travels along the boundary between two materials. As the body wave reaches the boundary, some of its energy is transferred to the surface wave, which then propagates along the interface.

Overall, the vector-tensor relation describes the transfer of energy from the body wave to the surface wave, and how the properties of the materials and their interface affect this transfer. I hope this helps in your project and if you have any further questions, please do not hesitate to ask. Good luck with your research!