Wave scattering/dispersion? (body waves and surface waves)

[dorist84]

Homework Statement

I was asked to "figure out" when body waves (p-waves and s-waves) "turn into" surface waves (Rayleigh and Love waves). I've read several articles dealing with each topic seperately - but they mostly speak of how to calculate the phase velocity after computing a Fourier transform and so forth. I think my problem is that I still don't understand some of the fundamentals concerning the waveforms themselves.

When the body wave "turns into" a surface wave, is this considered wave scattering?

Homework Equations

My initial instinct was to simply look at several waveforms which are plotted as a function of time and to take an average of the difference in times between the S-wave arrival and body wave arrival.

For instance, I would look at one waveform, note the S-wave arrival, note the body wave arrival, and then note the difference between the two, and repeat for several other waveforms. I would then take an average of all of them.

Of course, I will filter the data before doing any of these "calculations"

The Attempt at a Solution

My attempt at a solution is listed above. But WHY do I not think this would work?

1. Because I think there is a fundamental concept concerning wave dispersion and scattering here that I am neglecting to account for in simply saying "Oh, let's just look at the difference and calculate an average."

2. You can't just look at a waveform and arbitrarily compute arrival times? Too much room for error and would lead to arbitrary computations.

3. Too simple of calculations involved. Doesn't seem to make sense.

ANOTHER SUGGESTION:

--Perhaps I can calculate the phase velocities for the body waves and surface waves and calculate an average difference between the two?

Any suggestions on helping to clarify what it means to "figure out when P-waves and S-waves turn into surface waves" would be greatly appreciated and how this could possibly relate to phase velocity and filtering/fourier transforms...and I mean greatly. :-)

Thank you so much. Take care.

--doris

 

[Jhero]

Dear Doris,

Thank you for your post. It seems like you have a good understanding of the fundamentals of wave propagation and dispersion. To answer your question, it is important to first understand the difference between body waves and surface waves.

Body waves are seismic waves that travel through the interior of the Earth, while surface waves travel along the surface of the Earth. P-waves (primary waves) and S-waves (secondary waves) are types of body waves, while Rayleigh and Love waves are types of surface waves. P-waves and S-waves travel faster than surface waves, but they also have different properties and behaviors.

Now, to answer your question about when body waves "turn into" surface waves, it is not a sudden or precise transition. Instead, it is a gradual process that depends on the properties of the Earth materials and the characteristics of the seismic waves. In general, as a seismic wave travels through the Earth, it will gradually change from a body wave to a surface wave, and this process can be influenced by factors such as the frequency of the wave, the distance it travels, and the type of Earth materials it encounters.

To better understand this process, you can use a method called seismic tomography. This involves analyzing the different arrival times of seismic waves at different locations on the Earth's surface to create a 3D image of the Earth's interior. By studying these images, scientists can gain insights into the structure and properties of the Earth's layers and how seismic waves behave as they travel through them.

In terms of your suggested methods, calculating the phase velocities for body waves and surface waves and comparing them could be a good approach. However, it is important to keep in mind that this will only give you an average value and may not accurately represent the behavior of individual waves.

I hope this helps to clarify the concept of when body waves turn into surface waves. Keep up the good work in your studies and don't hesitate to ask for further clarification if needed.