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

1. May 21, 2008

### dorist84

1. The problem statement, all variables and given/known data

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?

2. Relevant 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"

3. 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