Absorption of energy in a seismic pulse

[AlecYates]

Hey,

Just doing some reading on this and I'm a little confused as to why absorption produces a progressive lengthening of a seismic pulse.

Quote from the textbook "In general, the effect of absorption is to produce a progressive lengthening of the seismic pulse".

I understand how the pulse changes shape as higher frequencies attenuate more rapidly due to a constant absorption coefficient (which expresses the proportion of energy lost during transmission), though not so much why this effect lengthens the pulse.

So I guess I'm asking why is it that a pulse increases in length as opposed to just changing shape in the vertical? What is it about this effect that lengthens a seismic pulse?

Cheers

 

[davenn]

Hi Alec

Think I'm right in saying this ... ( some one else is sure to chime in if I'm not)

we see a lengthening of the pulse ( wave train) as the higher freq's have been attenuated the only signal remaining is the lower freq. one which is longer in wavelength

so as the attenuation slowly decreases the higher freq's with distance from the source, the lower freq's also slowly become more dominant. ( the overall amplitude ( the vertical part ) of the signal is also being attenuated as you said
Seismometers designed to record teleseisms are tuned to record the lower frequencies
like my one here

The upper trace is a long period sensor the lower sensor is a short period sensor
(the short period sensor won't even record the distant events unless they are huge events)

My long period sensor is particularly sensitive to wavelength (periods ) between 10 and 30 seconds
The short period sensor is sensitive to periods of 1sec to 0.1 sec ( 1 Hz to 10Hz)EDIT: something I initially forgot to mention ... the slow increase in wavelength is referred to as frequency dispersion.
Not sure of your level of knowledge in seismology ... this paper may be above or maybe below your level ... http://www.geos.ed.ac.uk/homes/imain/Attenuation.pdf

for more papers do a google search on frequency dispersion of seismic waves
Velocity dispersion also plays a part as well

does that help ?

cheers
Dave

 

[davenn]

there's a quake on my system at the moment

a M 5.7 up in the Solomon Is. ~ 3500 km NNE of my station
here is the gram before it disappears in another ~ 24 hrs

you can see the short period P and S waves and the long period surface waves on this gram

( each line across the gram is 1 hour --- you can see it marked off in 10 minute intervals)

Small amplitude P wave arriving at 10 mins past the hour, slightly larger S wave at ~ 15 mins past the hour
then around 18 min past the hour the lower freq surface waves start to arrive

The P and S waves have already undergone considerable attenuation by this timecheers
Dave

 

[AlecYates]

"Not sure of your level of knowledge in seismology"

low I imagine, it's only been a recent attempt at moving beyond a surface level knowledge of seismology in an attempt to pursue a career in it. Currently doing some pre-study before beginning a graduate course in geophysics.

checked up on frequency dispersion. Eventually got back to the velocity = frequency x wavelength. So it makes sense to me that given we know a wave moves through homogeneous material at a constant velocity, if the higher frequencies are being attenuated faster, to ensure the same velocity the wavelength has to increase to balance this?

 

[davenn]

Hi Alec

checked up on frequency dispersion. Eventually got back to the velocity = frequency x wavelength. So it makes sense to me that given we know a wave moves through homogeneous material at a constant velocity, if the higher frequencies are being attenuated faster, to ensure the same velocity the wavelength has to increase to balance this?

this is where velocity dispersion comes into play as well

The velocity isn't constant. Higher frequency waves have a higher velocity
but they are also subject to the highest attenuation

jus for some close approximates

P wave --- ~ 7 km / sec (6 - 8 km/s)
S wave --- ~ 4 km / sec ( 3 - 5 km/s)
surface waves ( Love and Rayleigh waves) --- ~ 3 km / sec

The P waves were the highest freq dropping lower to the S waves and then lower again to the surface waves. And have different velocities accordingly. You can see the result of that in my seismogram with the difference in arrival time of the different waves

If I did a FFT on my data for that above quake, I would find that the P wave frequency ( and therefore its velocity) would be lower than what would be recorded closer to the event.

I hope you really enjoy your studies
I really enjoyed my time at university ( I went in as an adult student was already 30 yrs old at the time I started). I'm no expert in the field, just really passionate cheers
Dave

 

[Squatchmichae]

Careful regarding the comment that high-frequency body waves travel faster--while there are pathological examples in which body waves do travel faster when they have higher frequency, longer-wavelength signals often arrive at receivers first. This is because these longer wavelengths sample deeper Earth structure, where the intrinsic propagation speeds are faster. Often, very shallow Earth structure supports lower propagation speeds, sometimes with p-wave speeds low as 100s of m/sec. Very high frequency seismic waves (say 100s of Hz) used in exploration geophysics have wavelengths at 10s of meters. By contrast, a 0.1 Hz wave that reaches lower structure thereby has a wavelength 1000x longer: 10s of km in length.

 

[davenn]

Careful regarding the comment that high-frequency body waves travel faster--while there are pathological examples in which body waves do travel faster when they have higher frequency, longer-wavelength signals often arrive at receivers first. This is because these longer wavelengths sample deeper Earth structure, where the intrinsic propagation speeds are faster. Often, very shallow Earth structure supports lower propagation speeds, sometimes with p-wave speeds low as 100s of m/sec. Very high frequency seismic waves (say 100s of Hz) used in exploration geophysics have wavelengths at 10s of meters. By contrast, a 0.1 Hz wave that reaches lower structure thereby has a wavelength 1000x longer: 10s of km in length.

You would have to show me examples for me to believe that

P waves always arrive first, I haven't seen a seismogram where they haven't

Dave

 

[Squatchmichae]

Hi Dave,
I never claimed p-waves (a type of body wave) travels slower than shear or surface waves. I simply stated that higher frequency body waves can travel faster slower than their lower frequency counter-parts. So, a 100Hz p-wave may arrive at a seismometer later than 0.1 Hz p-wave. Re-reading my response, I didn't state that p-waves arrive later than other phases, simply that waveforms with lower frequency content from (the same) p-phase group may show up first.

 

[davenn]

Re-reading my response, I didn't state that p-waves arrive later than other phases, simply that waveforms with lower frequency content from (the same) p-phase group may show up first.

Yes your initial comments were unclear and easily mis-understood

We periodically see early P arrivals, that is, the arrival of small P pulses before the main P arrival and these ARE the P waves that come via a higher velocity layer(s)

The comments I made in Post #5 still stand and answer the OP's questions without getting into the complex subsets of Pn, pp, p'p etc etc