Amplitude Attenuation

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Melina Barrett
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1 Amplitude Attenuation 1

2 Overview Seismic signals become quieter as they propagate. Two different processes are responsible for this: Spherical Divergence True Attenuation 2

3 Spherical Divergence Bang! Bang! Energy of explosion is initially concentrated in a small volume close to the source. 3

4 Spherical Divergence Bang! Seismic wave spreads out at the speed of sound 4

5 Spherical Divergence Bang! Same energy as initially but spread over a larger volume. NB energy spreads out in 3 dimensions, i.e. over a Hemisphere. 5

6 Spherical Divergence Sounds from distant sources are quieter than near ones. Energy density, in a uniform medium, decreases with 1/t 2 because the surface area of a sphere increases with radius squared. E.g. energy drops by 1/4 at 2 seconds compared to 1 second. 6

7 Spherical Divergence Energy of a seismic wave is proportional to amplitude squared. Hence, in a uniform medium, amplitude decreases with 1/t. E.g. signal amplitude at 2 seconds is half of that at 1 second. 7

8 Attenuation No energy is lost during spherical divergence. It is simply being diluted as the seismic waves spread out. In addition however, there is true loss of energy as friction converts sound into heat. This additional factor is called attenuation and it is frequency dependent. 8

9 Attenuation Frequency dependent attenuation of sound waves should be familiar to you. Think of the sound of a distant thunderstorm. It is a low rumble rather than a sharp crack because the high frequencies have been attenuated as the sound has travelled towards you. The same thing happens with seismic waves. 9

10 Attenuation Frequency dependent loss of amplitude with travel time. Controlled by quality factor (Q) of the medium. A = A o exp(-pft /Q ) A is amplitude at time, t, with A o the initial amplitude and f the frequency. A o Curves showing typical amount of attenuation with time 10

11 Attenuation A = A o exp(-pft /Q ) Q varies with the material through which the waves travel. Pillows have very low Q, that s why they muffle sounds if you put them over your ears! For rocks, Q ~100. In seismic reflection surveys, we are usually interested in reflectors a few kilometres down and so, at typical P-wave velocities of 2000 m/s, travel times are usually a few seconds. Let s assume 2 seconds. What would happen to a 100 Hz signal after 2 seconds? From above, A / A o = exp(-pft /Q ) = exp(-6.28) = The signal strength has dropped by more than a factor of 500. This is why frequencies above 100 Hz are usually undetectable in seismic surveys. 11

12 Attenuation Frequency dependent loss of amplitude with travel time. Results in change of signal shape with time as well as a loss of amplitude Initial short, sharp signal Signal after propagating for 2 seconds with Q=50. time (s)

13 Quick Test As you ve just seen, frequencies above 100 Hz are not normally useful. However, in some surveys, higher frequencies can be used. Under what circumstances might this happen? Hint: attenuation is small if ft /Q is small. 13

14 Quick Test Answers Attenuation is small if ft /Q is small. Hence, if f is large, t /Q should be small. High frequencies useable if t is small or ifq is large. Most frequent case is when t is small, e.g. if a shallow survey is required for engineering purposes. 14

Geophysical Applications Seismic Reflection Surveying

Geophysical Applications Seismic Reflection Surveying Seismic sources and receivers Basic requirements for a seismic source Typical sources on land and on water Basic impact assessment environmental and social concerns EPS435-Potential-08-01 Basic requirements