Looking for what you cant see (Seismic refraction)
MS Word version of this file
Physics in the New Zealand Curriculum:
level 7 A.O. 7.1 |
(a) demonstrate an understanding of concepts, principles, and models |
(b) apply concepts and principles to explain physical phenomena, systems, and devices |
What are Seismic Waves?
Energy travels through the Earth in seismic waves. As a seismic wave travels it causes the particles in the Earth to oscillate. These oscillations are related to the 'rock stiffness' or rigidity of the rock. Eventually seismic waves dissipate their energy to the earth and lose amplitude.
Like other waves, seismic waves obey the laws of physics. For example, seismic waves have difficulty passing from one medium into another, hence they reflect (partially) from such a boundary.
Waves also have different speeds in different media because each medium
has its own rigidity. Different speeds give rise to refraction effects, including critical
angle.
Wave path |
How the wave travels in the upper medium |
What happens at the boundary |
|
A |
Direct wave - along the surface | (doesn’t get to the boundary) | |
B |
Super-critical wave - down & along at an angle greater than the critical angle | B’ |
The wave is totally reflected back up to the surface (at an equal angle) |
C |
Critical wave - down & along at the critical angle | C’ |
refracted so much by the lower medium that it travels along the boundary ... |
C’’ |
and refracts back up towards the surface at the critical angle. | ||
D |
sub-critical wave - down & along at an angle less than the critical angle | D’ |
some of the energy is reflected back to the surface at an equal angle. |
D’’ |
while the rest of the waves energy is transmitted into the lower medium but at a new or refracted angle. | ||
E |
Vertical wave - straight down perpendicular to the boundary | E’ |
a small part of the waves energy is reflected straight back up |
E’’ |
while most is transmitted. The direction does not change but the speed does. | ||
How do we use this to
learn about what is under the ground?
We can calculate the seismic wave velocities in both layers and the depth to the boundary.
We determine the 2 velocities using the time it takes for the seismic waves to travel out.
Usually, seismic waves travel slowly in the top layer and faster in the lower layer (the
lower layer is more rigid).
Going on to diagram 2. below ...
The direct wave (A) travels slowly toward the geophones (on the right).
The critical wave (C) starts by travelling slowly down and across the top layer at the
critical angle. When it gets to the boundary it refracts and travels along the boundary at
the faster speed of the lower layer. At points along the bounday it refracts up toward the
surface, again, at the critical angle.
For geophones nearer the left hand side of the diagram, the direct wave will arrive first.
For geophones nearer the right hand side of the diagram, the refracted wave will arrive
before the direct wave because it has travelled much of its path at the faster speed.
The geophones are linked together and all start recording at the instant of the explosion.
Geophone records show the times that the first (& also later) seismic wave arrived at each geophone. The first seismic wave to arrive at the close geophones is the direct wave. However, more distant geophones record the refracted wave first.
For the close geophones the time difference between consecutive geophone arrivals is related to the speed of the direct wave and, of course, the distance between the geophones.
However, the difference in arrival times for two consecutive distant geophones is related to the speed of the refracted wave as it was travelling along the boundary (at the faster speed). Can you explain why?
(The actual arival time is related to the whole wave path - going down,
going across, going back up.)
Finding the velocities.
The geophone record will look like this ...
Putting lines on to find
gradients
We use the gradients of these 2 lines to calculate the velocities.
A Time vs Distance graph is needed to determine these gradients and for this we require the actual first arrival time from each geophone.
| Geophone position (m) | 30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
110 |
| Time for first arrival (s) | 0.0353 |
0.0471 |
0.0589 |
0.0706 |
0.0806 |
0.0872 |
0.0938 |
0.1000 |
0.1069 |
Analysis of real data
Now that you’ve been through the process once you can try some
real data. A student from the School of Earth Sciences, Victoria collected this seismic
record from Wainuiomata. This is a sedimentary basin with a slower sedimentary layer
overlying greywacke basement.
Your task is to determine the velocities and the depth of the sediment. Good Luck.
Geophone 1 (first vertical line on the left) was 100 m from the explosion and the
geophones are 8 m apart, so the last geophone (number 24) was 184 m from the explosion.
The vertical time scale is in milliseconds, starting from 0 (the time of the explosion) at
the dark line at the top of the plot to 200 milliseconds at the bottom of the plot.
Compare your results to what the Victoria Student got:
If your results were different then ask yourself "Are they significantly different?"
The student found, by recording explosions from both ends of the line of geophones, that the greywacke basement was not horizontal. It had been tilted down at the South end. This changes the velocities you get depending on whether you are looking up the slope or down the slope. The data above are from the explosion on the upslope end, and when the geophones are downslope from the explosion, the velocity measured on the surface is lower than the true velocity of the layer. However a dipping lower layer doesn’t affect the measured velocity in the upper layer.
This is a whole other topic, which we can’t go into here, except to say it can be worked out using similar wave theory to what we use in Year 12. If you would like to learn how to determine the velocity from dipping layers you could visit the page:
http://www.mines.edu/fs_home/tboyd/GP311/MODULES/SEIS/NOTES/dip1.html