PHYS/GEOL 406 Homework
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   Homework #6: Due Friday, March 5, by 5:00pm

Reading:

  • section 2.1
  • section 2.2.7, especially Figure 2.15 which shows the mess that a "simple" incident seismic wave creates when it hits a boundary
  • section 2.3.1-2.3.2 on attenuation. We're only going to concentrate on the exponential loss of Eq. (2.28).
  • section 2.4.1-2.4.2
  • section 4.1.1-4.1.3
  • secton 4.1.5-4.1.6; discusses the t2-x2 graph with an example in Fig. 4.8, 4.10, and others later in the chapter. Fig. 4.13 shows what I said in class about how multiple interfaces simply produce multiple straight lines in the t2-x2 graphs.
Assignment:
  1. At a certain location near Radford, the limestone has a porosity of 10%, with the pores filled with water. Find the P-wave speed in this formation. Refer to Table 2.1 in your text for useful information. Use 1,480m/s for the speed of P-waves in water.
  2. The refraction seismogram below reveals three layers. The first arrivals have been identified with software such as you have used. The three layers are actually just made to two different materials. The upper layer is the loose/unconsolidated overburden, the second layer is a combination of that and the underlying bedrock due to fracturing, and the third layer is the solid bedrock. Find the porosity of this second layer. You need to print out the seismogram (on its own page for clarity), draw your slopes and triangles carefully on that, and show all of your calculations for the velocities and the porosity. The geophones are spaced 3m apart. If you are unsure of where the three layers are, ask me.
  3. At a distance of 50m from a seismic source the amplitude of a seismic wave is 0.0200mm; at a distance of 375m from the source the amplitude is 0.0046mm. What is the absorption coefficient of the material through which the wave is passing?
  4. You are in a location where there is exposed granite. The absorption coefficient of this granite is α=0.24 km-1. You have an initial seismic wave amplitude of 0.600mm. If your geophones have to have an amplitude of 0.115mm to register a wave, what is the deepest interface to which you can see under these conditions?
  5. The question was asked about attenuation with things not going straight up and down. Let's investigate that with a reflection similar to the image on the bottom of page 62. Background:
    -Your seismic source can produce an initial seismic amplitude of 0.200mm.
    -Your seismic array can measure down to amplitudes of 0.085mm.
    -You are in an area with an attenuation coefficient of α=4.5km-1.
    -You want to have 10 geophones in position to catch a reflection hyperbola.
    -You do not want to catch any refracted waves (for whatever reason).
    -You know that the wave speed in the uppermost layer is 400m/s while that in the second layer is 1,700m/s.
    (a) What is the critical angle for this situation?
    (b) What is the furthest distance that a seismic wave could travel in this material and still be received by your array?
    (c) What is the furthest distance along the surface that you can put your geophones in order to catch only the reflected waves (i.e. no refractions)?
    (d) How far apart will these geophones be from each other?
    (e) How deep will the interface be between the upper and lower layer?
    (f) Draw this situation, showing how you determined your geometry above. Indicate the critical angle, the depth to the boundary, and the geophone locations.
  6. A reflection seismogram is shown below. There are two reflections indicated by the arrows.
    (a) Using the t2-x2 method from class, determine the wave speeds in the two upper layers.
    (b) Using the slopes of the refractions, find the wave speeds of the two upper layers.
    (c) Find the depth from the surface to the first two boundaries indicated by this seismogram.

That's all for homework #6.