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UNIVERSITETET I OSLO
Det matematisk-naturvitenskapelige fakultet
Exam in GEL2140 - Geophysics and global tectonics
Day of exam: Wednesday June 7th 2006
Exam hours: 2.30 pm – 5.30 pm
This examination paper consists of 5 pages.
Appendices: None
Permitted materials: Calculator
Make sure that your copy of this examination paper
is complete before answering.
NB! Exercise 1 and 2 count 40% each and exercise 3 counts 20%.
Exercise 1.
a) What is a seismic phase?
Draw a cross-section of the Earth and sketch the ray paths of the phases P, pP, PcP, S, SS and
SKS for an earthquake with hypocentre depth ca. 100 km.
b) Figure 1 (last page) shows the recording of an earthquake on the Southeast Indian Ocean
spreading ridge. The upper component is the vertical one, in the middle is the radial one, and the
lower is the transversal one. The travel time (given in seconds) is not measured relative to when
the earthquake occurred.
Identify and mark the P and S phase, Love and Rayleigh wave on the seismogram. Explain
briefly how you identified the phases and the waves.
NB! Figure 1 should be handed back together with the set of answers
c) Use the travel time curves in figure 2 to compute the epicentral angle (the delta distance),
measured in degrees, to the station at which the recording in figure 1 was made.
d) Write the expression for the ray parameter p for a spherically symmetric Earth model and
explain the symbols in the expression. Which particular property is attributed to the ray
parameter?
e) Figure 3 (next page) shows the velocity as a function of depth in the Earth’s interior for P-waves
(α) and S-waves (β). Suppose you want to study the uppermost structure in the outer core by
means of seismic waves. Which of the phases PKP and SKS would be most convenient for that
task? State the reasons for your answer.
f) Figure 4 shows the focal mechanism of the earthquake described above. Is it as expected for an
earthquake with the given location? State the reasons for your answer.
Figure 3
Figure 4
Exercise 2.
Assume a two-layer model where the surface and interface are plane and horizontal. The layer
velocities are constant and given by v1 (upper layer) and v2, where v1 < v2. A source at the surface
generates P-waves, and these are recorded by geophones deployed at the surface at increasing
distances from the source.
a) Show on a figure the wave paths of the direct, reflected and refracted waves.
Explain the terms critical angle, critical distance, cross-over distance and intercept-time.
b) The travel time of the direct wave to a geophone placed 250 m from the source, is 0.42 s. For
the refracted wave the travel time to geophones at distances 300 m and 800 m from the source is
0.48 s and 0.82 s, respectively.
Compute v1 and v2.
c) For the refracted wave we have the following expression:
t = (1/v2)·x + 2h1·﴾(1/v1)2 – (1/v2)2﴿½
What do t, x and h1 represent?
Compute h1 and the critical distance.
d) Assume then that the interface between layer 1 and layer 2 is dipping downward from the source
toward the geophones (but still being plane), and that the vertical distance from the source to the
interface is unchanged. Also the positions of the geophones are unchanged.
Explain how this will affect the travel times of the direct, reflected and refracted waves.
What is true velocity and apparent velocity in this context?
e) Finally we will consider a three-layer model, where the upper and middle layers are given by the
two-layer model described above. The third, and lower, layer has velocity v3 = v2, whereas the
density is somewhat higher than in layer 2.
Can a refracted wave be generated at the interface between layer 2 and layer 3? State the reasons
for your answer.
Can waves be reflected at the interface between layer 2 and layer 3? State the reasons for your
answer.
Exercise 3.
a) Describe which reservoir properties that can be determined on the basis of the following
geophysical well logs: the self-potential log, the resistivity log, the natural gamma ray log, the
gamma-gamma log, the neutron log, the sonic log.
b) Figure 5 shows a geological sequence, together with the self-potential log and the resistivity log
obtained in a borehole cutting through the sequence.
Explain the two logs on the basis of the geological sequence.
Figure 5
Figure 2