Geoscience Reference
In-Depth Information
14.0
6.75
16.0
7.00
18.0
7.35
20.0
7.50
22.0
7.90
24.0
8.10
26.0
8.40
28.0
8.70
30.0
8.90
(a) Plot the data on a time-distance graph and determine a crustal structure for the
line, assuming that it can be approximated by uniform horizontal layers. The water
is 3 km deep and has a P-wave velocity of 1.5 km s 1 .
(b) If the upper mantle has a normal P-wave velocity of 8.1 km s 1
in this region,
what is its minimum depth?
(c) Repeat the calculation assuming that the upper mantle has a velocity of only
7.6 km s 1 .
(d) Ideally, how long should the refraction line have been to make a measurement of
the upper-mantle velocity and depth?
(e) Explain how a record section would assist in determining the velocity structure.
19. Using the velocities for Love waves along continental ray paths (Fig. 4.6(a)), make a
rough estimate of the minimum time over which Love waves arrive at a seismometer
at epicentral distances of (a) 20 and (b) 100 . Assume that the seismometer records
waves with periods 20-250 s.
20. Calculate a velocity-depth model for the data shown in Fig. 4.42. Assume that the
structure is horizontally layered and that all layers have constant velocity. Use only
the reflections at 1.2, 1.5, 1.8, 2.0, 2.3 and 2.45 s.
21. For the simple example used in Section 4.4.3,
t 0 , 1 = 1 . 0s ,
α 1 = 3 . 6kms 1
0kms 1
t 0 , 2 =
1
.
5s
,
α 1 =
4
.
calculate the errors in velocity and thickness which result in the following cases.
(a) The travel times have an error of ± 0.05 s.
(b) The travel times have an error of ± 0.01 s.
(c) The RMS velocities have an error of ± 0.1 km s 1 .
Comment on the accuracy of interval velocity-depth models obtained from RMS
velocities and two-way travel times.
22. Calculate the normal-incidence P-wave reflection coefficients for the following inter-
faces:
(a) sandstone ( α = 3.0 km s 1 , ρ = 2.2 × 10 3
kg m 3 ) above a limestone ( α =
4.1 km s 1 , ρ = 2.2 × 10 3 kg m 3 );
(b) a possible lower-crustal interface of basalt ( α =
6.8 km s 1 ,
ρ =
×
2.8
10 3
kg m 3 )overgranulite ( α = 7.3 km s 1 , ρ = 3.2 × 10 3
kg m 3 ); and
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