Solutions to odd-numbered problems 487
(13a)
9.34 km/s.
(13b)
11.24 km/s.
(15)
For D = 0 km: p 40 = 8.3 s/degree, p 60 = 6.9 s/degree, i 40 = 26°,
i 60 = 21°. For D = 600 km: p 40 = 7.9 s/degree, p 60 = 6.6 s/degree,
i 40 = 52°, i 60 = 41°.
(17a)
4.5 s/degree.
(17b)
13.4 km/s.
(17c)
SKKS.
(19a)
t 1/e ( 0 T 2 ) = 58.3 hr, t 1/e ( 0 T 30 ) = 3.0 hr, t 1/e ( 0 S 30 ) = 4.2 hr.
(19b)
54,300 km for 0 T 30 , 76,450 km for 0 S 30 .
(21a)
3%.
(21b)
0.3%.
(23)
M c = 1.94 × 10
24 kg, N c = 11 g /cm
3 .
Chapter 4
(3)
Earthquake a: (φ, δ, λ) 1 = (310°, 65°, 90°) (thrust); (φ, δ, λ) 2 =
(130°, 25°, 90°) (thrust); P axis (azimuth, plunge) = (40°, 20°);
T axis = (220°, 70°); B axis = (130°, 0°).
Earthquake b: (φ, δ, λ) 1 = (176°, 80°, 195°) (right-lateral
strike-slip); (φ, δ, λ) 2 = (83°, 75°, 350°) (left-lateral strike-slip);
P axis (azimuth, plunge) = (40°, 18°); T axis = (309°, 3°);
B axis = (209°, 72°).
Earthquake c: (φ, δ, λ) 1 = (9°, 90°, 180°) (right-lateral
strike-slip); (φ, δ, λ) 2 = (99°, 90°, 0°) (left-lateral strike-slip);
P axis (azimuth, plunge) = (234°, 0°); T axis = (144°, 0°);
B axis = (undefined, 90°).
Earthquake d: First solution: (φ, δ, λ) 1 = (16°, 85°, 90°) (dip
slip); (φ, δ, λ) 2 = (196°, 5°, 90°) (thrust); P axis (azimuth, plunge)
= (106°, 40°); T axis = (286°, 50°); B axis = (196°, 0°). Second
solution: (φ, δ, λ) 1 = (78°, 66°, 25°) (left-lateral strike-slip);
(φ, δ, λ) 2 = (337°, 67°, 154°) (right-lateral strike-slip);
P axis (azimuth, plunge) = (28°, 1°); T axis = (297°, 34°);
B axis = (119°, 56°).
(7)
0.
(9a)
0 0 0
0 0 0
0 0
3
0
0
0
3
0
0
0
3
M
M
M
M
zz
zz
zz
zz
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
=
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
/
/
/
3
0
0
0
3
0
0
0
2
3
M
M
M
zz
zz
zz
+
−
−
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
/
/
/
.
(9b)
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
=
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
2 14
0
0
0
2 01 0
0
0
01 3
2 075
0
0
0
2 075 0
0
0
0
.
.
.
.
.
+
−
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
0 065
0
0
0
0 065
0
0
0
01 3
.
.
.
.
(Double-couple scalar moment)/(original scalar moment) = 0.999.
(CLVD scalar moment)/(original scalar moment) = 0.054.
(9c)
There are two solutions:
Solution 1:
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
=
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
2 14
0
0
0
2 01 0
0
0
01 3
1 135 0
0
0
0
0
0
0 1 135
.
.
.
.
.
+
−
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
1 005
0
0
0
2 01
0
0
0
1 005
.
.
.
.
(Double-couple scalar moment)/(original scalar moment) =
0.546.
(CLVD scalar moment)/(original scalar moment) = 0.838.
Solution 2:
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
=
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
2 14
0
0
0
2 01 0
0
0
01 3
0
0
0
0 0 94
0
0
0
094
.
.
.
.
.
+
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
2 14
0
0
0
1 07
0
0
0
10 7
.
.
.
.
(Double-couple scalar moment)/(original scalar moment) =
0.452.
(CLVD scalar moment)/(original scalar moment) = 0.892.
(11)
4.24 mm/yr, 0.85 mm/yr, 0.42 mm/yr.
(13)
M S = 5.2.
(15)
assuming µ = 3 × 10
11 ; 200,000 km; 43,333 km.
(17)
~0.04 Hz.
(19b)
0.003–0.03.
(21)
Japan: 8 mo. (M ≥ 6); 7 yr (M ≥ 7); 65 yr (M ≥ 8). S. California:
1 yr (M ≥ 6); 8 yr (M ≥ 7); ≈ 100 yr (M ≥ 8). New Madrid: 92 yr
(M ≥ 6); 920 yr (M ≥ 7); 9200 yr (M ≥ 8).
(C-1)
Earthquake a: 4 = (0.453, −0.785, 0.423);
2 = (0.098, 0.515, 0.852).
Earthquake b: 4 = (0.853, −0.150, 0.500);
2 = (0.492, −0.087, −0.866).
Earthquake c: 4 = (0.853, −0.150, 0.500);
2 = (−0.492, 0.087, 0.866).
Earthquake d: 4 = (−0.633, −0.754, 0.174);
2 = (0.758, −0.559, 0.337).
Earthquake e: 4 = (−0.633, −0.754, 0.173);
2 = (−0.758, 0.559, −0.337).
(C-3)
Earthquake a:
0 088
0 157
0 427
0 157
0 808
0 451
0 427
0 451
0 720
.
.
.
.
.
.
.
.
.
.
−
−
−
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
Earthquake b:
0 840 0 148
0 492
0 148 0 026
0 087
0 492 0 087
0 866
.
.
.
.
.
.
.
.
.
.
−
−
−
−
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
Earthquake c:
−
−
−
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
0 840 0 148
0 492
0 148 0 026
0 087
0 492 0 087
0 866
.
.
.
.
.
.
.
.
.
.