• date post

26-Jun-2020
• Category

## Documents

• view

0

0

Embed Size (px)

### Transcript of The Solid Earth Chapter 2 Answers to selected › instruction › HSU › 2016_spring...

• The Solid Earth Chapter 2

(1) (a)

B vD=B vC +CvD B vD

2 = 62 +102 − 2 ×10cos 25( ) B vD = 5.22

sin φ( ) = 10 × sin 25( )

5.22 φ =126o

(b)

A vJ =A vB+BvJ At 3 cm per year in E - W direction, time taken to move 3000 km is

3000 ×103

3×10−2 =108 a =100 Ma

(Diagrams are sketches and are not exactly to scale.)

• (2)

A vB=A vF+FvB

(Diagrams are sketches and not exactly to scale)

The B-F ridge approaches the trench eastwards at 0.8 cm per year. 2,200 km to the trench will take 275 Ma. Triple junction J approaches the northern trench at 4.2 cm per year. 1500 km takes 36 Ma when the last remnant of the Cooler plate is subducted in this region.

(3)

Lat Long Location Plate pair Azimuth Rate (mm/yr)

54°N 169°E W. Aleutian Trench N Am - Pac 133 74 52°N 169°W E. Aleutian Trench N Am - Pac 145 68 38°N 122°W San Francisco - San

Andreas Fault N Am - Pac 146 46

26°N 110°W Gulf of California N Am - Pac 129 46 13°S 112°W East Pacific Rise Naz - Pac 103 143 36°S 110°W East Pacific Rise Pac - Ant 281 94 59°S 150°W Antarctic - Pacific Ridge Pac - Ant 303 71 45°S 169°E S. New Zealand Pac - Aus 248 35 55°S 159°E Macquarrie Island Pac - Aus 212 27 52°S 140°E Southeast Indian Ridge Aus - Ant 359 69 28°S 74°E Southeast Indian Ridge Aus - Ant 045 58 7°N 60°E Carlsberg Ridge Ind - Afr 032 26 22°N 38°E Red Sea Ar - Afr 012 10 55°S 5°E Southwest Indian Ridge Afr - Ant 043 14 52°S 5°E Mid-Atlantic Ridge Afr – S Am 068 30

• 9oN 40oW Mid-Atlantic Ridge Afr – S Am 090 28 35oN 35oW Mid-Atlantic Ridge Afr – N Am 104 21 66oN 18oW Iceland Eur – N Am 105 18 36oN 8oW Gorringe Bank Afr - Eur 310 4 35oN 25oE E. Mediterranean Afr - Eur 353 9 12oS 120oE Java Trench Au – Eur 017 76 35oN 72oE Himalayas Ind - Eur 003 42 35oS 74oW S. Chile Trench Naz – S Am 079 80 4oS 82oW N. Peru Trench Naz – S Am 082 70 20oN 106oW Middle America Trench Co – N Am 034 41

(5) λp = 45°, φp = 0°, ω = 10-10 radians per year, R = 3400 km.

(a) subduction, strike-slip and ridge. (b) Magnetic lineations between a and b, b and c. (c) Use method of Sect. 2.4.2.

a: λx = 0°, φx = 0° b: λx = 0°, φx = 90° c: λx = 0°, φx = 180° d: λx = 0°, φx = -90°

At a:

a = cos−1 cos 45( )cos 0( )[ ] = cos−1 0.707[ ] = 45o

C = sin−1 cos 45( )sin 0( ) sin 45( )

 

 

= 0o

β = 90o

• v =ωRsin a( ) =10−10 × 3400 ×103 ×103 sin 45( ) = 0.24 mm a-1, azimuth 090, strike slip

At b:

a = cos−1 cos 45( )cos 0 + 90( )[ ] = 90o

C = sin−1 cos 45( )sin −90( ) sin 90( )

 

 

= −45o

β = 45o

v =ωRsin a( ) =10−10 × 3400 ×103 ×103 sin 90( ) = 0.34 mm a-1, azimuth 45, strike slip/extension

At c:

a = cos−1 cos 45( )cos 0 −180( )[ ] =135o

C = sin−1 cos 45( )sin −180( ) sin 135( )

 

 

= 0o

β = 90o

v =ωRsin a( ) = 0.24 mm a-1, azimuth 090, strike slip

At d:

a = cos−1 cos 45( )cos 0 + 90( )[ ] = 90o

C = sin−1 cos 45( )sin 90( ) sin 90( )

 

 

= 45o

β =135o

v =ωRsin a( ) = 0.34 mm a-1, azimuth 135, oblique subduction

(d)

(sketches only)

• Stable with hemispheric plates for all pole positions. Plates stay the same size but are subducted along half of their margin and created along the other half.

(6) AωB 3x10

-9 radians a-1, 30°N 0°E BωC -6x10

-9 radians a-1, 90°N 0°E R=6000 km.

(a) Use method of Sect. 2.4.3.

AωC=AωB+BωC xAC = −6 ×10

−9 cos 90( )cos 0( ) + 3×10−9 cos 30( )cos 0( ) = 2.6 ×10−9

yAC = −6 ×10 −9 cos 90( )sin 0( ) + 3×10−9 cos 30( )sin 0( )

= 0 zAC = −6 ×10

−9 sin 90( ) + 3×10−9 sin 30( ) = −4.5 ×10−9

AωC = 2.6 2 + 4.52 ×10−9 = 5.2 ×10−9

pole position :

λAC = sin −1 4.5 ×10−9

5.2 ×10−9 

 

  = −60 = 60oS

φAC = tan −1 0

2.6 

 

  = 0

(b) At b:

λX = 0, φX = 90. B relative to A: β = 030, v = 18 mm a -1

C relative to B: β = 270, v = 36 mm a-1

C relative to A: β = 300, v = 31 mm a-1

(not to scale) bc would go through C if plate B is subducting beneath plate C.

At d:

λX = 0, φX = −90. B relative to A: β = 150, v = 18 mm a-1

C relative to B: β = 270, v = 36 mm a-1

C relative to A: β = 240, v = 31 mm a-1

• (not to scale) Stable if plates B and C are subducting beneath A, or if plate A is subducting between plates B and C.

Extension is taking place between plates A and B and between plates A and C at b. The magnetic stripes on each plate are 78 km wide and strike E-W.

Extension is also taking place between plates B and C at d. The magnetic stripes on each plate are 180 km wide and strike N-S.

Ridges: d to North Pole; between a and b, b and c. Strike-slip: at a and c. Subduction: North Pole to b; between c and d, d and a.

(8)

(Sketch) Ridge half-spreading rates are 2.0 cm per year and 3.45 cm per year. Triple junction moves at 3.9 cm per year at 275 relative to plate C.

• (10)

(Sketch only)

(a) 11.6 cm per year (b) 6 cm per year parallel to BvN (e) (Sketches only, not to scale)

At A At B

(f) BJN: 6 cm per year for 2 Ma, 120 km spacing, 1.6 cm per year for 2 Ma, 32 km spacing. (Sketch, not to scale)

• (11) Similar to Q6.

λAB = 0, φAB = 90, ωAB = 3.82 ×10 −7 deg per year

λBC = −90, φBC = 0, ωBC = 2.86 ×10 −7 deg per year

(a)

xAC = 3.82cos 0( )cos 90( ) + 2.86cos −90( )cos 0( )( ) ×10−7

= 0 yAC = 3.82cos 0( )sin 90( ) + 2.86cos −90( )sin 0( )( ) ×10−7

= 3.82 ×10−7

zAC = 3.82sin 0( ) + 2.86sin −90( )( ) ×10−7

= −2.86 ×10−7

AωC = 3.82 2 + 2.862( ) ×10−7

= 4.77 ×10−7

λAC = sin −1 −2.86 4.77

 

  = −36.8o

φAC = sin −1 3.82

0 

 

  = 90o

(b) Magnetic lineations formed at ridge along equator between plates A and C from 0° to 90°W. Maximum spreading rate is 5 cm per year at 0°N, 0°W (the triple junction) - spreading is oblique. On far side of planet the boundary between plates A and C is a subduction zone with oblique subduction.

(c) The triple junction on the visible side of the planet is FFR, on the far side the triple junction is FFT. See Fig. 2.16 for stability of triple junctions. The FFR junction is not stable. The FFT junction will be stable if plate A is subducting beneath plate C (since then ac and bc will be coincident).