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Geology Notes

[Last Updated 22 January 2011]


Measuring the Earth
Rocks and Minerals
Plate Tectonics
Seismic Waves
Earthquake Magnitudes
Earthquake Rupture Parameters
Tsunamis


Measuring the Earth


PROBLEM

Calculate the area in km2 corresponding an area which is 1° wide in longitude and 1° wide in latitude and centered on Boston.

SOLUTION

The area on the surface of a sphere of radius R, with qmin < q < qmax and fmin < f < fmax, where q and f are spherical coordinate angles, is

A = ∫ dA = ∫qminqmax R2 sin q dqfminfmax df = R2(cos qmin - cos qmax)(fmax - fmin)

Boston, Massachusetts, is located at longitude - 71° 3' 37" W = - 71.060° and latitude 42° 21' 30" N = 42.358° (World Almanac and Book of Facts 2003). Thus, we want the area corresponding to the region with - 71.560° < longitude < - 70.560° and 41.858° < latitude < 42.858°. Since

f = longitude

and

q = 90° - latitude

we have

qmin = 90° - 42.858° = 47.142°
qmax = 90° - 41.858° = 48.142°
fmin = - 71.560° = - 1.2490 rad
fmax = - 70.560° = - 1.2315 rad

Thus,

A = (6.37 x 103 km)2(cos 47.142° - cos 48.142°)(- 1.2315 + 1.2490) = 9134 km2

World Almanac Education Group 2003, The World Almanac and Book of Facts 2003 (New York: World Almanac Books).

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Rocks and Minerals

A rock generally consists of a mixture of minerals, although it could also consist of a specific single mineral. A mineral is a substance with a particular chemical composition. An ore is a rock containing extractable minerals of some commercial value. A gemstone or gem is a piece of mineral which has been cut and polished.

QUESTION

Identify the following rocks, minerals, ores, or geological-mineral formations. If a rock, classify it as igneous, sedimentary, or metamorphic, and give its principal component. If a mineral, give its chemical composition.

(a) stalactite
(b) selenite
(c) alabaster
(d) calcite
(e) fibrous gypsum
(f) quartz
(g) pink gypsum
(h) corralline limestone
(i) barite
(j) petrified wood
(k) anhydrite
(l) malachite
(m) pyrite
(n) marbleized limestone
(o) orthoclase
(p) coquina
(q) epidote
(r) sandstone
(s) chalcopyrite
(t) azurite
(u) limonite
(v) gossan
(w) fault breccia
(x) magnetite
(y) coal
(z) basalt
(a) molybdenite

ANSWER

(a) stalactite: a mineral formation that develops from the ceiling or wall of a limestone cave, consisting of calcium carbonate (CaCO3) and other minerals precipitated from water solutions [W]
(b) selenite: one of the four crystalline varieties of gypsum; formula CaSO4 · 2H2O [W]
(c) alabaster: either (i) gypsum alabaster (modern alabaster), a fine-grained variety of gypsum, or (ii) calcite alabaster (ancient alabaster), which is either a stalagmitic deposit or a travertine (a sedimentary rock, a chemical precipitate of carbonate minerals) [W]
(d) calcite: the most stable polymorph (crystal structure) of calcium carbonate; formula CaCO3 [W]
(e) fibrous gypsum: a variety of gypsum
(f) quartz: the most common mineral in the Earth's continental crust, consisting of a lattice of silica tetrahedra; formula SiO2 [W]
(g) pink gypsum: a variety of gypsum
(h) corralline limestone: limestone originating from coral
(i) barite: barium sulfate; formula BaSO4 [A]
(j) petrified wood: fossil wood in which the organic matter has been replaced with minerals, most commonly a silicate such as quartz [W]
(k) anhydrite: anhydrous calcium sulfate; formula CaSO4 [W]
(l) malachite: a carbonate mineral; formula Cu2CO3(OH)2 [W]
(m) pyrite: an iron sulfide; formula FeS2 [W]
(n) marbleized limestone: limestone which has been metamorphosed into marble
(o) orthoclase: a tectosilicate mineral which forms igneous rock; formula KAlSi3O8 [W]
(p) coquina: an incompletely consolidated sedimentary rock composed mainly of calcite [W]
(q) epidote: a calcium aluminium iron sorosilicate mineral; formula Ca2(Al, Fe)3(SiO4)3OH [W]
(r) sandstone: a sedimentary rock consisting of quartz and/or feldspar [W]
(s) chalcopyrite: a copper iron sulfide mineral; formula CuFeS2 [W]
(t) azurite: copper carbonate hydroxide; formula Cu3(CO3)2(OH)2 [A]
(u) limonite: a mixture of hydrated iron(III) oxide-hydroxide, where the relative amounts of oxide and hydroxide varies [W]
(v) gossan: intensely oxidized, weathered, or decomposed rock; the top of a mineral vein [F], [W]
(w) fault breccia: angular rock fragments resulting from tectonic movement [M]
(x) magnetite: a ferrimagnetic mineral; formula Fe3O4 = FeO · Fe2O3 [W]
(y) coal: a fossil fuel, a sedimentary or metamorphic rock, formed when geological processes apply pressure to plant remains [W]
(z) basalt: a mafic extrusive volcanic rock [W]
(a) molybdenite: molybdenum disulfide; formula MoS2 [A]

Category Substance
Igneous Rocks
[rock formed when magma solidifies underground (plutonic rock) or above ground (volcanic rock)]
(z) basalt
Sedimentary Rocks
[rock formed from compacted sediments]
(r) sandstone
(p) coquina
(h) coralline limestone
Metamorphic Rocks
[rock resulting from the transformation of a preexisting rock type by heat and pressure]
(n) marbleized limestone
Ores
[rock containing extractable minerals of some commercial value]
(u) limonite
(v) gossan
Minerals
[substances with a specific chemical composition]
(k) anhydrite
(i) barite
(l) malachite
(o) orthoclase
(q) epidote
(t) azurite
(x) magnetite
(a) molybdenite
(f) quartz:

(b) selenite
gypsum:
(c) gypsum alabaster
(e) fibrous gypsum
(g) pink gypsum
(d) calcite:
(c) calcite alabaster
(m) pyrite:
(s) chalcopyrite
Geological-Mineral Formations
(a) stalactite
(j) petrified wood
(w) fault breccia
(y) coal


References

[A] Amethyst Galleries' Mineral Gallery
[F] Free Dictionary
[M] Marshak, Stephen 2003, Essentials of Geology: An Introduction to Planet Earth (New York: W. W. Norton & Company)
[W] Wikipedia

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Plate Tectonics


QUESTION

With what type of plate boundary are the following places or features associated:
(a) Himalayas
(b) Aleutian Islands
(c) Red Sea
(d) Andes Mountains
(e) San Andreas fault
(f) Iceland
(g) Japan
(h) Mount St. Helens

[from Tarbuck, Edward J., and Lutgens, Frederick K. 1996, Earth: An Introduction to Physical Geology, Fifth Edition (Upper Saddle River, New Jersey: Prentice Hall), question 18.17]

ANSWER

(a) The Himalayas are a mountain range which run between India and China at a continental-continental convergent plate boundary where the Australian-Indian plate is subducting under the Eurasian plate.

(b) The Aleutian Islands are a series of volcanic islands in the northern Pacific Ocean at an oceanic-oceanic convergent plate boundary where the Pacific plate is subducting under the North American plate.

(c) The Red Sea is located between Africa and Saudi Arabia at a divergent plate boundary where the African and Arabian plates are separating.

(d) The Andes Mountains are a mountain range along the west coast of South America at an oceanic-continental convergent plate boundary where the Nazca plate is subducting under the South American plate.

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Seismic Waves

QUESTION

Describe the four main types of seismic waves. In each case, state (a) the name of the wave, (b) the medium through which the wave propagates, (c) the nature of the wave motion, (d) what the speed of the wave depends on, and (e) a typical wave speed.

ANSWER

There are two types of body waves.

The primary (P) wave propagates through rock and water. It is a longitudinal or compressional wave, for which the medium vibrates along the direction of propagation of the wave. The P wave speed is given by

a = sqrt[(k + 4m/3)/r]

where k is the modulus of incompressibility, m is the modulus of rigidity, and r is the density. For granite, k = 2.7 x 1011 dynes/cm2, m = 2.6 x 1011 dynes/cm2, r = 2.75 g/cm3, and

a = sqrt{[2.7 x 1011 dynes/cm2 + (4/3)(2.6 x 1011 dynes/cm2)]/(2.75 g/cm3)} = 4.735 x 105 cm/s = 4.735 km/s

For water, k = 2 x 1010 dynes/cm2, m = 0, r = 1 g/cm3, and

a = sqrt[(2 x 1010 dynes/cm2)/(1 g/cm3)] = 1.414 x 105 cm/s = 1.414 km/s

The secondary (S) wave propagates through rock. It is a transverse or shear wave which cannot propagate through water.

There are two types of surface waves. They are both transverse waves which travel along the land surface of the Earth. The S wave speed is given by

b = sqrt(m/r) = sqrt[(2.6 x 1011 dyne/cm2) / (2.75 g/cm3)] = 3.075 x 105 cm/s = 3.075 km/s

for granite.

The Love wave is a horizontal transverse wave, which is like the secondary wave except that it has no vertical component. The Love wave is named after British mathematician A. E. H. Love, who produced a mathematical model for the wave in 1911. The Love wave speed cL is in the range b1 < cL < b2, where b1 is the S wave speed within the crust, and b2 is the S wave speed within the upper mantle (Lay and Wallace 1995, p. 129). b1 = 3.075 km/s for granite and b2 ~ 4.5 km/s (http://serc.carleton.edu/eet/seismicwave/teaching_notes.html).

The Rayleigh wave is a transverse wave with both vertical and horizontal components in a vertical plane which is aligned with the propagation direction of the wave. The wave produces motion in an elliptical path. The Rayleigh wave is named after John William Strutt, also known as Lord Rayleigh, who predicted the existence of the wave in 1885. The Rayleigh wave speed cR is in the range 0.90b < cR < 0.95b (Lay and Wallace, p. 122).

Lay, Thorne, and Wallace, Terry C. 1995, Modern Global Seismology (San Diego, California: Academic Press).

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Earthquake Magnitudes


QUESTIONS

Identify the magnitude scale described in each of the following cases.

1. In the late 1960's, the Geological Survey of Canada (GSA) started using this magnitude scale based on the maximum amplitude of Rayleigh's surface waves at 1 Hz.

2. This magnitude scale was developed by American geophysicist Charles Richter (1900-1985) in 1935. It is the base-ten logarithm of the maximum seismic wave amplitude, measured in microns, recorded on a standard (Wood-Anderson) seismograph at a distance of 100 km from the earthquake epicenter.

3. In 1977, Japanese seismologist Hiroo Kanamori defined this magnitude scale as a measure of the size or dissipated energy of an earthquake. It is related to the earthquake's dissipated energy.

4. This magnitude is based on the amplitude of the primary (P) wave train at 1 Hz and is used for earthquakes at teleseismic distances from ~ 16-100°. It was proposed by German-American seismologist Beno Gutenberg (1889-1960) in 1945.

5. In 1936, Beno Gutenberg and Charles Richter developed this magnitude scale which is used for shallow (depth < 70 km) earthquakes at teleseismic distances from ~ 20-180°. It uses the 20 s (0.05 Hz) Rayleigh wave.

ANSWERS

1. Nuttli magnitude mN
2. Richter magnitude ML
3. moment magnitude MW
4. body-wave magnitude mb
5. surface-wave magnitude Ms

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Earthquake Rupture Parameters

PROBLEM

The 1906 San Francisco earthquake had a moment magnitude of M = 7.8 (http://neic.usgs.gov/neis/eq_depot/usa/1906_04_18.html), a rupture length of 430 km (Bolt 1993), and a strike-slip faulting mechanism.
(a) Calculate the seismic moment released by the earthquake.
(b) Calculate the rupture area.
(c) Calculate the rupture width.

SOLUTION

(a) The seismic moment is

M0 = 101.5(M+6) N m = 101.5(7.8+6) N m = 1020.7 N m = 5.012 x 1020 N m

(b) Use the Wells and Coppersmith (1994) formula for rupture area for strike-slip faulting.

RA = 10-3.42+0.90M km2 = 10-3.42+0.90(7.8) km2 = 103.6 km2 = 3981 km2

(c) To obtain the rupture width, divide the rupture area by the rupture length.

RW = RA / RL = (3981 km) / (430 km) = 9.258 km

Bolt, Bruce A. 1993, Earthquakes (New York: W. H. Freeman).

Wells, Donald L., and Coppersmith, Kevin J. 1994, "New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement," Bull. Seism. Soc. Am., 84, 974-1002.

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Tsunamis

PROBLEM

A great earthquake of magnitude M = 8.9 occurs off the coast of Alaska with its epicenter located at (longitude, latitude) = (147.73W, 61.94N) = (-147.730, 61.940) deg, causing a tsunami. Neglect the focal depth of this earthquake and estimate the time it takes for the tsunami waves to reach (a) Tokyo, Japan; (b) San Francisco, California; (c) Honolulu, Hawaii; and (d) Auckland, New Zealand.

SOLUTION

We use coordinates for the cities from the Oxford Atlas of the World, Eleventh Edition.

(a) Tokyo

(longitude, latitude) = (139d 45m E, 35d 45m N) = (139.750, 35.750) deg

Convert to spherical coordinates.

rsite = 6.37 x 103 km
qsite = 90 deg - latitude = 90 deg - 35.750 deg = 54.250 deg
fsite = longitude = 139.750 deg

Convert to Cartesian coordinates.

xsite = r sin qsite cos fsite = - 3945.694 km
ysite = r sin qsite sin fsite = 3340.290 km
zsite = r cos qsite = 3721.675 km

Convert the epicenter coordinates to spherical coordinates.

repi = 6.37 x 103 km
qepi = 90 deg - latitude = 90 deg - 61.940 deg = 28.060 deg
fepi = longitude = - 147.730 deg

Convert to Cartesian coordinates.

xepi = r sin qepi cos fepi = - 2533.594 km
yepi = r sin qepi sin fepi = - 1599.823 km
zepi = r cos qsite = 5621.243 km

Calculate the straight line distance d from the epicenter to Tokyo.

d = sqrt[(xsite - xepi)2 + (ysite - yepi)2 + (zsite - zepi)2] = 5477.874 km

The distance dsurf along the surface of the Earth is related to d according to

dsurf = 2Re sin-1(d/2Re)

where Re = 6.37 x 103 km is the radius of the Earth. Thus,

dsurf = 5662.477 km

We take the speed of tsunami waves to be v = 800 km/hr (Keller and Pinter 1996). Thus, the time it takes for the tsunami waves to reach Tokyo is

t = dsurf/v = 7.078 hr

(b) San Francisco

(longitude, latitude) = (122d 25m W, 37d 47m N) = (-122.417, 37.783) deg

rsite = 6.37 x 103 km
qsite = 52.217 deg
fsite = - 122.417 deg

xsite = - 2698.806 km
ysite = - 4249.921 km
zsite = 3902.758 km

d = 3162.832 km
dsurf = 3196.257 km
t = 3.995 hr

(c) Honolulu

(longitude, latitude) = (157d 52m W, 21d 19m N) = (-157.867, 21.317) deg

rsite = 6.37 x 103 km
qsite = 68.683 deg
fsite = - 157.867 deg

xsite = - 5496.899 km
ysite = - 2235.800 km
zsite = 2315.643 km

d = 4484.711 km
dsurf = 4582.914 km
t = 5.729 hr

(d) Auckland

(longitude, latitude) = (174d 46m E, 36d 52m S) = (174.767, -36.867) deg

rsite = 6.37 x 103 km
qsite = 126.867 deg
fsite = 174.767 deg

xsite = - 5074.978 km
ysite = 464.849 km
zsite = - 3821.703 km

d = 9994.535 km
dsurf = 11490.079 km
t = 14.363 hr

Note: For a list of large earthquakes in or near the United States, go to http://neic.usgs.gov/neis/eqlists/large_usa.html.

Keller, E. A., and Pinter, N. 1996, Active Tectonics: Earthquake, Uplift, and Landscape (Upper Saddle River, New Jersey: Prentice Hall).

Oxford University Press 2003, Oxford Atlas of the World, Eleventh Edition (New York: Oxford University Press).

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