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PROBLEM 4–20 A mountain range can be represented as a periodic topography with a wavelength of 100 km and an amplitude of 1.2 km. Heat flow in a valley is measured to be 46 mW m-2. If the atmospheric gradi- ent is 6.5 K km-1 and k = 2.5 Wm-1 K-1, determine what the heat flow would have been without topog- raphy; that is, make a topographic correction.

PROBLEM 4–29 Estimate the effects of variations in bottom water temperature on measurements of oceanic heat flow by using the model of a semi-infinite half-space subjected to periodic surface temperature fluctuations. Such water temperature variations at a specific location on the ocean floor can be due to, for example, the transport of water with variable tem- perature past the site by deep ocean currents. Find the amplitude of water temperature variations that cause surface heat flux variations of 40 mW m-2 above and below the mean on a time scale of 1 day. As- sume that the thermal conductivity of sediments is 0.8 W m-1 K-1 and the sediment thermal diffusivity is 0.2 mm2 s-1.

PROBLEM 4–33 One way of determining the effects of erosion on subsurface temperatures is to consider the instantaneous removal of a thickness l of ground. Prior to the removal T = T0 + ßy, where y is the depth, ß is the geothermal gradient, and T0 is the surface temperature. After removal, the new surface is main- tained at temperature T0. Show that the subsurface temperature after the removal of the surface layer is given by

How is the surface heat flow affected by the removal of surface material?

PROBLEM 4–39 One of the estimates for the age of the Earth given by Lord Kelvin in the 1860s assumed that Earth was initially molten at a constant tem- perature Tm and that it subsequently cooled by con- duction with a constant surface temperature T0. The age of the Earth could then be determined from the present surface thermal gradient (dT/dy)0. Re- produce Kelvin’s result assuming Tm T0 = 1700 K, c=1 kJ kg-1 K-1, L =400 kJ kg-1, ? =1 mm2 s-1, and (dT/dy)0 = 25 K km-1 . In addition, determine the thickness of the solidified lithosphere. Note: Since the solidified layer is thin compared with the Earth’s radius, the curvature of the surface may be neglected.

PROBLEM4–43 Themantlerocksoftheasthenosphere from which the lithosphere forms are expected to contain a small amount of magma. If the mass frac- tion of magma is 0.05, determine the depth of the lithosphere–asthenosphere boundary for oceanic li- thosphere with an age of 60 Ma. Assume L = 400 kJ kg-1,c=1kJkg-1 K-1,Tm =1600K,T0 =275K,and ? = 1 mm2 s-1.

PROBLEM 4–52 The ocean ridges are made up of a series of parallel segments connected by transform faults, as shown in Figure 1–13. Because of the dif- ference of age there is a vertical offset on the fracture zones. Assuming the theory just derived is applica- ble, what is the vertical offset (a) at the ridge crest and (b) 100 km from the ridge crest in Figure 4–46 (?m = 3300kgm-3,?=1mm2s-1,av =3×10-5 K-1,T1- T0=1300K,u=50mmyr-1).

PROBLEM 5–7 What is the value of the acceleration of gravity at a distance b above the geoid at the equator (b « a)?

PROBLEM 5–18 A volcanic plug of diameter 10 km has a gravity anomaly of 0.3 mm s-2. Estimate the depth of the plug assuming that it can be modeled by a verti- cal cylinder whose top is at the surface. Assume that the plug has density of 3000 kg m-3 and the rock it intrudes has a density of 2800 kg m-3.

PROBLEM 4–20 A mountain range can be represented as a periodic topography with a wavelength of 100 km and an amplitude of 1.2 km. Heat flow in a valley is measured to be 46 mW m-2. If the atmospheric gradi- ent is 6.5 K km-1 and
k = 2.5 Wm-1 K-1, determine what the heat flow would have been without topog- raphy; that is, make a topographic correction.

PROBLEM 4–29 Estimate the effects of variations in bottom water temperature on measurements of oceanic heat flow by using the model of a semi-infinite half-space subjected to periodic surface temperature fluctuations. Such water temperature variations at a specific location on the ocean floor can be due to, for example, the transport of water with variable tem- perature past the site by deep ocean currents. Find the amplitude of water temperature variations that cause surface heat flux variations of 40 mW m-2 above and below the mean on a time scale of 1 day. As- sume that the thermal conductivity of sediments is 0.8 W m-1 K-1 and the sediment thermal diffusivity is 0.2 mm2 s-1.

PROBLEM 4–33 One way of determining the effects of erosion on subsurface temperatures is to consider the instantaneous removal of a thickness
l of ground. Prior to the removal
T =
T0 + ß
y, where
y is the depth, ß is the geothermal gradient, and
T0 is the surface temperature. After removal, the new surface is main- tained at temperature
T0. Show that the subsurface temperature after the removal of the surface layer is given by

How is the surface heat flow affected by the removal of surface material?

PROBLEM 4–39 One of the estimates for the age of the Earth given by Lord Kelvin in the 1860s assumed that Earth was initially molten at a constant tem- perature
Tm and that it subsequently cooled by con- duction with a constant surface temperature
T0. The age of the Earth could then be determined from the present surface thermal gradient (
dT/
dy)0. Re- produce Kelvin’s result assuming
Tm
T0 = 1700 K,
c=1 kJ kg-1 K-1,
L =400 kJ kg-1, ? =1 mm2 s-1, and (
dT/
dy)0 = 25 K km-1 . In addition, determine the thickness of the solidified lithosphere. Note: Since the solidified layer is thin compared with the Earth’s radius, the curvature of the surface may be neglected.

PROBLEM4–43 Themantlerocksoftheasthenosphere from which the lithosphere forms are expected to contain a small amount of magma. If the mass frac- tion of magma is 0.05, determine the depth of the lithosphere–asthenosphere boundary for oceanic li- thosphere with an age of 60 Ma. Assume
L = 400 kJ kg-1,

Geodynamics

First published in 1982, Don Turcotte and Jerry Schubert’s Geodynamics be-

came a classic textbook for several generations of students of geophysics and

geology. In this second edition, the authors bring this classic text completely

up-to-date. Important additions include a chapter on chemical geodynamics,

an updated coverage of comparative planetology based on recent planetary

missions, and a variety of other new topics.

Geodynamics provides the fundamentals necessary for an understanding of

the workings of the solid Earth. The Earth is a heat engine, with the source

of the heat the decay of radioactive elements and the cooling of the Earth

from its initial accretion. The work output includes earthquakes, volcanic

eruptions, and mountain building. Geodynamics comprehensively explains

these concepts in the context of the role of mantle convection and plate

tectonics. Observations such as the Earth’s gravity field, surface heat flow,

distribution of earthquakes, surface stresses and strains, and distribution of

elements are discussed. The rheological behavior of the solid Earth, from an

elastic solid to fracture to plastic deformation to fluid flow, is considered.

Important inputs come from a comparison of the similarities and differences

between the Earth, Venus, Mars, Mercury, and the Moon. An extensive set

of student exercises is included.

This new edition of Geodynamics will once again prove to be a classic

dents in geology, geophysics, and Earth science.

Donald L. Turcotte is Maxwell Upson Professor of Engineering, Depart-

ment of Geological Sciences, Cornell University. In addition to this book, he

is author or co-author of 3 books and 276 research papers, including Fractals

and Chaos in Geology and Geophysics (Cambridge University Press, 1992

and 1997) and Mantle Convection in the Earth and Planets (with Gerald

Schubert and Peter Olson; Cambridge University Press, 2001). Professor

Turcotte is a Fellow of the American Geophysical Union, Honorary Fellow

of the European Union of Geosciences, and Fellow of the Geological So-

ciety of America. He is the recipient of several medals, including the Day

Medal of the Geological Society of America, the Wegener Medal of the Euro-

pean Union of Geosciences, the Whitten Medal of the American Geophysical

Union, the Regents (New York State) Medal of Excellence, and Caltech’s

Distinguished Alumnus Award. Professor Turcotte is a member of the Na-

tional Academy of Sciences and the American Academy of Arts and Sciences.

Gerald

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