212 Seismology and Earth Structure
Gibson and Levander (1988) discuss posible artifacts in lower crustal reflection data.
The extensive literature on reflection seismology includes the introductory exploration texts listed above and advanced treatments, including
Claerbout (1976, 1985), Robinson and Treitel (1980), Waters (1981),
Sheriff and Geldart (1982), Robinson (1983), and Yilmaz (1987). The subject is closely allied to that of geophysical signal processing, discussed in
texts including Kanasewich (1981) and Hatton et al. (1986).
Applications of seismology to earth structure are discussed in texts and
the research literature. Introductory texts such as Bolt (1982), Bott (1982),
Gubbins (1990), Doyle (1995), Lay and Wallace (1995), Lowrie (1997),
Shearer (1999), and Udias (1999), have good overviews. Simon (1981) is
a manual for seismogram interpretation, showing examples of records
for earthquakes at various distances and depths. The classic texts by
Gutenberg (1959) and Jeffreys (1976) are excellent starting points for
further treatment of the data and methods. Bullen and Bolt (1985) has a
detailed discussion of ray theory for the spherical earth. Aki and Richards
(1980), Ben-Menahem and Singh (1981), and Kennett (1983) treat both
ray theory and more advanced methods. The normal mode simulation
of body wave propagation shown in Fig. 3.5-19 is available at http://
epsc.wustl.edu/seismology/michael/movie.html.
Karato and Spetzler (1990) review the physical mechanisms causing
anelasticity. Information about anisotropy can be found in Babuska and
Cara (1991) and Silver (1996). For discussion of scattering and attenuation, see Kanamori and Anderson (1977), Brennan and Smylie (1981),
Jackson (1993), Mitchell (1995), Sato and Fehler (1998), and Romanowicz
(1998). Garnero (2000) summarizes results for the lateral heterogeneity of
the lowermost mantle.
We alluded only briefly to the nonseismological geophysical data and to
chemical results applicable to study of the earth’s interior. In addition to
journal articles, useful texts are those by Wyllie (1971), Bullen (1975),
Ringwood (1975), Wood and Fraser (1977), Brown and Mussett (1993),
Bott (1982), Melchior (1986), Jacobs (1987), Lambeck (1988), Anderson
(1989), Stacey (1992), and Poirier (2000). Useful reviews can be found in
McElhinny (1979), Ahrens (1995a, b, c), Boschi et al. (1996), Boehler
(1996), Crossley (1997), Gurnis et al. (1998), and Davies (1999).
From such arguments, we might expect Mercury and Mars,
which are larger than the moon but smaller than the earth,
to have also reached their old age with little further active
tectonics. Mercury may still have a small liquid core, which
contributes to the observed magnetic field, due to tidal forces
from the sun. Venus, which is comparable in size to the earth,
might still be active but with episodic, rather than continuous,
plate tectonics. Seismology can contribute little to the active
discussion of these topics until seismometers are deployed on
these planets. Although only one seismometer has been operated on Mars and yielded inconclusive results, 13 seismometers
are planned for future missions.
Further reading
Refraction seismology and its use in crustal studies are covered in many
general geophysics texts, such as Fowler (1990) and Reynolds (1997).
More detailed treatments can be found in exploration textbooks like
Dobrin and Savit (1988), Sheriff and Geldart (1982), Telford et al. (1976),
and Kearey and Brooks (1984). Additional information can be obtained
in review papers such as Braile and Smith (1975), Kennett (1977), or
Spudich and Orcutt (1980). A summary of crustal structure results and
interpretations for the continental USA can be found in Pakiser and
Mooney (1989). Meissner (1986) presents an integrated treatment of
observations and models for the continental crust. Reviews on the nature
of the Mohorovibia discontinuity are given by Jarchow and Thompson
(1989), Braile and Chiang (1986), and Fountain and Christensen (1989).
13 Due to operational constraints, the seismometer was mounted on the lander
portion of the spacecraft, rather than in direct contact with Mars. It is rumored that
consideration was given to saving weight on the lander by moving the seismometer to
the orbiter.
Problems
(a) Derive the travel time to distance x for a wave that is incident
on the boundary at a distance y from the source, travels
for some distance just below the boundary, and then returns
to the surface at the same incidence angle at which it went
down.
(b) Find the y value giving an extremal travel time, and show
that it corresponds to the critical angle of incidence.
(c) Determine if this travel time is a minimum or a maximum.
5. Use the data for the reversed profile shown in Fig. P3.2 to find the
crust and mantle velocities, Moho dip, and crustal thickness.
6. (a) Derive the travel time for the head wave on the up-dip path of a
reversed profile with a dipping layer (Eqn 3.2.17).
(b) Show that the equations for the travel time of the head wave
for a dipping layer (Eqns 3.2.16 and 3.2.17) reduce to the flat
layer result in the case of zero dip.
7. Derive the Dix equation for interval velocity (Eqn 3.3.19) from the
formula for rms velocity.
8. Consider two pairs of seismograms. One pair have the same midpoint, but the offset for one record is the negative of the first. The
other pair have the same source point, but the offset for one record
1. Use the data from the refraction experiment in Fig. 3.2-5 to find the
crust and mantle velocities and the crustal thickness. Remember
that this is a reduced travel time plot.
2. For a case of two layers overlying a halfspace, derive an expression
for the thickness of the second (deeper) layer in terms of the second
crossover distance.
3. Analyze the data from the marine refraction experiment (Lewis,
1978) shown in Fig. P3.1, assuming for simplicity that the structure
consists of a water layer, a crustal layer, and a mantle halfspace.
(a) Assuming that the first arrivals are described by two line
segments, for head waves at the top of the crust and mantle,
find the corresponding velocities.
(b) Although the direct wave traveling in the water layer is not
shown, the P velocity for water is 1.5 km/s. Use the time
intercept for the crustal head wave to find the water depth.
(c) Use the time intercept for the P n wave to find the crustal
thickness.
4. To show that the head wave is predicted by Fermat’s principle,
consider a layer of thickness h with velocity v 0 , overlying a
halfspace with a higher velocity, v 1 .
Gibson and Levander (1988) discuss posible artifacts in lower crustal reflection data.
The extensive literature on reflection seismology includes the introductory exploration texts listed above and advanced treatments, including
Claerbout (1976, 1985), Robinson and Treitel (1980), Waters (1981),
Sheriff and Geldart (1982), Robinson (1983), and Yilmaz (1987). The subject is closely allied to that of geophysical signal processing, discussed in
texts including Kanasewich (1981) and Hatton et al. (1986).
Applications of seismology to earth structure are discussed in texts and
the research literature. Introductory texts such as Bolt (1982), Bott (1982),
Gubbins (1990), Doyle (1995), Lay and Wallace (1995), Lowrie (1997),
Shearer (1999), and Udias (1999), have good overviews. Simon (1981) is
a manual for seismogram interpretation, showing examples of records
for earthquakes at various distances and depths. The classic texts by
Gutenberg (1959) and Jeffreys (1976) are excellent starting points for
further treatment of the data and methods. Bullen and Bolt (1985) has a
detailed discussion of ray theory for the spherical earth. Aki and Richards
(1980), Ben-Menahem and Singh (1981), and Kennett (1983) treat both
ray theory and more advanced methods. The normal mode simulation
of body wave propagation shown in Fig. 3.5-19 is available at http://
epsc.wustl.edu/seismology/michael/movie.html.
Karato and Spetzler (1990) review the physical mechanisms causing
anelasticity. Information about anisotropy can be found in Babuska and
Cara (1991) and Silver (1996). For discussion of scattering and attenuation, see Kanamori and Anderson (1977), Brennan and Smylie (1981),
Jackson (1993), Mitchell (1995), Sato and Fehler (1998), and Romanowicz
(1998). Garnero (2000) summarizes results for the lateral heterogeneity of
the lowermost mantle.
We alluded only briefly to the nonseismological geophysical data and to
chemical results applicable to study of the earth’s interior. In addition to
journal articles, useful texts are those by Wyllie (1971), Bullen (1975),
Ringwood (1975), Wood and Fraser (1977), Brown and Mussett (1993),
Bott (1982), Melchior (1986), Jacobs (1987), Lambeck (1988), Anderson
(1989), Stacey (1992), and Poirier (2000). Useful reviews can be found in
McElhinny (1979), Ahrens (1995a, b, c), Boschi et al. (1996), Boehler
(1996), Crossley (1997), Gurnis et al. (1998), and Davies (1999).
From such arguments, we might expect Mercury and Mars,
which are larger than the moon but smaller than the earth,
to have also reached their old age with little further active
tectonics. Mercury may still have a small liquid core, which
contributes to the observed magnetic field, due to tidal forces
from the sun. Venus, which is comparable in size to the earth,
might still be active but with episodic, rather than continuous,
plate tectonics. Seismology can contribute little to the active
discussion of these topics until seismometers are deployed on
these planets. Although only one seismometer has been operated on Mars and yielded inconclusive results, 13 seismometers
are planned for future missions.
Further reading
Refraction seismology and its use in crustal studies are covered in many
general geophysics texts, such as Fowler (1990) and Reynolds (1997).
More detailed treatments can be found in exploration textbooks like
Dobrin and Savit (1988), Sheriff and Geldart (1982), Telford et al. (1976),
and Kearey and Brooks (1984). Additional information can be obtained
in review papers such as Braile and Smith (1975), Kennett (1977), or
Spudich and Orcutt (1980). A summary of crustal structure results and
interpretations for the continental USA can be found in Pakiser and
Mooney (1989). Meissner (1986) presents an integrated treatment of
observations and models for the continental crust. Reviews on the nature
of the Mohorovibia discontinuity are given by Jarchow and Thompson
(1989), Braile and Chiang (1986), and Fountain and Christensen (1989).
13 Due to operational constraints, the seismometer was mounted on the lander
portion of the spacecraft, rather than in direct contact with Mars. It is rumored that
consideration was given to saving weight on the lander by moving the seismometer to
the orbiter.
Problems
(a) Derive the travel time to distance x for a wave that is incident
on the boundary at a distance y from the source, travels
for some distance just below the boundary, and then returns
to the surface at the same incidence angle at which it went
down.
(b) Find the y value giving an extremal travel time, and show
that it corresponds to the critical angle of incidence.
(c) Determine if this travel time is a minimum or a maximum.
5. Use the data for the reversed profile shown in Fig. P3.2 to find the
crust and mantle velocities, Moho dip, and crustal thickness.
6. (a) Derive the travel time for the head wave on the up-dip path of a
reversed profile with a dipping layer (Eqn 3.2.17).
(b) Show that the equations for the travel time of the head wave
for a dipping layer (Eqns 3.2.16 and 3.2.17) reduce to the flat
layer result in the case of zero dip.
7. Derive the Dix equation for interval velocity (Eqn 3.3.19) from the
formula for rms velocity.
8. Consider two pairs of seismograms. One pair have the same midpoint, but the offset for one record is the negative of the first. The
other pair have the same source point, but the offset for one record
1. Use the data from the refraction experiment in Fig. 3.2-5 to find the
crust and mantle velocities and the crustal thickness. Remember
that this is a reduced travel time plot.
2. For a case of two layers overlying a halfspace, derive an expression
for the thickness of the second (deeper) layer in terms of the second
crossover distance.
3. Analyze the data from the marine refraction experiment (Lewis,
1978) shown in Fig. P3.1, assuming for simplicity that the structure
consists of a water layer, a crustal layer, and a mantle halfspace.
(a) Assuming that the first arrivals are described by two line
segments, for head waves at the top of the crust and mantle,
find the corresponding velocities.
(b) Although the direct wave traveling in the water layer is not
shown, the P velocity for water is 1.5 km/s. Use the time
intercept for the crustal head wave to find the water depth.
(c) Use the time intercept for the P n wave to find the crustal
thickness.
4. To show that the head wave is predicted by Fermat’s principle,
consider a layer of thickness h with velocity v 0 , overlying a
halfspace with a higher velocity, v 1 .