282 Earthquakes
Mavko (1981) reviews fault models and the use of geodetic data to study
faulting, and Burgmann et al. (2000) review the use of radar interferometry. References for topics related to the tectonic setting of earthquakes,
use of the Global Positioning System, and the relation of earthquakes to
fault mechanics are given at the end of Chapter 5.
A detailed discussion of earthquake magnitudes is presented by Geller
and Kanamori (1977). Relations between fault parameters are given in
Kanamori and Anderson (1975); source spectra and scaling laws are discussed by Geller (1976). Our treatment of moment magnitude and earthquake energy follows Kanamori (1977a) and Hanks and Kanamori (1979).
Atkinson and Beresnev (1997) discuss the relation between stress drop as
a source parameter and as a tectonic quantity. Okal and Romanowicz
(1994) give an overview of frequency–magnitude relations. Turcotte
(1992) and Main (1996) review self-similar models for earthquakes.
References for topics related to earthquake forecasting and seismic gaps
are given at the end of Chapter 1. In particular, Kagan and Jackson (1991)
discuss the challenge of testing forecasts.
A voluminous literature deals with studies of individual earthquakes,
especially those that are of special interest because of their size, damage, tectonic setting, or location near centers of seismological research.
Some recent examples include issues of the Bulletin of the Seismological
Society of America dealing with the 1989 Loma Prieta (October 1991
issue), 1992 Landers (June 1994 issue), and 1994 Northridge (February 1996 issue) earthquakes. Detailed studies of other earthquakes can
often be found using the American Geological Institute’s Georef WWW
search tool, available through many earth science departments and
libraries. The locations and focal mechanisms of post-1977 earthquakes
around the world are available at http://www.seismology.harvard.edu/
CMTsearch.html, and information about earthquakes in specific areas,
including seismograms, can often be found at WWW sites compiled
at http://www.geophys.washington.edu/seismosurfing.html or http://
www.iris.edu.
Further reading
Other treatments of earthquake sources are given by texts such as
Ben-Menahem and Singh (1981), Gubbins (1990), Lay and Wallace
(1995), and Shearer (1999). Many of the results presented here without
proof are derived in Aki and Richards (1980).
Some specific topics are covered in individual reviews. Kanamori (1994)
gives an overview of earthquake source parameters and earthquake
mechanics; papers in Kanamori and Boschi (1983) review various topics
about earthquake sources. Structural geology texts such as Ragan (1968)
discuss stereonet techniques. Jarosch and Aboodi (1970) derive analytic
expressions for the relations between the fault and auxiliary planes and
the stress axes. Helmberger and Burdick (1979), Kanamori and Stewart
(1976), and Okal (1992) discuss body wave modeling. For reasons including compatibility of notation, our treatment of body wave modeling follows the latter two, that for surface wave modeling follows Kanamori and
Stewart (1976), and that for moment tensor inversion follows Kanamori
and Given (1981). Jost and Hermann (1989) give a general review of
moment tensor inversion, and Dziewonski et al. (1981) summarize the
Harvard CMT approach. Okal and Geller (1979) explore spurious isotropic moment tensor components due to lateral heterogeneity, Michael
and Geller (1984) discuss inverting surface wave data with one nodal plane
constrained, and Romanowicz and Guillemant (1984) discuss inverting
surface waves for depth determination.
Opposing (double-couple versus slump) source models for the 1929
Grand Banks earthquake are explored by Hasegawa and Kanamori (1987)
and Bent (1995); Tappin et al. (1999) discuss a slump origin for the 1998
New Guinea tsunami. Julian and Sipkin (1985) and Wallace (1985) consider CLVD versus double-couple models for earthquakes in the Long
Valley caldera. Heaton and Hartzell (1988) discuss source study using
near-field earthquake ground motions.
General treatments of geodesy include those by Lambeck (1988) and
Torge (1991). Geodetic solutions for faults are given by Okada (1985).
Problems
1. Using the travel time chart in Fig. 3.5-4 for earthquakes at a depth
of 600 km, graph the take-off angle of the P wave for stations at
distances from 2000 to 10,000 km. Assume that the P velocity at
600 km depth is 10 km/s. Use enough points for a smooth graph.
2. Plot the following focal mechanisms on a stereonet by using the
relations in Section 4.2.5 to find the second nodal plane. Indicate
the compressional and dilatational quadrants, mark the P and T
axes, and describe the type of faulting. Use the conventions of
Fig. 4.2-2, and remember that dip is defined from the −x 2 axis
and is less than 90°.
(a) φ = 330°, δ = 65°, λ = 70°
(b) φ = 280°, δ = 60°, λ = 270°
(c) φ = 280°, δ = 60°, λ = 90°
(d) φ = 40°, δ = 80°, λ = 20°
(e) φ = 40°, δ = 80°, λ = 200°
3. Figure P4.1 gives a stereonet and first motion data for four earthquakes on stereonets of the same scale. Closed circles show compressions, and open circles show dilatations. To evaluate the focal
mechanism for each earthquake:
(i) Find nodal planes that you consider the best solution. Show
these planes on the first motion plots, and measure their
strikes and dips.
(ii) Find two planes bounding the acceptable range for each
nodal plane.
(iii) For each best choice nodal plane, give the motion (rightlateral strike-slip, left-lateral strike-slip, dip-slip – thrust or
normal) implied by the focal mechanism for slip on that
nodal plane. If the faulting is a combination of the above,
give the dominant type.
(iv) Find the B, P, and T axes and the two possible slip angles
(one for each nodal plane) implied by the best choice nodal
planes. Check that these are consistent with the answers to
part iii.
4. If a P wave leaves the focal sphere exactly on a nodal plane, it
should theoretically have zero amplitude. Explain why this is not
the case in reality.
5. Derive the travel time for sP (Eqn 4.3.11) using a geometry similar
to that of Fig. 4.3-6 (bottom).
6. For a fault plane solution in which one plane has strike φ 1 and
dip δ 1 , and the second plane is striking at φ 2 , show that tan λ 1 =
cot (φ 2 − φ 1 )/cos δ 1 . For what angles will this not apply?
7. Compute the Love wave amplitude radiation pattern for an
isotropic source.
8. Use the expression for the moment tensor of a double couple
(Eqn 4.4.5) to prove that it obeys the tensor transformation law
(Eqn 2.3.18).
9. (a) Show how the moment tensor for a vertical dipole can be
decomposed into an isotropic source and a CLVD.
Mavko (1981) reviews fault models and the use of geodetic data to study
faulting, and Burgmann et al. (2000) review the use of radar interferometry. References for topics related to the tectonic setting of earthquakes,
use of the Global Positioning System, and the relation of earthquakes to
fault mechanics are given at the end of Chapter 5.
A detailed discussion of earthquake magnitudes is presented by Geller
and Kanamori (1977). Relations between fault parameters are given in
Kanamori and Anderson (1975); source spectra and scaling laws are discussed by Geller (1976). Our treatment of moment magnitude and earthquake energy follows Kanamori (1977a) and Hanks and Kanamori (1979).
Atkinson and Beresnev (1997) discuss the relation between stress drop as
a source parameter and as a tectonic quantity. Okal and Romanowicz
(1994) give an overview of frequency–magnitude relations. Turcotte
(1992) and Main (1996) review self-similar models for earthquakes.
References for topics related to earthquake forecasting and seismic gaps
are given at the end of Chapter 1. In particular, Kagan and Jackson (1991)
discuss the challenge of testing forecasts.
A voluminous literature deals with studies of individual earthquakes,
especially those that are of special interest because of their size, damage, tectonic setting, or location near centers of seismological research.
Some recent examples include issues of the Bulletin of the Seismological
Society of America dealing with the 1989 Loma Prieta (October 1991
issue), 1992 Landers (June 1994 issue), and 1994 Northridge (February 1996 issue) earthquakes. Detailed studies of other earthquakes can
often be found using the American Geological Institute’s Georef WWW
search tool, available through many earth science departments and
libraries. The locations and focal mechanisms of post-1977 earthquakes
around the world are available at http://www.seismology.harvard.edu/
CMTsearch.html, and information about earthquakes in specific areas,
including seismograms, can often be found at WWW sites compiled
at http://www.geophys.washington.edu/seismosurfing.html or http://
www.iris.edu.
Further reading
Other treatments of earthquake sources are given by texts such as
Ben-Menahem and Singh (1981), Gubbins (1990), Lay and Wallace
(1995), and Shearer (1999). Many of the results presented here without
proof are derived in Aki and Richards (1980).
Some specific topics are covered in individual reviews. Kanamori (1994)
gives an overview of earthquake source parameters and earthquake
mechanics; papers in Kanamori and Boschi (1983) review various topics
about earthquake sources. Structural geology texts such as Ragan (1968)
discuss stereonet techniques. Jarosch and Aboodi (1970) derive analytic
expressions for the relations between the fault and auxiliary planes and
the stress axes. Helmberger and Burdick (1979), Kanamori and Stewart
(1976), and Okal (1992) discuss body wave modeling. For reasons including compatibility of notation, our treatment of body wave modeling follows the latter two, that for surface wave modeling follows Kanamori and
Stewart (1976), and that for moment tensor inversion follows Kanamori
and Given (1981). Jost and Hermann (1989) give a general review of
moment tensor inversion, and Dziewonski et al. (1981) summarize the
Harvard CMT approach. Okal and Geller (1979) explore spurious isotropic moment tensor components due to lateral heterogeneity, Michael
and Geller (1984) discuss inverting surface wave data with one nodal plane
constrained, and Romanowicz and Guillemant (1984) discuss inverting
surface waves for depth determination.
Opposing (double-couple versus slump) source models for the 1929
Grand Banks earthquake are explored by Hasegawa and Kanamori (1987)
and Bent (1995); Tappin et al. (1999) discuss a slump origin for the 1998
New Guinea tsunami. Julian and Sipkin (1985) and Wallace (1985) consider CLVD versus double-couple models for earthquakes in the Long
Valley caldera. Heaton and Hartzell (1988) discuss source study using
near-field earthquake ground motions.
General treatments of geodesy include those by Lambeck (1988) and
Torge (1991). Geodetic solutions for faults are given by Okada (1985).
Problems
1. Using the travel time chart in Fig. 3.5-4 for earthquakes at a depth
of 600 km, graph the take-off angle of the P wave for stations at
distances from 2000 to 10,000 km. Assume that the P velocity at
600 km depth is 10 km/s. Use enough points for a smooth graph.
2. Plot the following focal mechanisms on a stereonet by using the
relations in Section 4.2.5 to find the second nodal plane. Indicate
the compressional and dilatational quadrants, mark the P and T
axes, and describe the type of faulting. Use the conventions of
Fig. 4.2-2, and remember that dip is defined from the −x 2 axis
and is less than 90°.
(a) φ = 330°, δ = 65°, λ = 70°
(b) φ = 280°, δ = 60°, λ = 270°
(c) φ = 280°, δ = 60°, λ = 90°
(d) φ = 40°, δ = 80°, λ = 20°
(e) φ = 40°, δ = 80°, λ = 200°
3. Figure P4.1 gives a stereonet and first motion data for four earthquakes on stereonets of the same scale. Closed circles show compressions, and open circles show dilatations. To evaluate the focal
mechanism for each earthquake:
(i) Find nodal planes that you consider the best solution. Show
these planes on the first motion plots, and measure their
strikes and dips.
(ii) Find two planes bounding the acceptable range for each
nodal plane.
(iii) For each best choice nodal plane, give the motion (rightlateral strike-slip, left-lateral strike-slip, dip-slip – thrust or
normal) implied by the focal mechanism for slip on that
nodal plane. If the faulting is a combination of the above,
give the dominant type.
(iv) Find the B, P, and T axes and the two possible slip angles
(one for each nodal plane) implied by the best choice nodal
planes. Check that these are consistent with the answers to
part iii.
4. If a P wave leaves the focal sphere exactly on a nodal plane, it
should theoretically have zero amplitude. Explain why this is not
the case in reality.
5. Derive the travel time for sP (Eqn 4.3.11) using a geometry similar
to that of Fig. 4.3-6 (bottom).
6. For a fault plane solution in which one plane has strike φ 1 and
dip δ 1 , and the second plane is striking at φ 2 , show that tan λ 1 =
cot (φ 2 − φ 1 )/cos δ 1 . For what angles will this not apply?
7. Compute the Love wave amplitude radiation pattern for an
isotropic source.
8. Use the expression for the moment tensor of a double couple
(Eqn 4.4.5) to prove that it obeys the tensor transformation law
(Eqn 2.3.18).
9. (a) Show how the moment tensor for a vertical dipole can be
decomposed into an isotropic source and a CLVD.