Seismic waves
Elastic seismic energy released during an earthquake
travels away from the hypocenter as body waves through
the Earth and also, as a result of wave interference near
the Earth’s surface, as surface waves. On the seismic timescale, usually deciseconds up to almost 1 h for the longest
free oscillations of the whole planet, the Earth behaves as
an elastic body.
Compressional or P-waves (P for primary) propagate
by stretching and contracting the medium parallel to the
direction the wave travels through the entire Earth,
whereas in the case of shear or S-waves (S for secondary),
swinging is perpendicular to the direction of propagation.
Shear waves cannot travel through fluids. The fact that
already in early world-wide records of P- and S-waves
after the great 1897 magnitude 8.1 Assam earthquake no
direct S-waves were found that had traveled through the
Earth’s center led Dixon Oldham (1858–1936) to infer
the existence of an Earth core and to conclude that it was
liquid. This, however, relates only to the outer core, as
the existence of a solid inner core was later proved by Inge
Lehmann (1888–1993) in 1936.
Seismic P-waves travel at sound velocities of about
1.5 km per second in water and faster, i.e., several km
per second, in most rocks. In sedimentary rocks,
P-waves are as fast as between about 1.5 and 6 km per second, whereas in crystalline, igneous, and metamorphic
crustal rocks they usually are faster, between about 4 and
7 km per second, and in the uppermost mantle around
8 km per second. In highly porous rocks or loose sediments, seismic velocities often are similar to those in water
or even lower. S-waves travel about 1.7 times more slowly
than P-waves. The velocity ratio between P- and S-waves
depends, e.g., on fluid content and therefore differs
slightly between various tectonic settings and in the presence of significant amounts of fluid or major fluid motion.
Therefore, it can be used to study the role of fluids for
earthquake processes (e.g., Schurr et al., 2003; EberhartPhillips et al., 2008).
There are also two types of surface waves, Rayleigh
waves (LR) and Love waves (LQ). While Rayleigh waves
swing in the vertical plane with particles moving along a
retrograde ellipse, particle motion of Love-waves is horizontal and transverse to the travel direction. Love waves
are the fastest surface waves and travel with velocities
close to the subsurface velocity of S-waves, whereas Rayleigh waves travel slightly slower, with about 90 % of the
shear wave velocity. Although surface waves generated by
crustal earthquakes are associated with generally larger
amplitudes of ground motion than body waves, their
periods are also significantly longer (see Figure 1b).
Therefore, in the local distance of several tens to hundred
kilometers, the largest destructions are usually associated
with shear waves and Love waves, and not with true surface waves.
Seismic waves are reflected and refracted at lithological, rheological, diagenetic, or other boundaries with a
contrast in acoustic impedance, i.e., the product of seismic
velocity and density. Besides reflection and refraction,
seismic waves can also undergo conversion, e.g., from a
P- to an S-wave, and vice versa. Thus, the body waves
P and S originating from the earthquake source will be
split in many phases, due to the interaction with many
velocity discontinuities and inhomogeneities along their
way through the subsurface and the deeper parts of the
Earth’s interior. These different phases usually arrive
along different and sometimes rather complicated travel
paths at different times at a distant seismograph. The different wave onsets can be identified one after the other;
however, one has to keep in mind that the arrival of some
theoretically possible but weaker later waves may be
masked through the coda of other, earlier waves. Because
of damping and geometric spreading, but also focusing
effects due to the complicated velocity structure and inhomogeneities of the subsurface and the deep interior of the
Earth, the amplitudes of P- and S-waves vary with distance from their source in a complicated way despite the
overall tendency to decay with distance. Besides this the
amplitude ratio between P- and S-waves also depends on
the angle at which their seismic rays leave the source
(Aki and Richards, 2002).
Seismic records and fault plane solutions
High precision modern seismographs most basically
consisting of an inertial pendulum mass and auxiliary
electronic transducers and amplifiers record ground
motion, which may be as low as less than 10
À10 m for a
magnitude 2 earthquake and as large as 10 cm in case of
a large seismic event. Because of the small size of most
earthquake signals, these need to be amplified. This is
commonly done by attaching a coil to the mass that moves
through the magnetic field of a magnet attached to the
frame of the instrument, thus transducing the mechanical
movement into an equivalent electronic signal, which
can be then amplified and converted into a digital signal.
Further, highly accurate synchronized timing between
the seismic records at many stations is crucial for precisely
locating seismic sources. Whereas older instruments had
provided only analogue records on slowly moving paper,
modern seismometers provide digital records in high temporal resolution.
Seismic records may be used to identify the focal mechanism of the earthquake and to reconstruct motion along a
seismic fault. The oldest and simplest way is to compare
P-wave first-motion polarity recorded for a given event
by several seismic stations that lie in different directions
and at different distances from the focus. Consider motion
along a dipping fault such that the material above the fault,
the so-called hanging-wall, moves upwards. Then, this
material is subject to compression and the region beneath
the fault undergoes dilatation, i.e., extension. With the
compensatory downward motion of the region beneath
the fault, there will be two regions of compression and
extension, separated by the fault plane and an auxiliary
212
EARTHQUAKES
Elastic seismic energy released during an earthquake
travels away from the hypocenter as body waves through
the Earth and also, as a result of wave interference near
the Earth’s surface, as surface waves. On the seismic timescale, usually deciseconds up to almost 1 h for the longest
free oscillations of the whole planet, the Earth behaves as
an elastic body.
Compressional or P-waves (P for primary) propagate
by stretching and contracting the medium parallel to the
direction the wave travels through the entire Earth,
whereas in the case of shear or S-waves (S for secondary),
swinging is perpendicular to the direction of propagation.
Shear waves cannot travel through fluids. The fact that
already in early world-wide records of P- and S-waves
after the great 1897 magnitude 8.1 Assam earthquake no
direct S-waves were found that had traveled through the
Earth’s center led Dixon Oldham (1858–1936) to infer
the existence of an Earth core and to conclude that it was
liquid. This, however, relates only to the outer core, as
the existence of a solid inner core was later proved by Inge
Lehmann (1888–1993) in 1936.
Seismic P-waves travel at sound velocities of about
1.5 km per second in water and faster, i.e., several km
per second, in most rocks. In sedimentary rocks,
P-waves are as fast as between about 1.5 and 6 km per second, whereas in crystalline, igneous, and metamorphic
crustal rocks they usually are faster, between about 4 and
7 km per second, and in the uppermost mantle around
8 km per second. In highly porous rocks or loose sediments, seismic velocities often are similar to those in water
or even lower. S-waves travel about 1.7 times more slowly
than P-waves. The velocity ratio between P- and S-waves
depends, e.g., on fluid content and therefore differs
slightly between various tectonic settings and in the presence of significant amounts of fluid or major fluid motion.
Therefore, it can be used to study the role of fluids for
earthquake processes (e.g., Schurr et al., 2003; EberhartPhillips et al., 2008).
There are also two types of surface waves, Rayleigh
waves (LR) and Love waves (LQ). While Rayleigh waves
swing in the vertical plane with particles moving along a
retrograde ellipse, particle motion of Love-waves is horizontal and transverse to the travel direction. Love waves
are the fastest surface waves and travel with velocities
close to the subsurface velocity of S-waves, whereas Rayleigh waves travel slightly slower, with about 90 % of the
shear wave velocity. Although surface waves generated by
crustal earthquakes are associated with generally larger
amplitudes of ground motion than body waves, their
periods are also significantly longer (see Figure 1b).
Therefore, in the local distance of several tens to hundred
kilometers, the largest destructions are usually associated
with shear waves and Love waves, and not with true surface waves.
Seismic waves are reflected and refracted at lithological, rheological, diagenetic, or other boundaries with a
contrast in acoustic impedance, i.e., the product of seismic
velocity and density. Besides reflection and refraction,
seismic waves can also undergo conversion, e.g., from a
P- to an S-wave, and vice versa. Thus, the body waves
P and S originating from the earthquake source will be
split in many phases, due to the interaction with many
velocity discontinuities and inhomogeneities along their
way through the subsurface and the deeper parts of the
Earth’s interior. These different phases usually arrive
along different and sometimes rather complicated travel
paths at different times at a distant seismograph. The different wave onsets can be identified one after the other;
however, one has to keep in mind that the arrival of some
theoretically possible but weaker later waves may be
masked through the coda of other, earlier waves. Because
of damping and geometric spreading, but also focusing
effects due to the complicated velocity structure and inhomogeneities of the subsurface and the deep interior of the
Earth, the amplitudes of P- and S-waves vary with distance from their source in a complicated way despite the
overall tendency to decay with distance. Besides this the
amplitude ratio between P- and S-waves also depends on
the angle at which their seismic rays leave the source
(Aki and Richards, 2002).
Seismic records and fault plane solutions
High precision modern seismographs most basically
consisting of an inertial pendulum mass and auxiliary
electronic transducers and amplifiers record ground
motion, which may be as low as less than 10
À10 m for a
magnitude 2 earthquake and as large as 10 cm in case of
a large seismic event. Because of the small size of most
earthquake signals, these need to be amplified. This is
commonly done by attaching a coil to the mass that moves
through the magnetic field of a magnet attached to the
frame of the instrument, thus transducing the mechanical
movement into an equivalent electronic signal, which
can be then amplified and converted into a digital signal.
Further, highly accurate synchronized timing between
the seismic records at many stations is crucial for precisely
locating seismic sources. Whereas older instruments had
provided only analogue records on slowly moving paper,
modern seismometers provide digital records in high temporal resolution.
Seismic records may be used to identify the focal mechanism of the earthquake and to reconstruct motion along a
seismic fault. The oldest and simplest way is to compare
P-wave first-motion polarity recorded for a given event
by several seismic stations that lie in different directions
and at different distances from the focus. Consider motion
along a dipping fault such that the material above the fault,
the so-called hanging-wall, moves upwards. Then, this
material is subject to compression and the region beneath
the fault undergoes dilatation, i.e., extension. With the
compensatory downward motion of the region beneath
the fault, there will be two regions of compression and
extension, separated by the fault plane and an auxiliary
212
EARTHQUAKES