176 Seismology and Earth Structure
As shown, a single spherical S wave front is quickly broken
into various wave fronts by reflections off the surface, mantle
discontinuities, and the core. As the wave fronts arrive at the
surface, they cause arrivals that we call S, ScS, sS, etc.
In the first frame, Fig. 3.5-19a, which is 60 s after the earthquake, the wave front maintains much of its initially spherical
shape. The upgoing part of the wave front is headed toward the
surface, but will not reach it for another 67 s. The downgoing
part of the wave front is headed toward the core, where it will
be fully reflected and give rise to ScS.
In Fig. 3.5-19b, 300 s after the earthquake, the wave front
still maintains its integrity, though the upper part is now reflecting off the surface, and the lower part is about to reach the
core. The slower upper mantle velocities cause bends in both
the reflected and the unreflected waves. The S wave front is
reaching the surface 12.5° away from the source, and at closer
distances has already reflected downward. When these downgoing waves reach the surface again, they will be called the
sS and sScS phases. The downgoing portion of the initial wave
front that will become ScS has not yet reached the core.
By 600 s after the earthquake (Fig. 3.5-19c) added complexity is evident. The upgoing wave that reflected at the core will
generate ScS and its multiples (ScS2, ScS3, etc.). The surfacereflected wave is separating into two parts. One is heading into
the lower mantle and will eventually reach the surface as the
sScS and sS phases. The other will turn higher up in the mantle
and arrive at the surface as the SS phase. Behind the sS, ScS,
and sScS wave fronts are upper mantle echoes reflected from
the 220, 400, and 670 km discontinuities. However, despite all
that is going on, the only phase yet recorded at the surface is S,
now arriving 31° away from the source. sS will begin to arrive
in another 63 s, at a distance of 24°.
By 900 s after the origin time (Fig. 3.5-19d), four segments of
the broken wave front are reaching the surface: S at 52°, sS at
39°, SS at 38°, and ScS at 33°. The sS and SS wave fronts have
begun to separate. In contrast, the ScS and S wave fronts have
begun to come back together because they enter the core
shadow, where the S/ScS wave front continues as a diffracted
S diff wave. Behind the S and ScS waves in the lower mantle are
the sS and sScS waves, which follow similar paths except for
their surface reflections. The distance between S and sS (and
also between ScS and sScS) is a function of the depth of the
earthquake. The three wave front segments labeled SS form
a characteristic “Y” shape that results from the waves turning in the mid-mantle. The “Y” ’s junction represents the
superposition of the part of the wave front that is heading
down toward the bottoming point and the part of the wave
front that has already turned and is heading back up again.
Behind SS, the phase SSS that bounces twice on the underside
of the surface, is beginning to form.
In Fig. 3.5-19e, 1200 s after the earthquake, most of the
initial S wave front is actually S diff because S grazes the core at
about 100°. The surface-reflected sS wave now also diffracts
around the core as sS diff . SSS is now fully developed, and is
reaching the surface behind SS. The polarity of SSS is different
from that of SS, because each successive surface bounce
changes its phase by π /2 (Section 3.5.1). The initial S-wave
polarity is into the page (light-colored), whereas SSS is primarily out of the page (dark colored) because it has been
phase-shifted twice. The smaller-amplitude phases evident are
reflections from the upper mantle discontinuities in the velocity model at depths of 220, 400, and 670 km, and so come in
threes. One set of these, labeled as ScS 220 S, ScS 400 S, and
ScS 670 S, are underside reflections that precede ScS2.
By 1500 s after the earthquake (Fig. 3.5-19f), the initial wave
front is entirely diffracted S diff , reaching the surface at a distance of 111°. Because waves travel much faster at the base of
the mantle than in the upper mantle, S diff at the CMB has gone
further, reaching 152°. A set of mid-mantle reflections labeled
S 220 S, S 400 S, and S 670 S, which are also visible in the previous
panel, appear ahead of SS. These peel off the upgoing S/S diff
wave front as it interacts with the discontinuities. Because they
are related to SS, they also have the “Y”-shape characteristic
of underside-reflected phases. The upgoing parts of the “Y”
formed from the upgoing S phase, but the downgoing parts
(right side of the “Y”) peel off S diff and are better called
S diff200 S diff , S diff400 S diff , and S diff670 S diff . The waves with the
largest amplitudes, SS and SSS, are arriving at the surface at
distances of 76° and 63°.
In Fig. 3.5-19g, 1800 s after the earthquake, S4 has begun
to be observed at the surface (71°), following SS (97°) and
SSS (83°). The next surface reflection, S5, is now developing.
The ScS2 multiple reflection is arriving at the surface 36° from
the earthquake. The downgoing part of SS is from S diff reflecting at the surface, so it will arrive at the surface at distances
greater than 200° as the phase S diff S diff . By now, 30 minutes
after the earthquake, seismic energy has spread throughout
the mantle. Multiple ScS waves are still reverberating between
the surface and the core. At the CMB, the leading S diff wave
has wrapped around the antipode and is heading back toward
the epicenter.
This simulation illustrates that although the ray paths used
to describe body waves in the earth are intuitively appealing
and useful, they are simple ways of characterizing a complicated wave field. An earthquake generates an initially spherical
wave front whose interaction with various interfaces gives rise
to many wave fronts. We use names for the arrivals that the
wave fronts cause at the surface, so different parts of the same
wave front, or the same part at different times, are given different names. Hence our intuition based on geometric rays can
lead us to miss some of the richness that occurs. For example,
we tend to view diffraction as an exotic effect different from the
direct ray path, but the simulation shows no major change as
the direct wave becomes the diffracted wave, although there
is a loss of high frequencies. Hence the simulation shows no
obvious core shadow zone, because seismic energy reaches
the shadow zone by diffraction and multiple reflections. The
essential point is that the wave fields are the physical entities,
whereas rays are useful approximations whose limitations
should be kept in mind.
As shown, a single spherical S wave front is quickly broken
into various wave fronts by reflections off the surface, mantle
discontinuities, and the core. As the wave fronts arrive at the
surface, they cause arrivals that we call S, ScS, sS, etc.
In the first frame, Fig. 3.5-19a, which is 60 s after the earthquake, the wave front maintains much of its initially spherical
shape. The upgoing part of the wave front is headed toward the
surface, but will not reach it for another 67 s. The downgoing
part of the wave front is headed toward the core, where it will
be fully reflected and give rise to ScS.
In Fig. 3.5-19b, 300 s after the earthquake, the wave front
still maintains its integrity, though the upper part is now reflecting off the surface, and the lower part is about to reach the
core. The slower upper mantle velocities cause bends in both
the reflected and the unreflected waves. The S wave front is
reaching the surface 12.5° away from the source, and at closer
distances has already reflected downward. When these downgoing waves reach the surface again, they will be called the
sS and sScS phases. The downgoing portion of the initial wave
front that will become ScS has not yet reached the core.
By 600 s after the earthquake (Fig. 3.5-19c) added complexity is evident. The upgoing wave that reflected at the core will
generate ScS and its multiples (ScS2, ScS3, etc.). The surfacereflected wave is separating into two parts. One is heading into
the lower mantle and will eventually reach the surface as the
sScS and sS phases. The other will turn higher up in the mantle
and arrive at the surface as the SS phase. Behind the sS, ScS,
and sScS wave fronts are upper mantle echoes reflected from
the 220, 400, and 670 km discontinuities. However, despite all
that is going on, the only phase yet recorded at the surface is S,
now arriving 31° away from the source. sS will begin to arrive
in another 63 s, at a distance of 24°.
By 900 s after the origin time (Fig. 3.5-19d), four segments of
the broken wave front are reaching the surface: S at 52°, sS at
39°, SS at 38°, and ScS at 33°. The sS and SS wave fronts have
begun to separate. In contrast, the ScS and S wave fronts have
begun to come back together because they enter the core
shadow, where the S/ScS wave front continues as a diffracted
S diff wave. Behind the S and ScS waves in the lower mantle are
the sS and sScS waves, which follow similar paths except for
their surface reflections. The distance between S and sS (and
also between ScS and sScS) is a function of the depth of the
earthquake. The three wave front segments labeled SS form
a characteristic “Y” shape that results from the waves turning in the mid-mantle. The “Y” ’s junction represents the
superposition of the part of the wave front that is heading
down toward the bottoming point and the part of the wave
front that has already turned and is heading back up again.
Behind SS, the phase SSS that bounces twice on the underside
of the surface, is beginning to form.
In Fig. 3.5-19e, 1200 s after the earthquake, most of the
initial S wave front is actually S diff because S grazes the core at
about 100°. The surface-reflected sS wave now also diffracts
around the core as sS diff . SSS is now fully developed, and is
reaching the surface behind SS. The polarity of SSS is different
from that of SS, because each successive surface bounce
changes its phase by π /2 (Section 3.5.1). The initial S-wave
polarity is into the page (light-colored), whereas SSS is primarily out of the page (dark colored) because it has been
phase-shifted twice. The smaller-amplitude phases evident are
reflections from the upper mantle discontinuities in the velocity model at depths of 220, 400, and 670 km, and so come in
threes. One set of these, labeled as ScS 220 S, ScS 400 S, and
ScS 670 S, are underside reflections that precede ScS2.
By 1500 s after the earthquake (Fig. 3.5-19f), the initial wave
front is entirely diffracted S diff , reaching the surface at a distance of 111°. Because waves travel much faster at the base of
the mantle than in the upper mantle, S diff at the CMB has gone
further, reaching 152°. A set of mid-mantle reflections labeled
S 220 S, S 400 S, and S 670 S, which are also visible in the previous
panel, appear ahead of SS. These peel off the upgoing S/S diff
wave front as it interacts with the discontinuities. Because they
are related to SS, they also have the “Y”-shape characteristic
of underside-reflected phases. The upgoing parts of the “Y”
formed from the upgoing S phase, but the downgoing parts
(right side of the “Y”) peel off S diff and are better called
S diff200 S diff , S diff400 S diff , and S diff670 S diff . The waves with the
largest amplitudes, SS and SSS, are arriving at the surface at
distances of 76° and 63°.
In Fig. 3.5-19g, 1800 s after the earthquake, S4 has begun
to be observed at the surface (71°), following SS (97°) and
SSS (83°). The next surface reflection, S5, is now developing.
The ScS2 multiple reflection is arriving at the surface 36° from
the earthquake. The downgoing part of SS is from S diff reflecting at the surface, so it will arrive at the surface at distances
greater than 200° as the phase S diff S diff . By now, 30 minutes
after the earthquake, seismic energy has spread throughout
the mantle. Multiple ScS waves are still reverberating between
the surface and the core. At the CMB, the leading S diff wave
has wrapped around the antipode and is heading back toward
the epicenter.
This simulation illustrates that although the ray paths used
to describe body waves in the earth are intuitively appealing
and useful, they are simple ways of characterizing a complicated wave field. An earthquake generates an initially spherical
wave front whose interaction with various interfaces gives rise
to many wave fronts. We use names for the arrivals that the
wave fronts cause at the surface, so different parts of the same
wave front, or the same part at different times, are given different names. Hence our intuition based on geometric rays can
lead us to miss some of the richness that occurs. For example,
we tend to view diffraction as an exotic effect different from the
direct ray path, but the simulation shows no major change as
the direct wave becomes the diffracted wave, although there
is a loss of high frequencies. Hence the simulation shows no
obvious core shadow zone, because seismic energy reaches
the shadow zone by diffraction and multiple reflections. The
essential point is that the wave fields are the physical entities,
whereas rays are useful approximations whose limitations
should be kept in mind.