168 Seismology and Earth Structure
outer core, waves refract upward and emerge in the shadow
zone. These phases are known as PKIKP, because P waves in
the inner core are denoted by “I.” In addition, waves reflect
at the boundary between the inner and outer cores, giving the
phase PKiKP.
6 (The lower-case “i” is analogous to the lowercase “c” in PcP.) The travel time curve thus has a PKIKP
branch DF, where D is the distance at which PKIKP is first
observed, and a back branch for PKiKP. The back branch
begins at C, where PKiKP and PKP are the same, and extends
through D back to zero distance (Figs 3.5-3 and 4), because
the reflection occurs at vertical incidence. Hence the portion of
the travel time curve containing CD and DF is due to the rapid
increase of velocity at the inner core–outer core boundary, and
is analogous to a triplication.
Seismic energy also enters the shadow zone via P and S waves
that diffract around the core (Section 2.5.10). The ray paths for
the diffracted P waves (denoted P d or P diff ) shown in Fig. 3.5-7
represent energy that diffracted around the core, left the CMB,
and traveled back to the surface. This process is much like that
discussed for the head wave (Section 3.2.1). Thus, once the
direct P wave becomes the diffracted wave at a distance near
100°, its travel time curve (Fig. 3.5-4) loses the curvature it had,
because successive rays penetrated deeper to higher-velocity
material. Instead, it becomes linear because all the diffracted
waves bottom at the CMB, and so have the same ray parameter
and hence apparent velocity. As for the head wave, assuming
that the energy followed a ray path gives the diffracted wave’s
travel time but cannot fully describe its amplitude, because
diffraction involves energy propagating as waves, not rays.
However, we will see that more complete formulations such as
normal modes predict both the times and the amplitudes of the
diffracted phases.
Figure 3.5-7 shows that the travel time curve for the core
phases is complicated because it combines the effects of a
geometric shadow zone, which gives two PKP branches, a
triplication-like feature containing the PKIKP and PKiKP
branches, and a diffraction branch. In reality, even these models
are simplifications of a more complex reality. Figure 3.5-8,
showing the travel times of several million PKP arrivals, illustrates several significant deviations from the theoretical curves
in Fig. 3.5-7. First, the arrivals do not fall along narrow lines.
This is partly due to errors of observation, but also due to the
heterogeneous structure of the crust, mantle, and core, which
makes some arrivals early and others late. Second, the PKP-BC
branch continues beyond its geometrically predicted limit of
153°. This is because the PKP-BC wave diffracts around the
inner core, although its amplitude decreases rapidly in the
process, so there are few observations beyond 160°.
Third, and most importantly, the PKP travel times show an
additional branch not predicted by geometric ray theory. These
arrivals, labeled PKP precursors, appear to be a continuation
of the PKP-AB branch and arrive as much as 20 s before the
Fig. 3.5-8 Arrival times of PKP waves recorded by the International
Seismological Centre during 1964–87. A point is plotted if there are at
least 200 arrivals in the catalog for that time and distance. Although these
arrival times are similar to the predicted travel time curves in Fig. 3.5-7,
there are some differences. The PKP-BC branch is observed beyond its
geometrical limit (153°) due to diffraction around the inner core, and
precursors to the PKP-DF branch are observed that result from seismic
scattering at the CMB and in the mantle. (Courtesy of K. Koper.)
6 Observations of this phase by Inge Lehmann (1888–1993) in 1936 provided the
first evidence for the existence of the inner core.
PKP-DF branch. These arrivals puzzled seismologists until it
was realized that they were waves reflected, or scattered, from
inhomogeneous structures in the mantle. This scattering is
analogous to that discussed in Section 3.3.7 in the context of
migration in reflection seismology. Because the scatterers are
comparable in size (about 10–15 km) to the wavelengths of
short-period P waves in the lower mantle, they behave as
Huygens’ sources (Section 2.5.10). Thus a PKP-AB wave
interacting with a scatterer at the CMB radiates waves in all
directions (Fig. 3.5-9). Those arriving before PKP-DF are
clearly observed, whereas those arriving afterwards are lost
amid PKP-DF. The range of observable scattered PKP waves is
shown as the shaded regions in Fig. 3.5-9, illustrating another
way in which seismic energy reaches the shadow zone. Although
most such scattering occurs near the CMB, modeling of the
PKP precursors suggest that waves are also scattered by small
reflectors throughout the mantle, as shown by the dark shaded
region in Fig. 3.5-9.
Some core phases begin as S waves (Fig. 3.5-5). Although no
S waves propagate in the liquid outer core, phases like SKS
travel through the mantle as an S wave and through the core
as a P wave. SKKS is similar to SKS, but also involves an
underside reflection at the CMB. Because the P velocity of the
uppermost core (about 8.1 km/s) is not much larger than the S
velocity of the lowermost mantle (about 7.2 km/s), SKS and
SKKS waves do not change direction significantly as they cross
the CMB. Thus SKS, SKKS, SKKKS, etc. are the only waves
that bottom near the top of the core and are used to constrain
the outer core’s velocity structure.
PKP precursors
1300
1250
1200
1150
1100
100
Distance (°)
PKP-AB
PKP-BC
PKP-DF
PKP-DF
Travel time (s)
120
140
160
180
outer core, waves refract upward and emerge in the shadow
zone. These phases are known as PKIKP, because P waves in
the inner core are denoted by “I.” In addition, waves reflect
at the boundary between the inner and outer cores, giving the
phase PKiKP.
6 (The lower-case “i” is analogous to the lowercase “c” in PcP.) The travel time curve thus has a PKIKP
branch DF, where D is the distance at which PKIKP is first
observed, and a back branch for PKiKP. The back branch
begins at C, where PKiKP and PKP are the same, and extends
through D back to zero distance (Figs 3.5-3 and 4), because
the reflection occurs at vertical incidence. Hence the portion of
the travel time curve containing CD and DF is due to the rapid
increase of velocity at the inner core–outer core boundary, and
is analogous to a triplication.
Seismic energy also enters the shadow zone via P and S waves
that diffract around the core (Section 2.5.10). The ray paths for
the diffracted P waves (denoted P d or P diff ) shown in Fig. 3.5-7
represent energy that diffracted around the core, left the CMB,
and traveled back to the surface. This process is much like that
discussed for the head wave (Section 3.2.1). Thus, once the
direct P wave becomes the diffracted wave at a distance near
100°, its travel time curve (Fig. 3.5-4) loses the curvature it had,
because successive rays penetrated deeper to higher-velocity
material. Instead, it becomes linear because all the diffracted
waves bottom at the CMB, and so have the same ray parameter
and hence apparent velocity. As for the head wave, assuming
that the energy followed a ray path gives the diffracted wave’s
travel time but cannot fully describe its amplitude, because
diffraction involves energy propagating as waves, not rays.
However, we will see that more complete formulations such as
normal modes predict both the times and the amplitudes of the
diffracted phases.
Figure 3.5-7 shows that the travel time curve for the core
phases is complicated because it combines the effects of a
geometric shadow zone, which gives two PKP branches, a
triplication-like feature containing the PKIKP and PKiKP
branches, and a diffraction branch. In reality, even these models
are simplifications of a more complex reality. Figure 3.5-8,
showing the travel times of several million PKP arrivals, illustrates several significant deviations from the theoretical curves
in Fig. 3.5-7. First, the arrivals do not fall along narrow lines.
This is partly due to errors of observation, but also due to the
heterogeneous structure of the crust, mantle, and core, which
makes some arrivals early and others late. Second, the PKP-BC
branch continues beyond its geometrically predicted limit of
153°. This is because the PKP-BC wave diffracts around the
inner core, although its amplitude decreases rapidly in the
process, so there are few observations beyond 160°.
Third, and most importantly, the PKP travel times show an
additional branch not predicted by geometric ray theory. These
arrivals, labeled PKP precursors, appear to be a continuation
of the PKP-AB branch and arrive as much as 20 s before the
Fig. 3.5-8 Arrival times of PKP waves recorded by the International
Seismological Centre during 1964–87. A point is plotted if there are at
least 200 arrivals in the catalog for that time and distance. Although these
arrival times are similar to the predicted travel time curves in Fig. 3.5-7,
there are some differences. The PKP-BC branch is observed beyond its
geometrical limit (153°) due to diffraction around the inner core, and
precursors to the PKP-DF branch are observed that result from seismic
scattering at the CMB and in the mantle. (Courtesy of K. Koper.)
6 Observations of this phase by Inge Lehmann (1888–1993) in 1936 provided the
first evidence for the existence of the inner core.
PKP-DF branch. These arrivals puzzled seismologists until it
was realized that they were waves reflected, or scattered, from
inhomogeneous structures in the mantle. This scattering is
analogous to that discussed in Section 3.3.7 in the context of
migration in reflection seismology. Because the scatterers are
comparable in size (about 10–15 km) to the wavelengths of
short-period P waves in the lower mantle, they behave as
Huygens’ sources (Section 2.5.10). Thus a PKP-AB wave
interacting with a scatterer at the CMB radiates waves in all
directions (Fig. 3.5-9). Those arriving before PKP-DF are
clearly observed, whereas those arriving afterwards are lost
amid PKP-DF. The range of observable scattered PKP waves is
shown as the shaded regions in Fig. 3.5-9, illustrating another
way in which seismic energy reaches the shadow zone. Although
most such scattering occurs near the CMB, modeling of the
PKP precursors suggest that waves are also scattered by small
reflectors throughout the mantle, as shown by the dark shaded
region in Fig. 3.5-9.
Some core phases begin as S waves (Fig. 3.5-5). Although no
S waves propagate in the liquid outer core, phases like SKS
travel through the mantle as an S wave and through the core
as a P wave. SKKS is similar to SKS, but also involves an
underside reflection at the CMB. Because the P velocity of the
uppermost core (about 8.1 km/s) is not much larger than the S
velocity of the lowermost mantle (about 7.2 km/s), SKS and
SKKS waves do not change direction significantly as they cross
the CMB. Thus SKS, SKKS, SKKKS, etc. are the only waves
that bottom near the top of the core and are used to constrain
the outer core’s velocity structure.
PKP precursors
1300
1250
1200
1150
1100
100
Distance (°)
PKP-AB
PKP-BC
PKP-DF
PKP-DF
Travel time (s)
120
140
160
180